Application of Lyapunov's Second Method in the Stability Analysis of ...

African Journals Online (AJOL)

In this paper, Lyapunov's method for determining the stability of non-linear systems under dynamic states is presented. The paper highlights a practical application of the method to investigate the stability of crude oil/natural gas separation process. Mathematical state models for the separation process, used in the ...

Lyapunov vectors and assimilation in the unstable subspace: theory and applications

International Nuclear Information System (INIS)

Palatella, Luigi; Carrassi, Alberto; Trevisan, Anna

2013-01-01

Based on a limited number of noisy observations, estimation algorithms provide a complete description of the state of a system at current time. Estimation algorithms that go under the name of assimilation in the unstable subspace (AUS) exploit the nonlinear stability properties of the forecasting model in their formulation. Errors that grow due to sensitivity to initial conditions are efficiently removed by confining the analysis solution in the unstable and neutral subspace of the system, the subspace spanned by Lyapunov vectors with positive and zero exponents, while the observational noise does not disturb the system along the stable directions. The formulation of the AUS approach in the context of four-dimensional variational assimilation (4DVar-AUS) and the extended Kalman filter (EKF-AUS) and its application to chaotic models is reviewed. In both instances, the AUS algorithms are at least as efficient but simpler to implement and computationally less demanding than their original counterparts. As predicted by the theory when error dynamics is linear, the optimal subspace dimension for 4DVar-AUS is given by the number of positive and null Lyapunov exponents, while the EKF-AUS algorithm, using the same unstable and neutral subspace, recovers the solution of the full EKF algorithm, but dealing with error covariance matrices of a much smaller dimension and significantly reducing the computational burden. Examples of the application to a simplified model of the atmospheric circulation and to the optimal velocity model for traffic dynamics are given. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (paper)

Lyapunov Functions to Caputo Fractional Neural Networks with Time-Varying Delays

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Ravi Agarwal

2018-05-01

Full Text Available One of the main properties of solutions of nonlinear Caputo fractional neural networks is stability and often the direct Lyapunov method is used to study stability properties (usually these Lyapunov functions do not depend on the time variable. In connection with the Lyapunov fractional method we present a brief overview of the most popular fractional order derivatives of Lyapunov functions among Caputo fractional delay differential equations. These derivatives are applied to various types of neural networks with variable coefficients and time-varying delays. We show that quadratic Lyapunov functions and their Caputo fractional derivatives are not applicable in some cases when one studies stability properties. Some sufficient conditions for stability of equilibrium of nonlinear Caputo fractional neural networks with time dependent transmission delays, time varying self-regulating parameters of all units and time varying functions of the connection between two neurons in the network are obtained. The cases of time varying Lipschitz coefficients as well as nonLipschitz activation functions are studied. We illustrate our theory on particular nonlinear Caputo fractional neural networks.

New zero-input overflow stability proofs based on Lyapunov theory

NARCIS (Netherlands)

Werter, M.J.; Ritzerfeld, J.H.F.

1989-01-01

The authors demonstrate some proofs of zero-input overflow-oscillation suppression in recursive digital filters. The proofs are based on the second method of Lyapunov. For second-order digital filters with complex conjugated poles, the state describes a trajectory in the phase plane, spiraling

Stability analysis of polynomial fuzzy models via polynomial fuzzy Lyapunov functions

OpenAIRE

Bernal Reza, Miguel Ángel; Sala, Antonio; JAADARI, ABDELHAFIDH; Guerra, Thierry-Marie

2011-01-01

In this paper, the stability of continuous-time polynomial fuzzy models by means of a polynomial generalization of fuzzy Lyapunov functions is studied. Fuzzy Lyapunov functions have been fruitfully used in the literature for local analysis of Takagi-Sugeno models, a particular class of the polynomial fuzzy ones. Based on a recent Taylor-series approach which allows a polynomial fuzzy model to exactly represent a nonlinear model in a compact set of the state space, it is shown that a refinemen...

Lyapunov vs. geometrical stability analysis of the Kepler and the restricted three body problems

International Nuclear Information System (INIS)

Yahalom, A.; Levitan, J.; Lewkowicz, M.; Horwitz, L.

2011-01-01

In this Letter we show that although the application of standard Lyapunov analysis predicts that completely integrable Kepler motion is unstable, the geometrical analysis of Horwitz et al. predicts the observed stability. This seems to us to provide evidence for both the incompleteness of the standard Lyapunov analysis and the strength of the geometrical analysis. Moreover, we apply this approach to the three body problem in which the third body is restricted to move on a circle of large radius which induces an adiabatic time dependent potential on the second body. This causes the second body to move in a very interesting and intricate but periodic trajectory; however, the standard Lyapunov analysis, as well as methods based on the parametric variation of curvature associated with the Jacobi metric, incorrectly predict chaotic behavior. The geometric approach predicts the correct stable motion in this case as well. - Highlights: → Lyapunov analysis predicts Kepler motion to be unstable. → Geometrical analysis predicts the observed stability. → Lyapunov analysis predicts chaotic behavior in restricted three body problem. → The geometric approach predicts the correct stable motion in restricted three body problem.

Piecewise quadratic Lyapunov functions for stability verification of approximate explicit MPC

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Morten Hovd

2010-04-01

Full Text Available Explicit MPC of constrained linear systems is known to result in a piecewise affine controller and therefore also piecewise affine closed loop dynamics. The complexity of such analytic formulations of the control law can grow exponentially with the prediction horizon. The suboptimal solutions offer a trade-off in terms of complexity and several approaches can be found in the literature for the construction of approximate MPC laws. In the present paper a piecewise quadratic (PWQ Lyapunov function is used for the stability verification of an of approximate explicit Model Predictive Control (MPC. A novel relaxation method is proposed for the LMI criteria on the Lyapunov function design. This relaxation is applicable to the design of PWQ Lyapunov functions for discrete-time piecewise affine systems in general.

Lyapunov functions and global stability for SIR and SEIR models with age-dependent susceptibility

KAUST Repository

Korobeinikov, Andrei; Melnik, Andrey V.

2013-01-01

We consider global asymptotic properties for the SIR and SEIR age structured models for infectious diseases where the susceptibility depends on the age. Using the direct Lyapunov method with Volterra type Lyapunov functions, we establish conditions for the global stability of a unique endemic steady state and the infection-free steady state.

Collective Lyapunov modes

International Nuclear Information System (INIS)

Takeuchi, Kazumasa A; Chaté, Hugues

2013-01-01

We show, using covariant Lyapunov vectors in addition to standard Lyapunov analysis, that there exists a set of collective Lyapunov modes in large chaotic systems exhibiting collective dynamics. Associated with delocalized Lyapunov vectors, they act collectively on the trajectory and hence characterize the instability of its collective dynamics. We further develop, for globally coupled systems, a connection between these collective modes and the Lyapunov modes in the corresponding Perron–Frobenius equation. We thereby address the fundamental question of the effective dimension of collective dynamics and discuss the extensivity of chaos in the presence of collective dynamics. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (paper)

The linearization method in hydrodynamical stability theory

CERN Document Server

Yudovich, V I

1989-01-01

This book presents the theory of the linearization method as applied to the problem of steady-state and periodic motions of continuous media. The author proves infinite-dimensional analogues of Lyapunov's theorems on stability, instability, and conditional stability for a large class of continuous media. In addition, semigroup properties for the linearized Navier-Stokes equations in the case of an incompressible fluid are studied, and coercivity inequalities and completeness of a system of small oscillations are proved.

A Lyapunov theory based UPFC controller for power flow control

Energy Technology Data Exchange (ETDEWEB)

Zangeneh, Ali; Kazemi, Ahad; Hajatipour, Majid; Jadid, Shahram [Center of Excellence for Power Systems Automation and Operation, Iran University of Science and Technology, Tehran (Iran)

2009-09-15

Unified power flow controller (UPFC) is the most comprehensive multivariable device among the FACTS controllers. Capability of power flow control is the most important responsibility of UPFC. According to high importance of power flow control in transmission lines, the proper controller should be robust against uncertainty and disturbance and also have suitable settling time. For this purpose, a new controller is designed based on the Lyapunov theory and its stability is also evaluated. The Main goal of this paper is to design a controller which enables a power system to track reference signals precisely and to be robust in the presence of uncertainty of system parameters and disturbances. The performance of the proposed controller is simulated on a two bus test system and compared with a conventional PI controller. The simulation results show the power and accuracy of the proposed controller. (author)

A simple extension of contraction theory to study incremental stability properties

DEFF Research Database (Denmark)

Jouffroy, Jerome

Contraction theory is a recent tool enabling to study the stability of nonlinear systems trajectories with respect to one another, and therefore belongs to the class of incremental stability methods. In this paper, we extend the original definition of contraction theory to incorporate...... in an explicit manner the control input of the considered system. Such an extension, called universal contraction, is quite analogous in spirit to the well-known Input-to-State Stability (ISS). It serves as a simple formulation of incremental ISS, external stability, and detectability in a differential setting....... The hierarchical combination result of contraction theory is restated in this framework, and a differential small-gain theorem is derived from results already available in Lyapunov theory....

Stability Analysis for Car Following Model Based on Control Theory

International Nuclear Information System (INIS)

Meng Xiang-Pei; Li Zhi-Peng; Ge Hong-Xia

2014-01-01

Stability analysis is one of the key issues in car-following theory. The stability analysis with Lyapunov function for the two velocity difference car-following model (for short, TVDM) is conducted and the control method to suppress traffic congestion is introduced. Numerical simulations are given and results are consistent with the theoretical analysis. (electromagnetism, optics, acoustics, heat transfer, classical mechanics, and fluid dynamics)

Generalized direct Lyapunov method for the analysis of stability and attraction in general time systems

International Nuclear Information System (INIS)

Druzhinina, O V; Shestakov, A A

2002-01-01

A generalized direct Lyapunov method is put forward for the study of stability and attraction in general time systems of the following types: the classical dynamical system in the sense of Birkhoff, the general system in the sense of Zubov, the general system in the sense of Seibert, the general system with delay, and the general 'input-output' system. For such systems, with the help of generalized Lyapunov functions with respect to two filters, two quasifilters, or two filter bases, necessary and sufficient conditions for stability and attraction are obtained under minimal assumptions about the mathematical structure of the general system

Lyapunov stability robust analysis and robustness design for linear continuous-time systems

NARCIS (Netherlands)

Luo, J.S.; Johnson, A.; Bosch, van den P.P.J.

1995-01-01

The linear continuous-time systems to be discussed are described by state space models with structured time-varying uncertainties. First, the explicit maximal perturbation bound for maintaining quadratic Lyapunov stability of the closed-loop systems is presented. Then, a robust design method is

Lyapunov functions for the fixed points of the Lorenz model

International Nuclear Information System (INIS)

Bakasov, A.A.; Govorkov, B.B. Jr.

1992-11-01

We have shown how the explicit Lyapunov functions can be constructed in the framework of a regular procedure suggested and completed by Lyapunov a century ago (''method of critical cases''). The method completely covers all practically encountering subtle cases of stability study for ordinary differential equations when the linear stability analysis fails. These subtle cases, ''the critical cases'', according to Lyapunov, include both bifurcations of solutions and solutions of systems with symmetry. Being properly specialized and actually powerful in case of ODE's, this Lyapunov's method is formulated in simple language and should attract a wide interest of the physical audience. The method leads to inevitable construction of the explicit Lyapunov function, takes automatically into account the Fredholm alternative and avoids infinite step calculations. Easy and apparent physical interpretation of the Lyapunov function as a potential or as a time-dependent entropy provides one with more details about the local dynamics of the system at non-equilibrium phase transition points. Another advantage is that this Lyapunov's method consists of a set of very detailed explicit prescriptions which allow one to easy programmize the method for a symbolic processor. The application of the Lyapunov theory for critical cases has been done in this work to the real Lorenz equations and it is shown, in particular, that increasing σ at the Hopf bifurcation point suppresses the contribution of one of the variables to the destabilization of the system. The relation of the method to contemporary methods and its place among them have been clearly and extensively discussed. Due to Appendices, the paper is self-contained and does not require from a reader to approach results published only in Russian. (author). 38 refs

Lyapunov Exponents

CERN Document Server

Crauel, Hans; Eckmann, Jean-Pierre

1991-01-01

Since the predecessor to this volume (LNM 1186, Eds. L. Arnold, V. Wihstutz)appeared in 1986, significant progress has been made in the theory and applications of Lyapunov exponents - one of the key concepts of dynamical systems - and in particular, pronounced shifts towards nonlinear and infinite-dimensional systems and engineering applications are observable. This volume opens with an introductory survey article (Arnold/Crauel) followed by 26 original (fully refereed) research papers, some of which have in part survey character. From the Contents: L. Arnold, H. Crauel: Random Dynamical Systems.- I.Ya. Goldscheid: Lyapunov exponents and asymptotic behaviour of the product of random matrices.- Y. Peres: Analytic dependence of Lyapunov exponents on transition probabilities.- O. Knill: The upper Lyapunov exponent of Sl (2, R) cocycles:Discontinuity and the problem of positivity.- Yu.D. Latushkin, A.M. Stepin: Linear skew-product flows and semigroups of weighted composition operators.- P. Baxendale: Invariant me...

Parameter-dependent PWQ Lyapunov function stability criteria for uncertain piecewise linear systems

Directory of Open Access Journals (Sweden)

Morten Hovd

2018-01-01

Full Text Available The calculation of piecewise quadratic (PWQ Lyapunov functions is addressed in view of stability analysis of uncertain piecewise linear dynamics. As main contribution, the linear matrix inequality (LMI approach proposed in (Johansson and Rantzer, 1998 for the stability analysis of PWL and PWA dynamics is extended to account for parametric uncertainty based on a improved relaxation technique. The results are applied for the analysis of a Phase Locked Loop (PLL benchmark and the ability to guarantee a stability region in the parameter space well beyond the state of the art is demonstrated.

Robust lyapunov controller for uncertain systems

KAUST Repository

Laleg-Kirati, Taous-Meriem

2017-02-23

Various examples of systems and methods are provided for Lyapunov control for uncertain systems. In one example, a system includes a process plant and a robust Lyapunov controller configured to control an input of the process plant. The robust Lyapunov controller includes an inner closed loop Lyapunov controller and an outer closed loop error stabilizer. In another example, a method includes monitoring a system output of a process plant; generating an estimated system control input based upon a defined output reference; generating a system control input using the estimated system control input and a compensation term; and adjusting the process plant based upon the system control input to force the system output to track the defined output reference. An inner closed loop Lyapunov controller can generate the estimated system control input and an outer closed loop error stabilizer can generate the system control input.

Non Lyapunov stability of a constant spatially developing 2-D gas flow

Science.gov (United States)

Balint, Agneta M.; Balint, Stefan; Tanasie, Loredana

2017-01-01

Different types of stabilities (global, local) and instabilities (global absolute, local convective) of the constant spatially developing 2-D gas flow are analyzed in a particular phase space of continuously differentiable functions, endowed with the usual algebraic operations and the topology generated by the uniform convergence on the plane. For this purpose the Euler equations linearized at the constant flow are used. The Lyapunov stability analysis was presented in [1] and this paper is a continuation of [1].

Lyapunov Functions and Solutions of the Lyapunov Matrix Equation for Marginally Stable Systems

DEFF Research Database (Denmark)

Kliem, Wolfhard; Pommer, Christian

2000-01-01

We consider linear systems of differential equations $I \\ddot{x}+B \\dot{x}+C{x}={0}$ where $I$ is the identity matrix and $B$ and $C$ are general complex $n$ x $n$ matrices. Our main interest is to determine conditions for complete marginalstability of these systems. To this end we find solutions...... of the Lyapunov matrix equation and characterize the set of matrices $(B, C)$ which guarantees marginal stability. The theory is applied to gyroscopic systems, to indefinite damped systems, and to circulatory systems, showing how to choose certain parameter matrices to get sufficient conditions for marginal...... stability.Comparison is made with some known results for equations with real system matrices.Moreover more general cases are investigated and several examples are given....

A New Approach to the Method of Lyapunov Functionals and Its Applications

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Yunguo Jin

2013-01-01

Full Text Available We show some results which can replace the graph theory used to construct global Lyapunov functions in some coupled systems of differential equations. We present an example of an epidemic model with stage structure and latency spreading in a heterogeneous host population and obtain a more general threshold for the extinction and persistence of a disease. Using some results obtained by mathematical induction and suitable Lyapunov functionals, we prove the global stability of the endemic equilibrium. For some coupled systems of differential equations, by a similar approach to the discussion of the epidemic model, the conditions of threshold property or global stability can be established without the assumption that the relative matrix is irreducible.

Large-Signal Lyapunov-Based Stability Analysis of DC/AC Inverters and Inverter-Based Microgrids

Science.gov (United States)

Kabalan, Mahmoud

Microgrid stability studies have been largely based on small-signal linearization techniques. However, the validity and magnitude of the linearization domain is limited to small perturbations. Thus, there is a need to examine microgrids with large-signal nonlinear techniques to fully understand and examine their stability. Large-signal stability analysis can be accomplished by Lyapunov-based mathematical methods. These Lyapunov methods estimate the domain of asymptotic stability of the studied system. A survey of Lyapunov-based large-signal stability studies showed that few large-signal studies have been completed on either individual systems (dc/ac inverters, dc/dc rectifiers, etc.) or microgrids. The research presented in this thesis addresses the large-signal stability of droop-controlled dc/ac inverters and inverter-based microgrids. Dc/ac power electronic inverters allow microgrids to be technically feasible. Thus, as a prelude to examining the stability of microgrids, the research presented in Chapter 3 analyzes the stability of inverters. First, the 13 th order large-signal nonlinear model of a droop-controlled dc/ac inverter connected to an infinite bus is presented. The singular perturbation method is used to decompose the nonlinear model into 11th, 9th, 7th, 5th, 3rd and 1st order models. Each model ignores certain control or structural components of the full order model. The aim of the study is to understand the accuracy and validity of the reduced order models in replicating the performance of the full order nonlinear model. The performance of each model is studied in three different areas: time domain simulations, Lyapunov's indirect method and domain of attraction estimation. The work aims to present the best model to use in each of the three domains of study. Results show that certain reduced order models are capable of accurately reproducing the performance of the full order model while others can be used to gain insights into those three areas of

Polyhedral Lyapunov functions structurally ensure global asymptotic stability of dynamical networks iff the Jacobian is non-singular

NARCIS (Netherlands)

Blanchini, Franco; Giordano, G.

2017-01-01

For a vast class of dynamical networks, including chemical reaction networks (CRNs) with monotonic reaction rates, the existence of a polyhedral Lyapunov function (PLF) implies structural (i.e., parameter-free) local stability. Global structural stability is ensured under the additional

Lyapunov-based Stability of Feedback Interconnections of Negative Imaginary Systems

KAUST Repository

Ghallab, Ahmed G.

2017-10-19

Feedback control systems using sensors and actuators such as piezoelectric sensors and actuators, micro-electro-mechanical systems (MEMS) sensors and opto-mechanical sensors, are allowing new advances in designing such high precision technologies. The negative imaginary control systems framework allows for robust control design for such high precision systems in the face of uncertainties due to unmodelled dynamics. The stability of the feedback interconnection of negative imaginary systems has been well established in the literature. However, the proofs of stability feedback interconnection which are used in some previous papers have a shortcoming due to a matrix inevitability issue. In this paper, we provide a new and correct Lyapunov-based proof of one such result and show that the result is still true.

Lyapunov-based Stability of Feedback Interconnections of Negative Imaginary Systems

KAUST Repository

Ghallab, Ahmed G.; Mabrok, Mohamed; Petersen, Ian R.

2017-01-01

Feedback control systems using sensors and actuators such as piezoelectric sensors and actuators, micro-electro-mechanical systems (MEMS) sensors and opto-mechanical sensors, are allowing new advances in designing such high precision technologies. The negative imaginary control systems framework allows for robust control design for such high precision systems in the face of uncertainties due to unmodelled dynamics. The stability of the feedback interconnection of negative imaginary systems has been well established in the literature. However, the proofs of stability feedback interconnection which are used in some previous papers have a shortcoming due to a matrix inevitability issue. In this paper, we provide a new and correct Lyapunov-based proof of one such result and show that the result is still true.

Sliding Mode Controller and Lyapunov Redesign Controller to Improve Microgrid Stability

DEFF Research Database (Denmark)

Hossain, Eklas; Perez, Ron; Padmanaban, Sanjeevikumar

2017-01-01

technique is used to enhance stability of microgrids. Besides adopting this technique here, Sliding Mode Controller (SMC) and Lyapunov Redesign Controller (LRC), two of the most prominent nonlinear control techniques, are individually implemented to control microgrid system stability with desired robustness....... CPL power is then varied to compare robustness of these two control techniques. This investigation revealed the better performance of the LRC system compared to SMC to retain stability in microgrid with dense CPL load. All the necessary results are simulated in Matlab/Simulink platform for authentic......To mitigate the microgrid instability despite the presence of dense Constant Power Load (CPL) loads in the system, a number of compensation techniques have already been gone through extensive research, proposed, and implemented around the world. In this paper, a storage based load side compensation...

Stability theory of critical cases and the bifurcation points of the stationary solutions of the Lorenz model

International Nuclear Information System (INIS)

Bakasov, A.A.; Govorkov, B.B. Jr.

1990-08-01

The critical case in stability theory is the case when it is impossible to study the stability of solutions over the linear part of ordinary differential equations. This situation is usual at the bifurcation points. There exists a powerful and constructive approach to investigate the stability - the theory of critical cases created by Lyapunov. The famous Lorenz model is used in this article as an illustration of the power of the method (new results). (author). 27 refs

A computational proof of concept of a machine-intelligent artificial pancreas using Lyapunov stability and differential game theory.

Science.gov (United States)

Greenwood, Nigel J C; Gunton, Jenny E

2014-07-01

This study demonstrated the novel application of a "machine-intelligent" mathematical structure, combining differential game theory and Lyapunov-based control theory, to the artificial pancreas to handle dynamic uncertainties. Realistic type 1 diabetes (T1D) models from the literature were combined into a composite system. Using a mixture of "black box" simulations and actual data from diabetic medical histories, realistic sets of diabetic time series were constructed for blood glucose (BG), interstitial fluid glucose, infused insulin, meal estimates, and sometimes plasma insulin assays. The problem of underdetermined parameters was side stepped by applying a variant of a genetic algorithm to partial information, whereby multiple candidate-personalized models were constructed and then rigorously tested using further data. These formed a "dynamic envelope" of trajectories in state space, where each trajectory was generated by a hypothesis on the hidden T1D system dynamics. This dynamic envelope was then culled to a reduced form to cover observed dynamic behavior. A machine-intelligent autonomous algorithm then implemented game theory to construct real-time insulin infusion strategies, based on the flow of these trajectories through state space and their interactions with hypoglycemic or near-hyperglycemic states. This technique was tested on 2 simulated participants over a total of fifty-five 24-hour days, with no hypoglycemic or hyperglycemic events, despite significant uncertainties from using actual diabetic meal histories with 10-minute warnings. In the main case studies, BG was steered within the desired target set for 99.8% of a 16-hour daily assessment period. Tests confirmed algorithm robustness for ±25% carbohydrate error. For over 99% of the overall 55-day simulation period, either formal controller stability was achieved to the desired target or else the trajectory was within the desired target. These results suggest that this is a stable, high

Moment Lyapunov Exponent and Stochastic Stability of Binary Airfoil under Combined Harmonic and Non-Gaussian Colored Noise Excitations

Science.gov (United States)

Hu, D. L.; Liu, X. B.

Both periodic loading and random forces commonly co-exist in real engineering applications. However, the dynamic behavior, especially dynamic stability of systems under parametric periodic and random excitations has been reported little in the literature. In this study, the moment Lyapunov exponent and stochastic stability of binary airfoil under combined harmonic and non-Gaussian colored noise excitations are investigated. The noise is simplified to an Ornstein-Uhlenbeck process by applying the path-integral method. Via the singular perturbation method, the second-order expansions of the moment Lyapunov exponent are obtained, which agree well with the results obtained by the Monte Carlo simulation. Finally, the effects of the noise and parametric resonance (such as subharmonic resonance and combination additive resonance) on the stochastic stability of the binary airfoil system are discussed.

Riemannian theory of Hamiltonian chaos and Lyapunov exponents

Science.gov (United States)

Casetti, Lapo; Clementi, Cecilia; Pettini, Marco

1996-12-01

A nonvanishing Lyapunov exponent λ1 provides the very definition of deterministic chaos in the solutions of a dynamical system; however, no theoretical mean of predicting its value exists. This paper copes with the problem of analytically computing the largest Lyapunov exponent λ1 for many degrees of freedom Hamiltonian systems as a function of ɛ=E/N, the energy per degree of freedom. The functional dependence λ1(ɛ) is of great interest because, among other reasons, it detects the existence of weakly and strongly chaotic regimes. This aim, the analytic computation of λ1(ɛ), is successfully reached within a theoretical framework that makes use of a geometrization of Newtonian dynamics in the language of Riemannian differential geometry. An alternative point of view about the origin of chaos in these systems is obtained independently of the standard explanation based on homoclinic intersections. Dynamical instability (chaos) is here related to curvature fluctuations of the manifolds whose geodesics are natural motions and is described by means of the Jacobi-Levi-Civita equation (JLCE) for geodesic spread. In this paper it is shown how to derive from the JLCE an effective stability equation. Under general conditions, this effective equation formally describes a stochastic oscillator; an analytic formula for the instability growth rate of its solutions is worked out and applied to the Fermi-Pasta-Ulam β model and to a chain of coupled rotators. Excellent agreement is found between the theoretical prediction and numeric values of λ1(ɛ) for both models.

Covariant Lyapunov vectors

International Nuclear Information System (INIS)

Ginelli, Francesco; Politi, Antonio; Chaté, Hugues; Livi, Roberto

2013-01-01

Recent years have witnessed a growing interest in covariant Lyapunov vectors (CLVs) which span local intrinsic directions in the phase space of chaotic systems. Here, we review the basic results of ergodic theory, with a specific reference to the implications of Oseledets’ theorem for the properties of the CLVs. We then present a detailed description of a ‘dynamical’ algorithm to compute the CLVs and show that it generically converges exponentially in time. We also discuss its numerical performance and compare it with other algorithms presented in the literature. We finally illustrate how CLVs can be used to quantify deviations from hyperbolicity with reference to a dissipative system (a chain of Hénon maps) and a Hamiltonian model (a Fermi–Pasta–Ulam chain). This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (paper)

Lyapunov exponents

CERN Document Server

Barreira, Luís

2017-01-01

This book offers a self-contained introduction to the theory of Lyapunov exponents and its applications, mainly in connection with hyperbolicity, ergodic theory and multifractal analysis. It discusses the foundations and some of the main results and main techniques in the area, while also highlighting selected topics of current research interest. With the exception of a few basic results from ergodic theory and the thermodynamic formalism, all the results presented include detailed proofs. The book is intended for all researchers and graduate students specializing in dynamical systems who are looking for a comprehensive overview of the foundations of the theory and a sample of its applications.

Generalized decompositions of dynamic systems and vector Lyapunov functions

Science.gov (United States)

Ikeda, M.; Siljak, D. D.

1981-10-01

The notion of decomposition is generalized to provide more freedom in constructing vector Lyapunov functions for stability analysis of nonlinear dynamic systems. A generalized decomposition is defined as a disjoint decomposition of a system which is obtained by expanding the state-space of a given system. An inclusion principle is formulated for the solutions of the expansion to include the solutions of the original system, so that stability of the expansion implies stability of the original system. Stability of the expansion can then be established by standard disjoint decompositions and vector Lyapunov functions. The applicability of the new approach is demonstrated using the Lotka-Volterra equations.

The Lyapunov-Krasovskii theorem and a sufficient criterion for local stability of isochronal synchronization in networks of delay-coupled oscillators

Science.gov (United States)

Grzybowski, J. M. V.; Macau, E. E. N.; Yoneyama, T.

2017-05-01

This paper presents a self-contained framework for the stability assessment of isochronal synchronization in networks of chaotic and limit-cycle oscillators. The results were based on the Lyapunov-Krasovskii theorem and they establish a sufficient condition for local synchronization stability of as a function of the system and network parameters. With this in mind, a network of mutually delay-coupled oscillators subject to direct self-coupling is considered and then the resulting error equations are block-diagonalized for the purpose of studying their stability. These error equations are evaluated by means of analytical stability results derived from the Lyapunov-Krasovskii theorem. The proposed approach is shown to be a feasible option for the investigation of local stability of isochronal synchronization for a variety of oscillators coupled through linear functions of the state variables under a given undirected graph structure. This ultimately permits the systematic identification of stability regions within the high-dimensionality of the network parameter space. Examples of applications of the results to a number of networks of delay-coupled chaotic and limit-cycle oscillators are provided, such as Lorenz, Rössler, Cubic Chua's circuit, Van der Pol oscillator and the Hindmarsh-Rose neuron.

A Lyapunov method for stability analysis of piecewise-affine systems over non-invariant domains

Science.gov (United States)

Rubagotti, Matteo; Zaccarian, Luca; Bemporad, Alberto

2016-05-01

This paper analyses stability of discrete-time piecewise-affine systems, defined on possibly non-invariant domains, taking into account the possible presence of multiple dynamics in each of the polytopic regions of the system. An algorithm based on linear programming is proposed, in order to prove exponential stability of the origin and to find a positively invariant estimate of its region of attraction. The results are based on the definition of a piecewise-affine Lyapunov function, which is in general discontinuous on the boundaries of the regions. The proposed method is proven to lead to feasible solutions in a broader range of cases as compared to a previously proposed approach. Two numerical examples are shown, among which a case where the proposed method is applied to a closed-loop system, to which model predictive control was applied without a-priori guarantee of stability.

Method of Lyapunov functions in problems of stability of solutions of systems of differential equations with impulse action

International Nuclear Information System (INIS)

Ignat'yev, A O

2003-01-01

A system of ordinary differential equations with impulse action at fixed moments of time is considered. The system is assumed to have the zero solution. It is shown that the existence of a corresponding Lyapunov function is a necessary and sufficient condition for the uniform asymptotic stability of the zero solution. Restrictions on perturbations of the right-hand sides of differential equations and impulse actions are obtained under which the uniform asymptotic stability of the zero solution of the 'unperturbed' system implies the uniform asymptotic stability of the zero solution of the 'perturbed' system

Homogeneous Stabilizer by State Feedback for Switched Nonlinear Systems Using Multiple Lyapunov Functions’ Approach

Directory of Open Access Journals (Sweden)

Hui Ye

2017-01-01

Full Text Available This paper investigates the problem of global stabilization for a class of switched nonlinear systems using multiple Lyapunov functions (MLFs. The restrictions on nonlinearities are neither linear growth condition nor Lipschitz condition with respect to system states. Based on adding a power integrator technique, we design homogeneous state feedback controllers of all subsystems and a switching law to guarantee that the closed-loop system is globally asymptotically stable. Finally, an example is given to illustrate the validity of the proposed control scheme.

Uniting Control Lyapunov and Control Barrier Functions

NARCIS (Netherlands)

Romdlony, Zakiyullah; Jayawardhana, Bayu

2014-01-01

In this paper, we propose a nonlinear control design for solving the problem of stabilization with guaranteed safety. The design is based on the merging of a Control Lyapunov Function and a Control Barrier Function. The proposed control method allows us to combine the design of a stabilizer based on

A development of the direct Lyapunov method for the analysis of transient stability of a system of synchronous generators based on the determination of non- stable equilibria on a multidimensional sphere

Directory of Open Access Journals (Sweden)

A. V. Stepanov

2014-01-01

Full Text Available A development of the direct Lyapunov method for the analysis of transient stability of a system of synchronous generators based on the determination of non- stable equilibria on a multidimensional sphere.We consider the problem of transient stability analysis for a system of synchronous generators under the action of strong perturbations. The aim of our work is to develop methods to analyze a transient stability of the system of synchronous generators, which allow getting trustworthy results on reserve transient stability under different perturbations. For the analysis of transient stability, we use the direct Lyapunov method.One of the problems for this method application is to find the Lypunov function that well reflects the properties of a parallel system of synchronous generators. The most reliable results were obtained when the analysis of transient stability was performed with a Lyapunov function of energy type. Another problem for application of the direct Lyapunov method is to determine the critical value of the Lyapunov function, which requires finding the non-stable equilibria of the system. Determination of the non-stable equilibria requires studying the Lyapunov function in a multidimensional space in a neighborhood of a stable equilibrium for the post-breakdown system; this is a complicated non-linear problem.In the paper, we propose a method for determination of the non-stable equilibria on a multidimensional sphere. The method is based on a search of a minimum of the Lyapunov function on a multidimensional sphere the center of which is a stable equilibrium. Our method allows, comparing with the other, e.g., gradient methods, reliable finding a non-stable equilibrium and calculating the critical value. The reliability of our method is proved by numerical experiments. The developed methods and a program realized in a MATLAB package can be recommended for design of a post-breakdown control system of synchronous generators or as a

A variational approach to Lyapunov type inequalities from ODEs to PDEs

CERN Document Server

Cañada, Antonio

2015-01-01

This book highlights the current state of Lyapunov-type inequalities through a detailed analysis. Aimed toward researchers and students working in differential equations and those interested in the applications of stability theory and resonant systems, the book begins with an overview Lyapunov’s original results and moves forward to include prevalent results obtained in the past ten years. Detailed proofs and an emphasis on basic ideas are provided for different boundary conditions for ordinary differential equations, including Neumann, Dirichlet, periodic, and antiperiodic conditions. Novel results of higher eigenvalues, systems of equations, partial differential equations as well as variational approaches are presented. To this respect, a new and unified variational point of view  is introduced for the treatment of such problems and a systematic discussion of different types of boundary conditions is featured. Various problems make the study of Lyapunov-type inequalities of interest to those in pure and ...

Bilinear Approximate Model-Based Robust Lyapunov Control for Parabolic Distributed Collectors

KAUST Repository

Elmetennani, Shahrazed

2016-11-09

This brief addresses the control problem of distributed parabolic solar collectors in order to maintain the field outlet temperature around a desired level. The objective is to design an efficient controller to force the outlet fluid temperature to track a set reference despite the unpredictable varying working conditions. In this brief, a bilinear model-based robust Lyapunov control is proposed to achieve the control objectives with robustness to the environmental changes. The bilinear model is a reduced order approximate representation of the solar collector, which is derived from the hyperbolic distributed equation describing the heat transport dynamics by means of a dynamical Gaussian interpolation. Using the bilinear approximate model, a robust control strategy is designed applying Lyapunov stability theory combined with a phenomenological representation of the system in order to stabilize the tracking error. On the basis of the error analysis, simulation results show good performance of the proposed controller, in terms of tracking accuracy and convergence time, with limited measurement even under unfavorable working conditions. Furthermore, the presented work is of interest for a large category of dynamical systems knowing that the solar collector is representative of physical systems involving transport phenomena constrained by unknown external disturbances.

Lyapunov, attractors and exponents

International Nuclear Information System (INIS)

Oliveira, C.R. de.

1987-01-01

Based on the fundamental principles of statistical mechanics and ergodic theory a definition is given to atractor, as an invariant measure. Many results which reinforce this definition are demonstrated. Chaos is related to the presence of an atractor with entropy above zero. The role of Lyapunov exponents is analyzed. (A.C.A.S.) [pt

Lyapunov Functions, Stationary Distributions, and Non-equilibrium Potential for Reaction Networks

DEFF Research Database (Denmark)

Anderson, David F; Craciun, Gheorghe; Gopalkrishnan, Manoj

2015-01-01

We consider the relationship between stationary distributions for stochastic models of reaction systems and Lyapunov functions for their deterministic counterparts. Specifically, we derive the well-known Lyapunov function of reaction network theory as a scaling limit of the non-equilibrium potent...

Sampled-Data Control of Spacecraft Rendezvous with Discontinuous Lyapunov Approach

Directory of Open Access Journals (Sweden)

Zhuoshi Li

2013-01-01

Full Text Available This paper investigates the sampled-data stabilization problem of spacecraft relative positional holding with improved Lyapunov function approach. The classical Clohessy-Wiltshire equation is adopted to describe the relative dynamic model. The relative position holding problem is converted into an output tracking control problem using sampling signals. A time-dependent discontinuous Lyapunov functionals approach is developed, which will lead to essentially less conservative results for the stability analysis and controller design of the corresponding closed-loop system. Sufficient conditions for the exponential stability analysis and the existence of the proposed controller are provided, respectively. Finally, a simulation result is established to illustrate the effectiveness of the proposed control scheme.

Lyapunov stability and poisson structure of the thermal TDHF and RPA equations

International Nuclear Information System (INIS)

Balian, R.; Veneroni, M.

1989-01-01

The thermal TDHF equation is analyzed in the Liouville representation of quantum mechanics, where the matrix elements of the single-particle (s.p) density ρ behave as classical dynamical variables. By introducing the Lie--Poisson bracket associated with the unitary group of the s.p. Hilbert space, we show that TDHF has a Hamiltonian, but non-canonical, classical form. Within this Poisson structure, either the s.p. energy or the s.p. grand potential Ω(ρ) act as a Hamilton function. The Lyapunov stability of both the TDHF and RPA equations around a HF state then follows, since the HF approximation for thermal equilibrium is determined by minimizing Ω(ρ). The RPA matrix in the Liouville space is expressed as the product of the Poisson tensor with the HF stability matrix, interpreted as a metric tensor generated by the entropy. This factorization displays the roles of the energy and entropy terms arising from Ω(ρ) in the RPA dynamics, and it helps to construct the RPA modes. Several extensions are considered. copyright 1989 Academic Press, Inc

Lyapunov stability and Poisson structure of the thermal TDHF and RPA equations

International Nuclear Information System (INIS)

Veneroni, M.; Balian, R.

1989-01-01

The thermal TDHF equation is analyzed in the Liouville representation of quantum mechanics, where the matrix elements of the single-particle (s.p.) density ρ behave as classical dynamical variables. By introducing the Lie-Poisson bracket associated with the unitary group of the s.p. Hilbert space, we show that TDHF has a hamiltonian, but non-canonical, classical form. Within this Poisson structure, either the s.p. energy or the s.p. grand potential Ω(ρ) act as a Hamilton function. The Lyapunov stability of both the TDHF and RPA equations around a HF state then follows, since the HF approximation for thermal equilibrium is determined by minimizing Ω(ρ). The RPA matrix in the Liouville space is expressed as the product of the Poisson tensor with the HF stability matrix, interpreted as a metric tensor generated by the entropy. This factorization displays the roles of the energy and entropy terms arising from Ω(ρ) in the RPA dynamics, and it helps to construct the RPA modes. Several extensions are considered

On the existence of polynomial Lyapunov functions for rationally stable vector fields

DEFF Research Database (Denmark)

Leth, Tobias; Wisniewski, Rafal; Sloth, Christoffer

2018-01-01

This paper proves the existence of polynomial Lyapunov functions for rationally stable vector fields. For practical purposes the existence of polynomial Lyapunov functions plays a significant role since polynomial Lyapunov functions can be found algorithmically. The paper extents an existing result...... on exponentially stable vector fields to the case of rational stability. For asymptotically stable vector fields a known counter example is investigated to exhibit the mechanisms responsible for the inability to extend the result further....

Construction of Lyapunov Function for Dissipative Gyroscopic System

International Nuclear Information System (INIS)

Xu Wei; Ao Ping; Yuan Bo

2011-01-01

We introduce a force decomposition to construct a potential function in deterministic dynamics described by ordinary differential equations in the context of dissipative gyroscopic systems. Such a potential function serves as the corresponding Lyapunov function for the dynamics, hence it gives both quantitative and qualitative descriptions for stability of motion. As an example we apply our force decomposition to a four-dimensional dissipative gyroscopic system. We explicitly obtain the potential function for all parameter regimes in the linear limit, including those regimes where the Lyapunov function was previously believed not to exist. (general)

An Isomorphism between Lyapunov Exponents and Shannon's Channel Capacity

Energy Technology Data Exchange (ETDEWEB)

Friedland, Gerald [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Metere, Alfredo [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States)

2017-06-07

We demonstrate that discrete Lyapunov exponents are isomorphic to numeric overflows of the capacity of an arbitrary noiseless and memoryless channel in a Shannon communication model with feedback. The isomorphism allows the understanding of Lyapunov exponents in terms of Information Theory, rather than the traditional definitions in chaos theory. The result also implies alternative approaches to the calculation of related quantities, such as the Kolmogorov Sinai entropy which has been linked to thermodynamic entropy. This work provides a bridge between fundamental physics and information theory. It suggests, among other things, that machine learning and other information theory methods can be employed at the core of physics simulations.

Sliding Mode Controller and Lyapunov Redesign Controller to Improve Microgrid Stability:A Comparative Analysis with CPL Power Variation

OpenAIRE

Hossain, Eklas; Perez, Ron; Padmanaban, Sanjeevikumar; Mihet-Popa, Lucian; Blaabjerg, Frede; Ramachandaramurthy, Vigna K.

2017-01-01

To mitigate the microgrid instability despite the presence of dense Constant Power Load (CPL) loads in the system, a number of compensation techniques have already been gone through extensive research, proposed, and implemented around the world. In this paper, a storage based load side compensation technique is used to enhance stability of microgrids. Besides adopting this technique here, Sliding Mode Controller (SMC) and Lyapunov Redesign Controller (LRC), two of the most prominent nonlinear...

Lyapunov equation for infinite-dimensional discrete bilinear systems

International Nuclear Information System (INIS)

Costa, O.L.V.; Kubrusly, C.S.

1991-03-01

Mean-square stability for discrete systems requires that uniform convergence is preserved between input and state correlation sequences. Such a convergence preserving property holds for an infinite-dimensional bilinear system if and only if the associate Lyapunov equation has a unique strictly positive solution. (author)

Relative Lyapunov Center Bifurcations

DEFF Research Database (Denmark)

Wulff, Claudia; Schilder, Frank

2014-01-01

Relative equilibria (REs) and relative periodic orbits (RPOs) are ubiquitous in symmetric Hamiltonian systems and occur, for example, in celestial mechanics, molecular dynamics, and rigid body motion. REs are equilibria, and RPOs are periodic orbits of the symmetry reduced system. Relative Lyapunov...... center bifurcations are bifurcations of RPOs from REs corresponding to Lyapunov center bifurcations of the symmetry reduced dynamics. In this paper we first prove a relative Lyapunov center theorem by combining recent results on the persistence of RPOs in Hamiltonian systems with a symmetric Lyapunov...... center theorem of Montaldi, Roberts, and Stewart. We then develop numerical methods for the detection of relative Lyapunov center bifurcations along branches of RPOs and for their computation. We apply our methods to Lagrangian REs of the N-body problem....

Non Lyapunov stability of the constant spatially developing 1-D gas flow in presence of solutions having strictly positive exponential growth rate

Science.gov (United States)

Balint, Stefan; Balint, Agneta M.

2017-01-01

Different types of stabilities (global, local) and instabilities (global absolute, local convective) of the constant spatially developing 1-D gas flow are analyzed in the phase space of continuously differentiable functions, endowed with the usual algebraic operations and the topology generated by the uniform convergence on the real axis. For this purpose the Euler equations linearized at the constant flow are used. The Lyapunov stability analysis was presented in [1] and this paper is a continuation of [1].

Using Covariant Lyapunov Vectors to Understand Spatiotemporal Chaos in Fluids

Science.gov (United States)

Paul, Mark; Xu, Mu; Barbish, Johnathon; Mukherjee, Saikat

2017-11-01

The spatiotemporal chaos of fluids present many difficult and fascinating challenges. Recent progress in computing covariant Lyapunov vectors for a variety of model systems has made it possible to probe fundamental ideas from dynamical systems theory including the degree of hyperbolicity, the fractal dimension, the dimension of the inertial manifold, and the decomposition of the dynamics into a finite number of physical modes and spurious modes. We are interested in building upon insights such as these for fluid systems. We first demonstrate the power of covariant Lyapunov vectors using a system of maps on a lattice with a nonlinear coupling. We then compute the covariant Lyapunov vectors for chaotic Rayleigh-Bénard convection for experimentally accessible conditions. We show that chaotic convection is non-hyperbolic and we quantify the spatiotemporal features of the spectrum of covariant Lyapunov vectors. NSF DMS-1622299 and DARPA/DSO Models, Dynamics, and Learning (MoDyL).

Stabilisation of discrete-time polynomial fuzzy systems via a polynomial lyapunov approach

Science.gov (United States)

Nasiri, Alireza; Nguang, Sing Kiong; Swain, Akshya; Almakhles, Dhafer

2018-02-01

This paper deals with the problem of designing a controller for a class of discrete-time nonlinear systems which is represented by discrete-time polynomial fuzzy model. Most of the existing control design methods for discrete-time fuzzy polynomial systems cannot guarantee their Lyapunov function to be a radially unbounded polynomial function, hence the global stability cannot be assured. The proposed control design in this paper guarantees a radially unbounded polynomial Lyapunov functions which ensures global stability. In the proposed design, state feedback structure is considered and non-convexity problem is solved by incorporating an integrator into the controller. Sufficient conditions of stability are derived in terms of polynomial matrix inequalities which are solved via SOSTOOLS in MATLAB. A numerical example is presented to illustrate the effectiveness of the proposed controller.

Potential and flux field landscape theory. I. Global stability and dynamics of spatially dependent non-equilibrium systems.

Science.gov (United States)

Wu, Wei; Wang, Jin

2013-09-28

found to be a Lyapunov functional of the deterministic spatially dependent system. Therefore, the intrinsic potential landscape can characterize the global stability of the deterministic system. The relative entropy functional of the stochastic spatially dependent non-equilibrium system is found to be the Lyapunov functional of the stochastic dynamics of the system. Therefore, the relative entropy functional quantifies the global stability of the stochastic system with finite fluctuations. Our theory offers an alternative general approach to other field-theoretic techniques, to study the global stability and dynamics of spatially dependent non-equilibrium field systems. It can be applied to many physical, chemical, and biological spatially dependent non-equilibrium systems.

Stability theory for dynamic equations on time scales

CERN Document Server

Martynyuk, Anatoly A

2016-01-01

This monograph is a first in the world to present three approaches for stability analysis of solutions of dynamic equations. The first approach is based on the application of dynamic integral inequalities and the fundamental matrix of solutions of linear approximation of dynamic equations. The second is based on the generalization of the direct Lyapunovs method for equations on time scales, using scalar, vector and matrix-valued auxiliary functions. The third approach is the application of auxiliary functions (scalar, vector, or matrix-valued ones) in combination with differential dynamic inequalities. This is an alternative comparison method, developed for time continuous and time discrete systems. In recent decades, automatic control theory in the study of air- and spacecraft dynamics and in other areas of modern applied mathematics has encountered problems in the analysis of the behavior of solutions of time continuous-discrete linear and/or nonlinear equations of perturbed motion. In the book “Men of Ma...

Diagonal recurrent neural network based adaptive control of nonlinear dynamical systems using lyapunov stability criterion.

Science.gov (United States)

Kumar, Rajesh; Srivastava, Smriti; Gupta, J R P

2017-03-01

In this paper adaptive control of nonlinear dynamical systems using diagonal recurrent neural network (DRNN) is proposed. The structure of DRNN is a modification of fully connected recurrent neural network (FCRNN). Presence of self-recurrent neurons in the hidden layer of DRNN gives it an ability to capture the dynamic behaviour of the nonlinear plant under consideration (to be controlled). To ensure stability, update rules are developed using lyapunov stability criterion. These rules are then used for adjusting the various parameters of DRNN. The responses of plants obtained with DRNN are compared with those obtained when multi-layer feed forward neural network (MLFFNN) is used as a controller. Also, in example 4, FCRNN is also investigated and compared with DRNN and MLFFNN. Robustness of the proposed control scheme is also tested against parameter variations and disturbance signals. Four simulation examples including one-link robotic manipulator and inverted pendulum are considered on which the proposed controller is applied. The results so obtained show the superiority of DRNN over MLFFNN as a controller. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Sliding Mode Controller and Lyapunov Redesign Controller to Improve Microgrid Stability: A Comparative Analysis with CPL Power Variation

Directory of Open Access Journals (Sweden)

Eklas Hossain

2017-11-01

Full Text Available To mitigate the microgrid instability despite the presence of dense Constant Power Load (CPL loads in the system, a number of compensation techniques have already been gone through extensive research, proposed, and implemented around the world. In this paper, a storage based load side compensation technique is used to enhance stability of microgrids. Besides adopting this technique here, Sliding Mode Controller (SMC and Lyapunov Redesign Controller (LRC, two of the most prominent nonlinear control techniques, are individually implemented to control microgrid system stability with desired robustness. CPL power is then varied to compare robustness of these two control techniques. This investigation revealed the better performance of the LRC system compared to SMC to retain stability in microgrid with dense CPL load. All the necessary results are simulated in Matlab/Simulink platform for authentic verification. Reasons behind inferior SMC performance and ways to mitigate that are also discussed. Finally, the effectiveness of SMC and LRC systems to attain stability in real microgrids is verified by numerical analysis.

LMI optimization approach to stabilization of time-delay chaotic systems

International Nuclear Information System (INIS)

Park, Ju H.; Kwon, O.M.

2005-01-01

Based on the Lyapunov stability theory and linear matrix inequality (LMI) technique, this paper proposes a novel control method for stabilization of a class of time-delay chaotic systems. A stabilization criterion is derived in terms of LMIs which can be easily solved by efficient convex optimization algorithms. A numerical example is included to show the advantage of the result derived

Exponential stability of fuzzy cellular neural networks with constant and time-varying delays

International Nuclear Information System (INIS)

Liu Yanqing; Tang Wansheng

2004-01-01

In this Letter, the global stability of delayed fuzzy cellular neural networks (FCNN) with either constant delays or time varying delays is proposed. Firstly, we give the existence and uniqueness of the equilibrium point by using the theory of topological degree and the properties of nonsingular M-matrix and the sufficient conditions for ascertaining the global exponential stability by constructing a suitable Lyapunov functional. Secondly, the criteria for guaranteeing the global exponential stability of FCNN with time varying delays are given and the estimation of exponential convergence rate with regard to speed of vary of delays is presented by constructing a suitable Lyapunov functional

New stability and stabilization for switched neutral control systems

International Nuclear Information System (INIS)

Xiong Lianglin; Zhong Shouming; Ye Mao; Wu Shiliang

2009-01-01

This paper concerns stability and stabilization issues for switched neutral systems and presents new classes of piecewise Lyapunov functionals and multiple Lyapunov functionals, based on which, two new switching rules are introduced to stabilize the neutral systems. One switching rule is designed from the solution of the so-called Lyapunov-Metzler linear matrix inequalities. The other is based on the determination of average dwell time computed from a new class of linear matrix inequalities (LMIs). And then, state-feedback control is derived for the switched neutral control system mainly based on the state switching rules. Finally, three examples are given to demonstrate the effectiveness of the proposed method.

Energy-based Lyapunov functions for forced Hamiltonian systems with dissipation

NARCIS (Netherlands)

Maschke, Bernhard M.J.; Ortega, Romeo; Schaft, Arjan J. van der

1998-01-01

It is well known that the total energy is a suitable Lyapunov function to study the stability of the trivial equilibrium of an isolated standard Hamiltonian system. In many practical instances, however, the system is in interaction with its environment through some constant forcing terms. This gives

Towards a rational theory for CFD global stability

International Nuclear Information System (INIS)

Baker, A.J.; Iannelli, G.S.

1989-01-01

The fundamental notion of the consistent stability of semidiscrete analogues of evolution PDEs is explored. Lyapunov's direct method is used to develop CFD semidiscrete algorithms which yield the TVD constraint as a special case. A general formula for supplying dissipation parameters for arbitrary multidimensional conservation law systems is proposed. The reliability of the method is demonstrated by the results of two numerical tests for representative Euler shocked flows. 18 refs

Interpolation of polytopic control Lyapunov functions for discrete–time linear systems

NARCIS (Netherlands)

Nguyen, T.T.; Lazar, M.; Spinu, V.; Boje, E.; Xia, X.

2014-01-01

This paper proposes a method for interpolating two (or more) polytopic control Lyapunov functions (CLFs) for discrete--time linear systems subject to polytopic constraints, thereby combining different control objectives. The corresponding interpolated CLF is used for synthesis of a stabilizing

Global robust exponential stability for interval neural networks with delay

International Nuclear Information System (INIS)

Cui Shihua; Zhao Tao; Guo Jie

2009-01-01

In this paper, new sufficient conditions for globally robust exponential stability of neural networks with either constant delays or time-varying delays are given. We show the sufficient conditions for the existence, uniqueness and global robust exponential stability of the equilibrium point by employing Lyapunov stability theory and linear matrix inequality (LMI) technique. Numerical examples are given to show the approval of our results.

Geodesic stability, Lyapunov exponents, and quasinormal modes

International Nuclear Information System (INIS)

Cardoso, Vitor; Miranda, Alex S.; Berti, Emanuele; Witek, Helvi; Zanchin, Vilson T.

2009-01-01

Geodesic motion determines important features of spacetimes. Null unstable geodesics are closely related to the appearance of compact objects to external observers and have been associated with the characteristic modes of black holes. By computing the Lyapunov exponent, which is the inverse of the instability time scale associated with this geodesic motion, we show that, in the eikonal limit, quasinormal modes of black holes in any dimensions are determined by the parameters of the circular null geodesics. This result is independent of the field equations and only assumes a stationary, spherically symmetric and asymptotically flat line element, but it does not seem to be easily extendable to anti-de Sitter spacetimes. We further show that (i) in spacetime dimensions greater than four, equatorial circular timelike geodesics in a Myers-Perry black-hole background are unstable, and (ii) the instability time scale of equatorial null geodesics in Myers-Perry spacetimes has a local minimum for spacetimes of dimension d≥6.

A Criterion for Stability of Synchronization and Application to Coupled Chua's Systems

International Nuclear Information System (INIS)

Wang Haixia; Lu Qishao; Wang Qingyun

2009-01-01

We investigate synchronization in an array network of nearest-neighbor coupled chaotic oscillators. By using of the Lyapunov stability theory and matrix theory, a criterion for stability of complete synchronization is deduced. Meanwhile, an estimate of the critical coupling strength is obtained to ensure achieving chaos synchronization. As an example application, a model of coupled Chua's circuits with linearly bidirectional coupling is studied to verify the validity of the criterion. (general)

Stability and response bounds of non-conservative linear systems

DEFF Research Database (Denmark)

Pommer, Christian

2003-01-01

For a linear system of second order differential equations the stability is studied by Lyapunov's direct method. The Lyapunov matrix equation is solved and a sufficient condition for stability is expressed by the system matrices. For a system which satisfies the condition for stability the Lyapunov...

Intercept Algorithm for Maneuvering Targets Based on Differential Geometry and Lyapunov Theory

Directory of Open Access Journals (Sweden)

Yunes Sh. ALQUDSI

2018-03-01

Full Text Available Nowadays, the homing guidance is utilized in the existed and under development air defense systems (ADS to effectively intercept the targets. The targets became smarter and capable to fly and maneuver professionally and the tendency to design missile with a small warhead became greater, then there is a pressure to produce a more precise and accurate missile guidance system based on intelligent algorithms to ensure effective interception of highly maneuverable targets. The aim of this paper is to present an intelligent guidance algorithm that effectively and precisely intercept the maneuverable and smart targets by virtue of the differential geometry (DG concepts. The intercept geometry and engagement kinematics, in addition to the direct intercept condition are developed and expressed in DG terms. The guidance algorithm is then developed by virtue of DG and Lyapunov theory. The study terminates with 2D engagement simulation with illustrative examples, to demonstrate that, the derived DG guidance algorithm is a generalized guidance approach and the well-known proportional navigation (PN guidance law is a subset of this approach.

The Multivariate Largest Lyapunov Exponent as an Age-Related Metric of Quiet Standing Balance

Directory of Open Access Journals (Sweden)

Kun Liu

2015-01-01

Full Text Available The largest Lyapunov exponent has been researched as a metric of the balance ability during human quiet standing. However, the sensitivity and accuracy of this measurement method are not good enough for clinical use. The present research proposes a metric of the human body’s standing balance ability based on the multivariate largest Lyapunov exponent which can quantify the human standing balance. The dynamic multivariate time series of ankle, knee, and hip were measured by multiple electrical goniometers. Thirty-six normal people of different ages participated in the test. With acquired data, the multivariate largest Lyapunov exponent was calculated. Finally, the results of the proposed approach were analysed and compared with the traditional method, for which the largest Lyapunov exponent and power spectral density from the centre of pressure were also calculated. The following conclusions can be obtained. The multivariate largest Lyapunov exponent has a higher degree of differentiation in differentiating balance in eyes-closed conditions. The MLLE value reflects the overall coordination between multisegment movements. Individuals of different ages can be distinguished by their MLLE values. The standing stability of human is reduced with the increment of age.

Lyapunov exponent for aging process in induction motor

Science.gov (United States)

Bayram, Duygu; Ünnü, Sezen Yıdırım; Şeker, Serhat

2012-09-01

focused on the controlling the mechanical parameters of the electrical machines. Brushless DC motor (BLDCM) and the other general purpose permanent magnet (PM) motors are the most widely examined motors [1, 8, 9]. But the researches, about Lyapunov Exponent, subjected to the induction motors are mostly focused on the control theory of the motors. Flux estimation of rotor, external load disturbances and speed tracking and vector control position system are the main research areas for induction motors [10, 11, 12-14]. For all the data sets which can be collected from an induction motor, vibration data have the key role for understanding the mechanical behaviours like aging, bearing damage and stator insulation damage [15-18]. In this paper aging of an induction motor is investigated by using the vibration signals. The signals consist of new and aged motor data. These data are examined by their 2 dimensional phase portraits and the geometric interpretation is applied for detecting the Lyapunov Exponents. These values are compared in order to define the character and state estimation of the aging processes.

Dynamic stability of running: The effects of speed and leg amputations on the maximal Lyapunov exponent

International Nuclear Information System (INIS)

Look, Nicole; Arellano, Christopher J.; Grabowski, Alena M.; Kram, Rodger; McDermott, William J.; Bradley, Elizabeth

2013-01-01

In this paper, we study dynamic stability during running, focusing on the effects of speed, and the use of a leg prosthesis. We compute and compare the maximal Lyapunov exponents of kinematic time-series data from subjects with and without unilateral transtibial amputations running at a wide range of speeds. We find that the dynamics of the affected leg with the running-specific prosthesis are less stable than the dynamics of the unaffected leg and also less stable than the biological legs of the non-amputee runners. Surprisingly, we find that the center-of-mass dynamics of runners with two intact biological legs are slightly less stable than those of runners with amputations. Our results suggest that while leg asymmetries may be associated with instability, runners may compensate for this effect by increased control of their center-of-mass dynamics

Lyapunov exponents a tool to explore complex dynamics

CERN Document Server

Pikovsky, Arkady

2016-01-01

Lyapunov exponents lie at the heart of chaos theory, and are widely used in studies of complex dynamics. Utilising a pragmatic, physical approach, this self-contained book provides a comprehensive description of the concept. Beginning with the basic properties and numerical methods, it then guides readers through to the most recent advances in applications to complex systems. Practical algorithms are thoroughly reviewed and their performance is discussed, while a broad set of examples illustrate the wide range of potential applications. The description of various numerical and analytical techniques for the computation of Lyapunov exponents offers an extensive array of tools for the characterization of phenomena such as synchronization, weak and global chaos in low and high-dimensional set-ups, and localization. This text equips readers with all the investigative expertise needed to fully explore the dynamical properties of complex systems, making it ideal for both graduate students and experienced researchers...

Comment on 'Exact analytical solution for the generalized Lyapunov exponent of the two-dimensional Anderson localization'

International Nuclear Information System (INIS)

Markos, P; Schweitzer, L; Weyrauch, M

2004-01-01

In a recent publication, Kuzovkov et al (2002 J. Phys.: Condens. Matter. 14 13777) announced an analytical solution of the two-dimensional Anderson localization problem via the calculation of a generalized Lyapunov exponent using signal theory. Surprisingly, for certain energies and small disorder strength they observed delocalized states. We study the transmission properties of the same model using well-known transfer matrix methods. Our results disagree with the findings obtained using signal theory. We point to the possible origin of this discrepancy and comment on the general strategy of using a generalized Lyapunov exponent for studying Anderson localization. (comment)

Using largest Lyapunov exponent to confirm the intrinsic stability of boiling water reactors

International Nuclear Information System (INIS)

Gavilian-Moreno, Carlos; Espinosa-Paredes, Gilberto

2016-01-01

The aim of this paper is the study of instability state of boiling water reactors with a method based in largest Lyapunov exponents (LLEs). Detecting the presence of chaos in a dynamical system is an important problem that is solved by measuring the LLE. Lyapunov exponents quantify the exponential divergence of initially close state-space trajectories and estimate the amount of chaos in a system. This method was applied to a set of signals from several nuclear power plant (NPP) reactors under commercial operating conditions that experienced instabilities events, apparently each of a different nature. Laguna Verde and Forsmark NPPs with in-phase instabilities, and Cofrentes NPP with out-of-phases instability. This study presents the results of intrinsic instability in the boiling water reactors of three NPPs. In the analyzed cases the limit cycle was not reached, which implies that the point of equilibrium exerts influence and attraction on system evolution

Using largest Lyapunov exponent to confirm the intrinsic stability of boiling water reactors

Energy Technology Data Exchange (ETDEWEB)

Gavilian-Moreno, Carlos [Iberdrola Generacion, S.A., Cofrentes Nuclear Power Plant, Project Engineering Department, Paraje le Plano S/N, Valencia (Spain); Espinosa-Paredes, Gilberto [Area de ingeniera en Recursos Energeticos, Universidad Autonoma Metropolitana-Iztapalapa, Mexico city (Mexico)

2016-04-15

The aim of this paper is the study of instability state of boiling water reactors with a method based in largest Lyapunov exponents (LLEs). Detecting the presence of chaos in a dynamical system is an important problem that is solved by measuring the LLE. Lyapunov exponents quantify the exponential divergence of initially close state-space trajectories and estimate the amount of chaos in a system. This method was applied to a set of signals from several nuclear power plant (NPP) reactors under commercial operating conditions that experienced instabilities events, apparently each of a different nature. Laguna Verde and Forsmark NPPs with in-phase instabilities, and Cofrentes NPP with out-of-phases instability. This study presents the results of intrinsic instability in the boiling water reactors of three NPPs. In the analyzed cases the limit cycle was not reached, which implies that the point of equilibrium exerts influence and attraction on system evolution.

Using Largest Lyapunov Exponent to Confirm the Intrinsic Stability of Boiling Water Reactors

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Carlos J. Gavilán-Moreno

2016-04-01

Full Text Available The aim of this paper is the study of instability state of boiling water reactors with a method based in largest Lyapunov exponents (LLEs. Detecting the presence of chaos in a dynamical system is an important problem that is solved by measuring the LLE. Lyapunov exponents quantify the exponential divergence of initially close state-space trajectories and estimate the amount of chaos in a system. This method was applied to a set of signals from several nuclear power plant (NPP reactors under commercial operating conditions that experienced instabilities events, apparently each of a different nature. Laguna Verde and Forsmark NPPs with in-phase instabilities, and Cofrentes NPP with out-of-phases instability. This study presents the results of intrinsic instability in the boiling water reactors of three NPPs. In the analyzed cases the limit cycle was not reached, which implies that the point of equilibrium exerts influence and attraction on system evolution.

Using genetic programming to find Lyapunov functions

NARCIS (Netherlands)

Soute, I.A.C.; Molengraft, van de M.J.G.; Angelis, G.Z.; Ryan, C; Spector, L.

2001-01-01

In this paper Genetic Programming is used to find Lyapunov functions for (non)linear dif ferential equations of autonomous systems. As Lyapunov functions can be difficult to find, we use OP to make the decisions concerning the form of the Lyapunov function. As an e5cample two systems are taken to

Nonlinear stability of ideal fluid equilibria

International Nuclear Information System (INIS)

Holm, D.D.

1988-01-01

The Lyapunov method for establishing stability is related to well- known energy principles for nondissipative dynamical systems. A development of the Lyapunov method for Hamiltonian systems due to Arnold establishes sufficient conditions for Lyapunov stability by using the energy plus other conserved quantities, together with second variations and convexity estimates. When treating the stability of ideal fluid dynamics within the Hamiltonian framework, a useful class of these conserved quantities consists of the Casimir functionals, which Poisson-commute with all functionals of the dynamical fluid variables. Such conserved quantities, when added to the energy, help to provide convexity estimates that bound the growth of perturbations. These convexity estimates, in turn, provide norms necessary for establishing Lyapunov stability under the nonlinear evolution. In contrast, the commonly used second variation or spectral stability arguments only prove linearized stability. As ideal fluid examples, in these lectures we discuss planar barotropic compressible fluid dynamics, the three-dimensional hydrostatic Boussinesq model, and a new set of shallow water equations with nonlinear dispersion due to Basdenkov, Morosov, and Pogutse[1985]. Remarkably, all three of these samples have the same Hamiltonian structure and, thus, possess the same Casimir functionals upon which their stability analyses are based. We also treat stability of modified quasigeostrophic flow, a problem whose Hamiltonian structure and Casimirs closely resemble Arnold's original example. Finally, we discuss some aspects of conditional stability and the applicability of Arnold's development of the Lyapunov technique. 100 refs

Estabilización del Péndulo Invertido Sobre Dos Ruedas mediante el método de Lyapunov

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O. Octavio Gutiérrez Frías

2013-01-01

Full Text Available Resumen: En este trabajo, se presenta un controlador no lineal para estabilizar el sistema Péndulo Invertido Sobre Dos Ruedas. Como primera etapa la estrategia de control, se basa en una linealización parcial por realimentación, para posteriormente proponer una función candidata de Lyapunov en combinación con el principio de invariancia de LaSalle con el fin de obtener el controlador esta- bilizador. El sistema en lazo cerrado obtenido es asintóticamente estable localmente alrededor del punto de equilibrio inestable, con un dominio de atracción calculable. Abstract: In this paper, a nonlinear controller is presented for the stabilization of the two wheels inverted pendulum. The control strategy is based on partial feedback linealization, in first stage and then a suitable function Lyapunov in conjunction with LaSalle's invariance principle is formed to obtain a stabilizing feedback controller. The obtained closed-loop system is locally asymptotically stable around its unstable equilibrium point, with a computable domain of attraction. Palabras clave: Sistema Subactuado, Péndulo Invertido Sobre Dos Ruedas, Método de Lyapunov, Control No Lineal, Keywords: Under Actuated System, Two Wheels Inverted Pendulum, Lyapunov Approach, Non-Linear Control

Robust lyapunov controller for uncertain systems

KAUST Repository

Laleg-Kirati, Taous-Meriem; Elmetennani, Shahrazed

2017-01-01

Various examples of systems and methods are provided for Lyapunov control for uncertain systems. In one example, a system includes a process plant and a robust Lyapunov controller configured to control an input of the process plant. The robust

Stability with respect to initial time difference for generalized delay differential equations

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Ravi Agarwal

2015-02-01

Full Text Available Stability with initial data difference for nonlinear delay differential equations is introduced. This type of stability generalizes the known concept of stability in the literature. It gives us the opportunity to compare the behavior of two nonzero solutions when both initial values and initial intervals are different. Several sufficient conditions for stability and for asymptotic stability with initial time difference are obtained. Lyapunov functions as well as comparison results for scalar ordinary differential equations are employed. Several examples are given to illustrate the theory.

Lyapunov Function Synthesis - Algorithm and Software

DEFF Research Database (Denmark)

Leth, Tobias; Sloth, Christoffer; Wisniewski, Rafal

2016-01-01

In this paper we introduce an algorithm for the synthesis of polynomial Lyapunov functions for polynomial vector fields. The Lyapunov function is a continuous piecewisepolynomial defined on simplices, which compose a collection of simplices. The algorithm is elaborated and crucial features are ex...

Stability and bifurcation analysis for a discrete-time bidirectional ring neural network model with delay

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Yan-Ke Du

2013-09-01

Full Text Available We study a class of discrete-time bidirectional ring neural network model with delay. We discuss the asymptotic stability of the origin and the existence of Neimark-Sacker bifurcations, by analyzing the corresponding characteristic equation. Employing M-matrix theory and the Lyapunov functional method, global asymptotic stability of the origin is derived. Applying the normal form theory and the center manifold theorem, the direction of the Neimark-Sacker bifurcation and the stability of bifurcating periodic solutions are obtained. Numerical simulations are given to illustrate the main results.

An analysis of global robust stability of uncertain cellular neural networks with discrete and distributed delays

International Nuclear Information System (INIS)

Park, Ju H.

2007-01-01

This paper considers the robust stability analysis of cellular neural networks with discrete and distributed delays. Based on the Lyapunov stability theory and linear matrix inequality (LMI) technique, a novel stability criterion guaranteeing the global robust convergence of the equilibrium point is derived. The criterion can be solved easily by various convex optimization algorithms. An example is given to illustrate the usefulness of our results

The Interval Stability of an Electricity Market Model

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Weijuan Wang

2014-01-01

Full Text Available Combined with the electric power market dynamic model put forward by Alvarado, an interval model of electricity markets is established and investigated in this paper pertaining to the range of demand elasticity with suppliers and consumers. The stability of an electricity market framework with demand elasticity interval is analyzed. The conclusions characterizing the interval model provided are derived by constructing a suitable Lyapunov function and using the theory of interval dynamical system in differential equations and matrix inequality theory and so forth. Applying the corollary obtained can judge the system stability by available data about demand elasticity. The obtained results are validated and illustrated by a case example.

Global robust asymptotical stability of multi-delayed interval neural networks: an LMI approach

International Nuclear Information System (INIS)

Li Chuandong; Liao Xiaofeng; Zhang Rong

2004-01-01

Based on the Lyapunov-Krasovskii stability theory for functional differential equations and the linear matrix inequality (LMI) technique, some delay-dependent criteria for interval neural networks (IDNN) with multiple time-varying delays are derived to guarantee global robust asymptotic stability. The main results are generalizations of some recent results reported in the literature. Numerical example is also given to show the effectiveness of our results

On global exponential stability of high-order neural networks with time-varying delays

International Nuclear Information System (INIS)

Zhang Baoyong; Xu Shengyuan; Li Yongmin; Chu Yuming

2007-01-01

This Letter investigates the problem of stability analysis for a class of high-order neural networks with time-varying delays. The delays are bounded but not necessarily differentiable. Based on the Lyapunov stability theory together with the linear matrix inequality (LMI) approach and the use of Halanay inequality, sufficient conditions guaranteeing the global exponential stability of the equilibrium point of the considered neural networks are presented. Two numerical examples are provided to demonstrate the effectiveness of the proposed stability criteria

On global exponential stability of high-order neural networks with time-varying delays

Energy Technology Data Exchange (ETDEWEB)

Zhang Baoyong [School of Automation, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu (China)]. E-mail: baoyongzhang@yahoo.com.cn; Xu Shengyuan [School of Automation, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu (China)]. E-mail: syxu02@yahoo.com.cn; Li Yongmin [School of Automation, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu (China) and Department of Mathematics, Huzhou Teacher' s College, Huzhou 313000, Zhejiang (China)]. E-mail: ymlwww@163.com; Chu Yuming [Department of Mathematics, Huzhou Teacher' s College, Huzhou 313000, Zhejiang (China)

2007-06-18

This Letter investigates the problem of stability analysis for a class of high-order neural networks with time-varying delays. The delays are bounded but not necessarily differentiable. Based on the Lyapunov stability theory together with the linear matrix inequality (LMI) approach and the use of Halanay inequality, sufficient conditions guaranteeing the global exponential stability of the equilibrium point of the considered neural networks are presented. Two numerical examples are provided to demonstrate the effectiveness of the proposed stability criteria.

Análisis de estabilidad de controladores borrosos tipo Mamdani mediante el cálculo del exponente de Lyapunov

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Leonardo-Alonso Martínez Rivera

2015-10-01

Full Text Available Resumen: Determinar la estabilidad de los controladores, ya sea mediante simulaciones o mediante técnicas analíticas, es vital en su diseño e implantación. El método analítico de estabilidad en el sentido de Lyapunov requiere encontrar una función candidata, como criterio suficiente pero no necesario para tal fin. Esta función candidata es elusiva para los controladores borrosos. Se propone, como posible solución a este problema, cuantificar la estabilidad de los controladores borrosos mediante el exponente de Lyapunov (EL calculado numéricamente. Las series de tiempo de la cuales se calculan los exponentes de Lyapunov son obtenidas de la salida de diversos controladores borrosos tipo Mamdani en lazo cerrado con la dinámica de la planta no lineal estabilizada en una región de operación admisible. Los experimentos fueron llevados al cabo mediante la implantación del método numérico en la plataforma MATLAB, integrándolo con datos provenientes de la simulación de diversos controladores borrosos. La planta a controlar es el sistema carro-péndulo invertido modelado con la formulación Euler Lagrange. En cada experimento se obtuvo la serie de tiempo correspondiente a la señal de control y se calculó el exponente de Lyapunov. Aunque se observan variaciones en magnitud, el exponente calculado resulta negativo en todos los casos. Esto indica que los controladores difusos tipo Mamdani empleados son sistemas disipativos. Como trabajo futuro se esboza el empleo del EL en control adaptable. Abstract: In order to design and implement any type of controller, their stability analysis is pivotal. At this regard, Lyapunov's analytical method consists in finding a candidate function as a sufficient but not necessary condition to validate the stability of the controller. In the case of fuzzy controllers such a candidate function is not always found, leading to an uncertainty about their stability. To

Improved asymptotic stability analysis for uncertain delayed state neural networks

International Nuclear Information System (INIS)

Souza, Fernando O.; Palhares, Reinaldo M.; Ekel, Petr Ya.

2009-01-01

This paper presents a new linear matrix inequality (LMI) based approach to the stability analysis of artificial neural networks (ANN) subject to time-delay and polytope-bounded uncertainties in the parameters. The main objective is to propose a less conservative condition to the stability analysis using the Gu's discretized Lyapunov-Krasovskii functional theory and an alternative strategy to introduce slack matrices. Two computer simulations examples are performed to support the theoretical predictions. Particularly, in the first example, the Hopf bifurcation theory is used to verify the stability of the system when the origin falls into instability. The second example is presented to illustrate how the proposed approach can provide better stability performance when compared to other ones in the literature

On the angle between the first and second Lyapunov vectors in spatio-temporal chaos

International Nuclear Information System (INIS)

Pazó, D; López, J M; Rodríguez, M A

2013-01-01

In a dynamical system the first Lyapunov vector (LV) is associated with the largest Lyapunov exponent and indicates—at any point on the attractor—the direction of maximal growth in tangent space. The LV corresponding to the second largest Lyapunov exponent generally points in a different direction, but tangencies between both vectors can in principle occur. Here we find that the probability density function (PDF) of the angle ψ spanned by the first and second LVs should be expected to be approximately symmetric around π/4 and to peak at 0 and π/2. Moreover, for small angles we uncover a scaling law for the PDF Q of ψ l = ln ψ with the system size L: Q(ψ l ) = L −1/2 f(ψ l L −1/2 ). We give a theoretical argument that justifies this scaling form and also explains why it should be universal (irrespective of the system details) for spatio-temporal chaos in one spatial dimension. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (paper)

Perturbation theory for Lyapunov exponents of an Anderson model on a strip

CERN Document Server

Schulz-Baldes, H

2003-01-01

It is proven that the localization length of an Anderson model on a strip of width $L$ is bounded above by $L/\\lambda^2$ for small values of the coupling constant $\\lambda$ of the disordered potential. For this purpose, a new formalism is developed in order to calculate the bottom Lyapunov exponent associated with random products of large symplectic matrices perturbatively in the coupling constant of the randomness.

STABILITY OF LINEAR SYSTEMS WITH MARKOVIAN JUMPS

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Jorge Enrique Mayta Guillermo

2016-12-01

Full Text Available In this work we will analyze the stability of linear systems governed by a Markov chain, this family is known in the specialized literature as linear systems with Markov jumps or by its acronyms in English MJLS as it is denoted in [1]. Linear systems governed by a Markov chain are dynamic systems with abrupt changes. We give some denitions of stability for the MJLS system, where these types of stability are equivalent as long as the state space of the Markov chain is nite. Finally we present a theorem that characterizes the stochastic stability by means of an equation of the Lyapunov type. The result is a generalization of a theorem in classical theory.

An algorithm for constructing Lyapunov functions

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Sigurdur Freyr Hafstein

2007-08-01

Full Text Available In this monograph we develop an algorithm for constructing Lyapunov functions for arbitrary switched dynamical systems $dot{mathbf{x}} = mathbf{f}_sigma(t,mathbf{x}$, possessing a uniformly asymptotically stable equilibrium. Let $dot{mathbf{x}}=mathbf{f}_p(t,mathbf{x}$, $pinmathcal{P}$, be the collection of the ODEs, to which the switched system corresponds. The number of the vector fields $mathbf{f}_p$ on the right-hand side of the differential equation is assumed to be finite and we assume that their components $f_{p,i}$ are $mathcal{C}^2$ functions and that we can give some bounds, not necessarily close, on their second-order partial derivatives. The inputs of the algorithm are solely a finite number of the function values of the vector fields $mathbf{f}_p$ and these bounds. The domain of the Lyapunov function constructed by the algorithm is only limited by the size of the equilibrium's region of attraction. Note, that the concept of a Lyapunov function for the arbitrary switched system $dot{mathbf{x}} = mathbf{f}_sigma(t,mathbf{x}$ is equivalent to the concept of a common Lyapunov function for the systems $dot{mathbf{x}}=mathbf{f}_p(t,mathbf{x}$, $pinmathcal{P}$, and that if $mathcal{P}$ contains exactly one element, then the switched system is just a usual ODE $dot{mathbf{x}}=mathbf{f}(t,mathbf{x}$. We give numerous examples of Lyapunov functions constructed by our method at the end of this monograph.

Conditional Lyapunov exponents and transfer entropy in coupled bursting neurons under excitation and coupling mismatch

Science.gov (United States)

Soriano, Diogo C.; Santos, Odair V. dos; Suyama, Ricardo; Fazanaro, Filipe I.; Attux, Romis

2018-03-01

This work has a twofold aim: (a) to analyze an alternative approach for computing the conditional Lyapunov exponent (λcmax) aiming to evaluate the synchronization stability between nonlinear oscillators without solving the classical variational equations for the synchronization error dynamical system. In this first framework, an analytic reference value for λcmax is also provided in the context of Duffing master-slave scenario and precisely evaluated by the proposed numerical approach; (b) to apply this technique to the study of synchronization stability in chaotic Hindmarsh-Rose (HR) neuronal models under uni- and bi-directional resistive coupling and different excitation bias, which also considered the root mean square synchronization error, information theoretic measures and asymmetric transfer entropy in order to offer a better insight of the synchronization phenomenon. In particular, statistical and information theoretical measures were able to capture similarity increase between the neuronal oscillators just after a critical coupling value in accordance to the largest conditional Lyapunov exponent behavior. On the other hand, transfer entropy was able to detect neuronal emitter influence even in a weak coupling condition, i.e. under the increase of conditional Lyapunov exponent and apparently desynchronization tendency. In the performed set of numerical simulations, the synchronization measures were also evaluated for a two-dimensional parameter space defined by the neuronal coupling (emitter to a receiver neuron) and the (receiver) excitation current. Such analysis is repeated for different feedback couplings as well for different (emitter) excitation currents, revealing interesting characteristics of the attained synchronization region and conditions that facilitate the emergence of the synchronous behavior. These results provide a more detailed numerical insight of the underlying behavior of a HR in the excitation and coupling space, being in accordance

Quantum synchronization in an optomechanical system based on Lyapunov control.

Science.gov (United States)

Li, Wenlin; Li, Chong; Song, Heshan

2016-06-01

We extend the concepts of quantum complete synchronization and phase synchronization, which were proposed in A. Mari et al., Phys. Rev. Lett. 111, 103605 (2013)PRLTAO0031-900710.1103/PhysRevLett.111.103605, to more widespread quantum generalized synchronization. Generalized synchronization can be considered a necessary condition or a more flexible derivative of complete synchronization, and its criterion and synchronization measure are proposed and analyzed in this paper. As examples, we consider two typical generalized synchronizations in a designed optomechanical system. Unlike the effort to construct a special coupling synchronization system, we purposefully design extra control fields based on Lyapunov control theory. We find that the Lyapunov function can adapt to more flexible control objectives, which is more suitable for generalized synchronization control, and the control fields can be achieved simply with a time-variant voltage. Finally, the existence of quantum entanglement in different generalized synchronizations is also discussed.

Un algoritmo de replanificación en tiempo real basado en un índice de estabilidad de Lyapunov para líneas de metro

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A. Berbey

2014-04-01

Full Text Available Resumen: En este trabajo, se propone un nuevo índice basado en el método directo de Lyapunov para el diseño de un algoritmo de reprogramación en tiempo real para líneas de metro. En este estudio se utiliza una versión modificada de un modelo de espacio de estados en tiempo real discreto, que considera los efectos de saturación en la línea de metro. Una vez que el modelo de espacio de estados se ha obtenido, el método directo de Lyapunov se aplica con el fin de analizar la estabilidad del sistema de la línea de metro. Como resultado de este análisis no sólo se propone un nuevo índice de estabilidad, sino también la creación de tres zonas de estabilidad para indicar el estado actual del sistema. Finalmente, se presenta un nuevo algoritmo que permite la reprogramación del calendario de los trenes en tiempo real en presencia de perturbaciones medianas. Abstract: A new Lyapunov-based index for designing a rescheduling algorithm in real time for metro lines has been proposed in this paper. A modified real time discrete space state model which considers saturation effects in the metro line has been utilized in this study. Once the space state model has been obtained, the direct method of Lyapunov is applied in order to analyze the stability of the metro line system. As a result of this analysis not only a new stability index is proposed, but also the establishment of three stability zones to indicate the current state of the system. Finally, a new algorithm which allows the rescheduling of the timetable in the real time of the trains under presence of medium disturbances has been presented. Palabras clave: Sistema de metro, estabilidad de Lyapunov, planificación en tiempo real, Keywords: Metro system, Lyapunov stability, real time planning, traffic regulation

Fixed-Time Stability Analysis of Permanent Magnet Synchronous Motors with Novel Adaptive Control

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Maoxing Liu

2017-01-01

Full Text Available We firstly investigate the fixed-time stability analysis of uncertain permanent magnet synchronous motors with novel control. Compared with finite-time stability where the convergence rate relies on the initial permanent magnet synchronous motors state, the settling time of fixed-time stability can be adjusted to desired values regardless of initial conditions. Novel adaptive stability control strategy for the permanent magnet synchronous motors is proposed, with which we can stabilize permanent magnet synchronous motors within fixed time based on the Lyapunov stability theory. Finally, some simulation and comparison results are given to illustrate the validity of the theoretical results.

On the stability with respect to the form of scalar charged solitons with allowance for an electromagnetic field

International Nuclear Information System (INIS)

Rybakov, Yu.P.; Chakrabarti, S.

1981-01-01

Stability by the form of scalar charged solitons with account of electromagnetic field is studied by the Lyapunov method. Conditions of stability for the Sing model are investigated. The model is shown to admit the existence of pointless spherically-symmetric solitons in the absence of the electromagnetic field. Perturbation theory by a non-dimensional parameter is applied for evaluating the effect of electromagnetic field on the stability of pointless solitons [ru

Design of Connectivity Preserving Flocking Using Control Lyapunov Function

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Bayu Erfianto

2016-01-01

Full Text Available This paper investigates cooperative flocking control design with connectivity preserving mechanism. During flocking, interagent distance is measured to determine communication topology of the flocks. Then, cooperative flocking motion is built based on cooperative artificial potential field with connectivity preserving mechanism to achieve the common flocking objective. The flocking control input is then obtained by deriving cooperative artificial potential field using control Lyapunov function. As a result, we prove that our flocking protocol establishes group stabilization and the communication topology of multiagent flocking is always connected.

Lyapunov exponent and topological entropy plateaus in piecewise linear maps

International Nuclear Information System (INIS)

Botella-Soler, V; Oteo, J A; Ros, J; Glendinning, P

2013-01-01

We consider a two-parameter family of piecewise linear maps in which the moduli of the two slopes take different values. We provide numerical evidence of the existence of some parameter regions in which the Lyapunov exponent and the topological entropy remain constant. Analytical proof of this phenomenon is also given for certain cases. Surprisingly however, the systems with that property are not conjugate as we prove by using kneading theory. (paper)

Robust Stability and H∞ Stabilization of Switched Systems with Time-Varying Delays Using Delta Operator Approach

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Chen Qin

2013-01-01

Full Text Available This paper considers the problems of the robust stability and robust H∞ controller design for time-varying delay switched systems using delta operator approach. Based on the average dwell time approach and delta operator theory, a sufficient condition of the robust exponential stability is presented by choosing an appropriate Lyapunov-Krasovskii functional candidate. Then, a state feedback controller is designed such that the resulting closed-loop system is exponentially stable with a guaranteed H∞ performance. The obtained results are formulated in the form of linear matrix inequalities (LMIs. Finally, a numerical example is provided to explicitly illustrate the feasibility and effectiveness of the proposed method.

Finite-Time Stability of Large-Scale Systems with Interval Time-Varying Delay in Interconnection

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T. La-inchua

2017-01-01

Full Text Available We investigate finite-time stability of a class of nonlinear large-scale systems with interval time-varying delays in interconnection. Time-delay functions are continuous but not necessarily differentiable. Based on Lyapunov stability theory and new integral bounding technique, finite-time stability of large-scale systems with interval time-varying delays in interconnection is derived. The finite-time stability criteria are delays-dependent and are given in terms of linear matrix inequalities which can be solved by various available algorithms. Numerical examples are given to illustrate effectiveness of the proposed method.

Exponential stability of neural networks with asymmetric connection weights

International Nuclear Information System (INIS)

Yang Jinxiang; Zhong Shouming

2007-01-01

This paper investigates the exponential stability of a class of neural networks with asymmetric connection weights. By dividing the network state variables into various parts according to the characters of the neural networks, some new sufficient conditions of exponential stability are derived via constructing a Lyapunov function and using the method of the variation of constant. The new conditions are associated with the initial values and are described by some blocks of the interconnection matrix, and do not depend on other blocks. Examples are given to further illustrate the theory

Some criteria for robust stability of Cohen-Grossberg neural networks with delays

International Nuclear Information System (INIS)

Xiong Weili; Xu Baoguo

2008-01-01

This paper considers the problem of robust stability of Cohen-Grossberg neural networks with time-varying delays. Based on the Lyapunov stability theory and linear matrix inequality (LMI) technique, some sufficient conditions are derived to ensure the global robust convergence of the equilibrium point. The proposed LMI conditions can be checked easily by recently developed algorithms solving LMIs. Comparisons between our results and previous results admits our results establish a new set of stability criteria for delayed Cohen-Grossberg neural networks. Numerical examples are given to illustrate the effectiveness of our results

Robust stability of uncertain Markovian jumping Cohen-Grossberg neural networks with mixed time-varying delays

International Nuclear Information System (INIS)

Sheng Li; Yang Huizhong

2009-01-01

This paper considers the robust stability of a class of uncertain Markovian jumping Cohen-Grossberg neural networks (UMJCGNNs) with mixed time-varying delays. The parameter uncertainties are norm-bounded and the mixed time-varying delays comprise discrete and distributed time delays. Based on the Lyapunov stability theory and linear matrix inequality (LMI) technique, some robust stability conditions guaranteeing the global robust convergence of the equilibrium point are derived. An example is given to show the effectiveness of the proposed results.

Determination of the Lyapunov exponents and the information dimension in some dynamical systems

International Nuclear Information System (INIS)

Ziar, A.

1992-01-01

Classical phase space for some dynamical systems relevant in nuclear physics are studied. The nuclei is described by convex billiards or in the mean field theory. In both cases, besides the Poincare surface of sections which gives a qualitative description, each trajectory is characterized by its maximum Lyapunov exponent. The analytic monodromy matrix for a free particle in convex billiards rotating around an axis perpendicular to the plan of billiards, is determined, generalizing a previous result obtained for static billiards. In the frame of the mean field theory, it is shown an interesting alternative to the Lyapunov exponent, which is the dimension of the manifold in the phase space associated to the trajectory, leading to the evaluation of the relative chaotic volume in phase space as a function of the different parameters. The dimension appears as a character which could be determined easily for the rotating mean field, where the dimension of the manifold on which the trajectory is lying could be equal to 5 or 4 for chaotic trajectories, and less or equal to 3 for regular ones

Lyapunov matrices approach to the parametric optimization of time-delay systems

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Duda Józef

2015-09-01

Full Text Available In the paper a Lyapunov matrices approach to the parametric optimization problem of time-delay systems with a P-controller is presented. The value of integral quadratic performance index of quality is equal to the value of Lyapunov functional for the initial function of the time-delay system. The Lyapunov functional is determined by means of the Lyapunov matrix

Stabilization Strategies of Supply Networks with Stochastic Switched Topology

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Shukai Li

2013-01-01

Full Text Available In this paper, a dynamical supply networks model with stochastic switched topology is presented, in which the stochastic switched topology is dependent on a continuous time Markov process. The goal is to design the state-feedback control strategies to stabilize the dynamical supply networks. Based on Lyapunov stability theory, sufficient conditions for the existence of state feedback control strategies are given in terms of matrix inequalities, which ensure the robust stability of the supply networks at the stationary states and a prescribed H∞ disturbance attenuation level with respect to the uncertain demand. A numerical example is given to illustrate the effectiveness of the proposed method.

Lyapunov Orbits in the Jupiter System Using Electrodynamic Tethers

Science.gov (United States)

Bokelmann, Kevin; Russell, Ryan P.; Lantoine, Gregory

2013-01-01

Various researchers have proposed the use of electrodynamic tethers for power generation and capture from interplanetary transfers. The effect of tether forces on periodic orbits in Jupiter-satellite systems are investigated. A perturbation force is added to the restricted three-body problem model and a series of simplifications allows development of a conservative system that retains the Jacobi integral. Expressions are developed to find modified locations of equilibrium positions. Modified families of Lyapunov orbits are generated as functions of tether size and Jacobi integral. Zero velocity curves and stability analyses are used to evaluate the dynamical properties of tether-modified orbits.

Globally exponential stability and periodic solutions of CNNS with variable coefficients and variable delays

International Nuclear Information System (INIS)

Liu Haifei; Wang Li

2006-01-01

In this Letter, by using the inequality method and the Lyapunov functional method, we analyze the globally exponential stability and the existence of periodic solutions of a class of cellular neutral networks with delays and variable coefficients. Some simple and new sufficient conditions ensuring the existence and uniqueness of globally exponential stability of periodic solutions for cellular neutral networks with variable coefficients and delays are obtained. In addition, one example is also worked out to illustrate our theory

Globally exponential stability and periodic solutions of CNNS with variable coefficients and variable delays

Energy Technology Data Exchange (ETDEWEB)

Liu Haifei [School of Management and Engineering, Nanjing University, Nanjing 210093 (China)]. E-mail: hfliu80@126.com; Wang Li [School of Management and Engineering, Nanjing University, Nanjing 210093 (China)

2006-09-15

In this Letter, by using the inequality method and the Lyapunov functional method, we analyze the globally exponential stability and the existence of periodic solutions of a class of cellular neutral networks with delays and variable coefficients. Some simple and new sufficient conditions ensuring the existence and uniqueness of globally exponential stability of periodic solutions for cellular neutral networks with variable coefficients and delays are obtained. In addition, one example is also worked out to illustrate our theory.

Evaluating Lyapunov exponent spectra with neural networks

International Nuclear Information System (INIS)

Maus, A.; Sprott, J.C.

2013-01-01

Highlights: • Cross-correlation is employed to remove spurious Lyapunov exponents from a spectrum. • Neural networks are shown to accurately model Lyapunov exponent spectra. • Neural networks compare favorably to local linear fits in modeling Lyapunov exponents. • Numerical experiments are performed with time series of varying length and noise. • Methods perform reasonably well on discrete time series. -- Abstract: A method using discrete cross-correlation for identifying and removing spurious Lyapunov exponents when embedding experimental data in a dimension greater than the original system is introduced. The method uses a distribution of calculated exponent values produced by modeling a single time series many times or multiple instances of a time series. For this task, global models are shown to compare favorably to local models traditionally used for time series taken from the Hénon map and delayed Hénon map, especially when the time series are short or contaminated by noise. An additional merit of global modeling is its ability to estimate the dynamical and geometrical properties of the original system such as the attractor dimension, entropy, and lag space, although consideration must be taken for the time it takes to train the global models

A Globally Stable Lyapunov Pointing and Rate Controller for the Magnetospheric MultiScale Mission (MMS)

Science.gov (United States)

Shah, Neerav

2011-01-01

The Magnetospheric MultiScale Mission (MMS) is scheduled to launch in late 2014. Its primary goal is to discover the fundamental plasma physics processes of reconnection in the Earth's magnetosphere. Each of the four MMS spacecraft is spin-stabilized at a nominal rate of 3 RPM. Traditional spin-stabilized spacecraft have used a number of separate modes to control nutation, spin rate, and precession. To reduce the number of modes and simplify operations, the Delta-H control mode is designed to accomplish nutation control, spin rate control, and precession control simultaneously. A nonlinear design technique, Lyapunov's method, is used to design the Delta-H control mode. A global spin rate controller selected as the baseline controller for MMS, proved to be insufficient due to an ambiguity in the attitude. Lyapunov's design method was used to solve this ambiguity, resulting in a controller that meets the design goals. Simulation results show the advantage of the pointing and rate controller for maneuvers larger than 90 deg and provide insight into the performance of this controller.

Adaptive Neural-Sliding Mode Control of Active Suspension System for Camera Stabilization

Directory of Open Access Journals (Sweden)

Feng Zhao

2015-01-01

Full Text Available The camera always suffers from image instability on the moving vehicle due to the unintentional vibrations caused by road roughness. This paper presents a novel adaptive neural network based on sliding mode control strategy to stabilize the image captured area of the camera. The purpose is to suppress vertical displacement of sprung mass with the application of active suspension system. Since the active suspension system has nonlinear and time varying characteristics, adaptive neural network (ANN is proposed to make the controller robustness against systematic uncertainties, which release the model-based requirement of the sliding model control, and the weighting matrix is adjusted online according to Lyapunov function. The control system consists of two loops. The outer loop is a position controller designed with sliding mode strategy, while the PID controller in the inner loop is to track the desired force. The closed loop stability and asymptotic convergence performance can be guaranteed on the basis of the Lyapunov stability theory. Finally, the simulation results show that the employed controller effectively suppresses the vibration of the camera and enhances the stabilization of the entire camera, where different excitations are considered to validate the system performance.

Global Exponential Stability of Delayed Cohen-Grossberg BAM Neural Networks with Impulses on Time Scales

Directory of Open Access Journals (Sweden)

Yongkun Li

2009-01-01

Full Text Available Based on the theory of calculus on time scales, the homeomorphism theory, Lyapunov functional method, and some analysis techniques, sufficient conditions are obtained for the existence, uniqueness, and global exponential stability of the equilibrium point of Cohen-Grossberg bidirectional associative memory (BAM neural networks with distributed delays and impulses on time scales. This is the first time applying the time-scale calculus theory to unify the discrete-time and continuous-time Cohen-Grossberg BAM neural network with impulses under the same framework.

Coordinated Control of Multiterminal DC Grid Power Injections for Improved Rotor-Angle Stability Based on Lyapunov Theory

DEFF Research Database (Denmark)

Eriksson, Robert

2014-01-01

The stability of an interconnected ac/dc system is affected by disturbances occurring in the system. Disturbances, such as three-phase faults, may jeopardize the rotor-angle stability and, thus, the generators fall out of synchronism. The possibility of fast change of the injected powers...... by the multiterminal dc grid can, by proper control action, enhance this stability. This paper proposes a new time optimal control strategy for the injected power of multiterminal dc grids to enhance the rotor-angle stability. The controller is time optimal, since it reduces the impact of a disturbance as fast...

A survey of quantum Lyapunov control methods.

Science.gov (United States)

Cong, Shuang; Meng, Fangfang

2013-01-01

The condition of a quantum Lyapunov-based control which can be well used in a closed quantum system is that the method can make the system convergent but not just stable. In the convergence study of the quantum Lyapunov control, two situations are classified: nondegenerate cases and degenerate cases. For these two situations, respectively, in this paper the target state is divided into four categories: the eigenstate, the mixed state which commutes with the internal Hamiltonian, the superposition state, and the mixed state which does not commute with the internal Hamiltonian. For these four categories, the quantum Lyapunov control methods for the closed quantum systems are summarized and analyzed. Particularly, the convergence of the control system to the different target states is reviewed, and how to make the convergence conditions be satisfied is summarized and analyzed.

Time-delay effects and simplified control fields in quantum Lyapunov control

International Nuclear Information System (INIS)

Yi, X X; Wu, S L; Wu, Chunfeng; Feng, X L; Oh, C H

2011-01-01

Lyapunov-based quantum control has the advantage that it is free from the measurement-induced decoherence and it includes the instantaneous information of the system in the control. The Lyapunov control is often confronted with time delay in the control fields and difficulty in practical implementations of the control. In this paper, we study the effect of time delay on the Lyapunov control and explore the possibility of replacing the control field with a pulse train or a bang-bang signal. The efficiency of the Lyapunov control is also presented through examining the convergence time of the system. These results suggest that the Lyapunov control is robust against time delay, easy to realize and effective for high-dimensional quantum systems.

Robust stability analysis of Takagi—Sugeno uncertain stochastic fuzzy recurrent neural networks with mixed time-varying delays

International Nuclear Information System (INIS)

Ali, M. Syed

2011-01-01

In this paper, the global stability of Takagi—Sugeno (TS) uncertain stochastic fuzzy recurrent neural networks with discrete and distributed time-varying delays (TSUSFRNNs) is considered. A novel LMI-based stability criterion is obtained by using Lyapunov functional theory to guarantee the asymptotic stability of TSUSFRNNs. The proposed stability conditions are demonstrated through numerical examples. Furthermore, the supplementary requirement that the time derivative of time-varying delays must be smaller than one is removed. Comparison results are demonstrated to show that the proposed method is more able to guarantee the widest stability region than the other methods available in the existing literature. (general)

Stability of Equilibrium Points of Fractional Difference Equations with Stochastic Perturbations

Directory of Open Access Journals (Sweden)

Shaikhet Leonid

2008-01-01

Full Text Available It is supposed that the fractional difference equation , has an equilibrium point and is exposed to additive stochastic perturbations type of that are directly proportional to the deviation of the system state from the equilibrium point . It is shown that known results in the theory of stability of stochastic difference equations that were obtained via V. Kolmanovskii and L. Shaikhet general method of Lyapunov functionals construction can be successfully used for getting of sufficient conditions for stability in probability of equilibrium points of the considered stochastic fractional difference equation. Numerous graphical illustrations of stability regions and trajectories of solutions are plotted.

Structured Lyapunov functions for synchronization of identical affine-in-control agents-Unified approach

Czech Academy of Sciences Publication Activity Database

Hengster-Movric, K.; Šebek, M.; Čelikovský, Sergej

2016-01-01

Roč. 353, č. 14 (2016), s. 3457-3486 ISSN 0016-0032 R&D Projects: GA ČR GA13-20433S Grant - others:GA ČR(CZ) GJ16-25493Y Institutional support: RVO:67985556 Keywords : Multi-agent nonlinear systems * structured Lyapunov functions Subject RIV: BC - Control Systems Theory Impact factor: 3.139, year: 2016 http://library.utia.cas.cz/separaty/2016/TR/celikovsky-0462691.pdf

Nolinear stability analysis of nuclear reactors : expansion methods for stability domains

International Nuclear Information System (INIS)

Yang, Chae Yong

1992-02-01

Two constructive methods for estimating asymptotic stability domains of nonlinear reactor models are developed in this study: an improved Chang and Thorp's method based on expansion of a Lyapunov function and a new method based on expansion of any positive definite function. The methods are established on the concept of stability definitions of Lyapunov itself. The first method provides a sequence of stability regions that eventually approaches the exact stability domain, but requires many expansions in order to obtain the entire stability region because the starting Lyapunov function usually corresponds to a small stability region and because most dynamic systems are stiff. The second method (new method) requires only a positive definite function and thus it is easy to come up with a starting region. From a large starting region, the entire stability region is estimated effectively after sufficient iterations. It is particularly useful for stiff systems. The methods are applied to several nonlinear reactor models known in the literature: one-temperature feedback model, two-temperature feedback model, and xenon dynamics model, and the results are compared. A reactor feedback model for a pressurized water reactor (PWR) considering fuel and moderator temperature effects is developed and the nonlinear stability regions are estimated for the various values of design parameters by using the new method. The steady-state properties of the nonlinear reactor system are analyzed via bifurcation theory. The analysis of nonlinear phenomena is carried out for the various forms of reactivity feedback coefficients that are both temperature- (or power-) independent and dependent. If one of two temperature coefficients is positive, unstable limit cycles or multiplicity of the steady-state solutions appear when the other temperature coefficient exceeds a certain critical value. As an example, even though the fuel temperature coefficient is negative, if the moderator temperature

Lyapunov spectra of density fluctuations in TBR-1

International Nuclear Information System (INIS)

Oiwa, N.N.; Fidler-Ferrara, N.

1993-01-01

The results for the Lyapunov exponents associated with density fluctuations measured by Langmuir probes placed in the scrape-off layer of the Tokamak TBR-1 are reported. By a judicious use of the Sano-Sawada and Eckmann-Ruelle algorithms conclusive values for the positive Lyapunov exponents for most of the analysed signals are used showing evidences of chaotic behavior. (author)

Global exponential stability and lag synchronization for delayed memristive fuzzy Cohen-Grossberg BAM neural networks with impulses.

Science.gov (United States)

Yang, Wengui; Yu, Wenwu; Cao, Jinde; Alsaadi, Fuad E; Hayat, Tasawar

2018-02-01

This paper investigates the stability and lag synchronization for memristor-based fuzzy Cohen-Grossberg bidirectional associative memory (BAM) neural networks with mixed delays (asynchronous time delays and continuously distributed delays) and impulses. By applying the inequality analysis technique, homeomorphism theory and some suitable Lyapunov-Krasovskii functionals, some new sufficient conditions for the uniqueness and global exponential stability of equilibrium point are established. Furthermore, we obtain several sufficient criteria concerning globally exponential lag synchronization for the proposed system based on the framework of Filippov solution, differential inclusion theory and control theory. In addition, some examples with numerical simulations are given to illustrate the feasibility and validity of obtained results. Copyright © 2017 Elsevier Ltd. All rights reserved.

A new delay-independent condition for global robust stability of neural networks with time delays.

Science.gov (United States)

Samli, Ruya

2015-06-01

This paper studies the problem of robust stability of dynamical neural networks with discrete time delays under the assumptions that the network parameters of the neural system are uncertain and norm-bounded, and the activation functions are slope-bounded. By employing the results of Lyapunov stability theory and matrix theory, new sufficient conditions for the existence, uniqueness and global asymptotic stability of the equilibrium point for delayed neural networks are presented. The results reported in this paper can be easily tested by checking some special properties of symmetric matrices associated with the parameter uncertainties of neural networks. We also present a numerical example to show the effectiveness of the proposed theoretical results. Copyright © 2015 Elsevier Ltd. All rights reserved.

Elements of magnetohydrodynamic stability theory

International Nuclear Information System (INIS)

Spies, G.O.

1976-11-01

The nonlinear equations of ideal magnetohydrodynamics are discussed along with the following topics: (1) static equilibrium, (2) strict linear theory, (3) stability of a system with one degree of freedom, (4) spectrum and variational principles in magnetohydrodynamics, (5) elementary proof of the modified energy principle, (6) sufficient stability criteria, (7) local stability, and (8) normal modes

Stability analysis for stochastic BAM nonlinear neural network with delays

Science.gov (United States)

Lv, Z. W.; Shu, H. S.; Wei, G. L.

2008-02-01

In this paper, stochastic bidirectional associative memory neural networks with constant or time-varying delays is considered. Based on a Lyapunov-Krasovskii functional and the stochastic stability analysis theory, we derive several sufficient conditions in order to guarantee the global asymptotically stable in the mean square. Our investigation shows that the stochastic bidirectional associative memory neural networks are globally asymptotically stable in the mean square if there are solutions to some linear matrix inequalities(LMIs). Hence, the global asymptotic stability of the stochastic bidirectional associative memory neural networks can be easily checked by the Matlab LMI toolbox. A numerical example is given to demonstrate the usefulness of the proposed global asymptotic stability criteria.

Stability analysis for stochastic BAM nonlinear neural network with delays

International Nuclear Information System (INIS)

Lv, Z W; Shu, H S; Wei, G L

2008-01-01

In this paper, stochastic bidirectional associative memory neural networks with constant or time-varying delays is considered. Based on a Lyapunov-Krasovskii functional and the stochastic stability analysis theory, we derive several sufficient conditions in order to guarantee the global asymptotically stable in the mean square. Our investigation shows that the stochastic bidirectional associative memory neural networks are globally asymptotically stable in the mean square if there are solutions to some linear matrix inequalities(LMIs). Hence, the global asymptotic stability of the stochastic bidirectional associative memory neural networks can be easily checked by the Matlab LMI toolbox. A numerical example is given to demonstrate the usefulness of the proposed global asymptotic stability criteria

Advanced Tokamak Stability Theory

Science.gov (United States)

Zheng, Linjin

2015-03-01

The intention of this book is to introduce advanced tokamak stability theory. We start with the derivation of the Grad-Shafranov equation and the construction of various toroidal flux coordinates. An analytical tokamak equilibrium theory is presented to demonstrate the Shafranov shift and how the toroidal hoop force can be balanced by the application of a vertical magnetic field in tokamaks. In addition to advanced theories, this book also discusses the intuitive physics pictures for various experimentally observed phenomena.

On the pth moment stability of the binary airfoil induced by bounded noise

International Nuclear Information System (INIS)

Wu, Jiancheng; Li, Xuan; Liu, Xianbin

2017-01-01

Highlights: • We obtain finite pth moment Lyapunov exponent for binary airfoil subject to a bounded noise. • Based on perturbation approach and Green's functions method, second differential eigenvalue equation governing moment Lyapunov exponent is established. • The types of singular points are investigated. • The eigenvalue problem is solved analytically and numerically. • The effects of noise and system parameters on the moment Lyapunov exponent and the stochastic stability of the system are discussed. - Abstract: In the paper, the stochastic stability of the binary airfoil subject to the effect of a bounded noise is studied through the determination of moment Lyapunov exponents. The noise excitation here is often used to model a realistic model of noise in many engineering application. The partial differential eigenvalue problem governing the moment Lyapunov exponent is established. Via the Feller boundary classification, the types of singular points are discussed here, and for the system discussed, the singular points only exist in end points. The fundamental methods used are the perturbation approach and the Green's functions method. With these methods, the second-order expansions of the moment Lyapunov exponents are obtained, which are shown to be in good agreement with those obtained using Monte Carlo simulation. The effects of noise and system parameters on the moment Lyapunov exponent and the stochastic stability of the binary airfoil system are discussed.

Lyapunov spectra and conjugate-pairing rule for confined atomic fluids

DEFF Research Database (Denmark)

Bernadi, Stefano; Todd, B.D.; Hansen, Jesper Schmidt

2010-01-01

In this work we present nonequilibrium molecular dynamics simulation results for the Lyapunov spectra of atomic fluids confined in narrow channels of the order of a few atomic diameters. We show the effect that realistic walls have on the Lyapunov spectra. All the degrees of freedom of the confin...... evolved Lyapunov vectors projected into a reduced dimensional phase space. We finally observe that the phase-space compression due to the thermostat remains confined into the wall region and does not significantly affect the purely Newtonian fluid region....

Global robust stability of neural networks with multiple discrete delays and distributed delays

International Nuclear Information System (INIS)

Gao Ming; Cui Baotong

2009-01-01

The problem of global robust stability is investigated for a class of uncertain neural networks with both multiple discrete time-varying delays and distributed time-varying delays. The uncertainties are assumed to be of norm-bounded form and the activation functions are supposed to be bounded and globally Lipschitz continuous. Based on the Lyapunov stability theory and linear matrix inequality technique, some robust stability conditions guaranteeing the global robust convergence of the equilibrium point are derived. The proposed LMI-based criteria are computationally efficient as they can be easily checked by using recently developed algorithms in solving LMIs. Two examples are given to show the effectiveness of the proposed results.

Continuation of probability density functions using a generalized Lyapunov approach

Energy Technology Data Exchange (ETDEWEB)

Baars, S., E-mail: s.baars@rug.nl [Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, P.O. Box 407, 9700 AK Groningen (Netherlands); Viebahn, J.P., E-mail: viebahn@cwi.nl [Centrum Wiskunde & Informatica (CWI), P.O. Box 94079, 1090 GB, Amsterdam (Netherlands); Mulder, T.E., E-mail: t.e.mulder@uu.nl [Institute for Marine and Atmospheric research Utrecht, Department of Physics and Astronomy, Utrecht University, Princetonplein 5, 3584 CC Utrecht (Netherlands); Kuehn, C., E-mail: ckuehn@ma.tum.de [Technical University of Munich, Faculty of Mathematics, Boltzmannstr. 3, 85748 Garching bei München (Germany); Wubs, F.W., E-mail: f.w.wubs@rug.nl [Johann Bernoulli Institute for Mathematics and Computer Science, University of Groningen, P.O. Box 407, 9700 AK Groningen (Netherlands); Dijkstra, H.A., E-mail: h.a.dijkstra@uu.nl [Institute for Marine and Atmospheric research Utrecht, Department of Physics and Astronomy, Utrecht University, Princetonplein 5, 3584 CC Utrecht (Netherlands); School of Chemical and Biomolecular Engineering, Cornell University, Ithaca, NY (United States)

2017-05-01

Techniques from numerical bifurcation theory are very useful to study transitions between steady fluid flow patterns and the instabilities involved. Here, we provide computational methodology to use parameter continuation in determining probability density functions of systems of stochastic partial differential equations near fixed points, under a small noise approximation. Key innovation is the efficient solution of a generalized Lyapunov equation using an iterative method involving low-rank approximations. We apply and illustrate the capabilities of the method using a problem in physical oceanography, i.e. the occurrence of multiple steady states of the Atlantic Ocean circulation.

OBSERVING LYAPUNOV EXPONENTS OF INFINITE-DIMENSIONAL DYNAMICAL SYSTEMS.

Science.gov (United States)

Ott, William; Rivas, Mauricio A; West, James

2015-12-01

Can Lyapunov exponents of infinite-dimensional dynamical systems be observed by projecting the dynamics into ℝ N using a 'typical' nonlinear projection map? We answer this question affirmatively by developing embedding theorems for compact invariant sets associated with C 1 maps on Hilbert spaces. Examples of such discrete-time dynamical systems include time- T maps and Poincaré return maps generated by the solution semigroups of evolution partial differential equations. We make every effort to place hypotheses on the projected dynamics rather than on the underlying infinite-dimensional dynamical system. In so doing, we adopt an empirical approach and formulate checkable conditions under which a Lyapunov exponent computed from experimental data will be a Lyapunov exponent of the infinite-dimensional dynamical system under study (provided the nonlinear projection map producing the data is typical in the sense of prevalence).

Global exponential stability of periodic solution for shunting inhibitory CNNs with delays [rapid communication

Science.gov (United States)

Li, Yongkun; Liu, Chunchao; Zhu, Lifei

2005-03-01

By using the continuation theorem of coincidence degree theory and constructing suitable Lyapunov functions, we study the existence and stability of periodic solution for shunting inhibitory cellular neural networks (SICNNs) with delays x˙ij(t)=-aij(t)xij(t)-∑Bkl∈Nr(i,j)Bijkl(t)fij(xkl(t))xij(t)-∑Ckl∈Nr(i,j)Cijkl(t)gij(xkl(t-τkl))xij(t)+Lij(t).

Adaptive Fuzzy-Lyapunov Controller Using Biologically Inspired Swarm Intelligence

Directory of Open Access Journals (Sweden)

Alejandro Carrasco Elizalde

2008-01-01

Full Text Available The collective behaviour of swarms produces smarter actions than those achieved by a single individual. Colonies of ants, flocks of birds and fish schools are examples of swarms interacting with their environment to achieve a common goal. This cooperative biological intelligence is the inspiration for an adaptive fuzzy controller developed in this paper. Swarm intelligence is used to adjust the parameters of the membership functions used in the adaptive fuzzy controller. The rules of the controller are designed using a computing-with-words approach called Fuzzy-Lyapunov synthesis to improve the stability and robustness of an adaptive fuzzy controller. Computing-with-words provides a powerful tool to manipulate numbers and symbols, like words in a natural language.

A robust nonlinear stabilizer as a controller for improving transient stability in micro-grids.

Science.gov (United States)

Azimi, Seyed Mohammad; Afsharnia, Saeed

2017-01-01

This paper proposes a parametric-Lyapunov approach to the design of a stabilizer aimed at improving the transient stability of micro-grids (MGs). This strategy is applied to electronically-interfaced distributed resources (EI-DRs) operating with a unified control configuration applicable to all operational modes (i.e. grid-connected mode, islanded mode, and mode transitions). The proposed approach employs a simple structure compared with other nonlinear controllers, allowing ready implementation of the stabilizer. A new parametric-Lyapunov function is proposed rendering the proposed stabilizer more effective in damping system transition transients. The robustness of the proposed stabilizer is also verified based on both time-domain simulations and mathematical proofs, and an ultimate bound has been derived for the frequency transition transients. The proposed stabilizer operates by deploying solely local information and there are no needs for communication links. The deteriorating effects of the primary resource delays on the transient stability are also treated analytically. Finally, the effectiveness of the proposed stabilizer is evaluated through time-domain simulations and compared with the recently-developed stabilizers performed on a multi-resource MG. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

A Lyapunov Function Based Remedial Action Screening Tool Using Real-Time Data

Energy Technology Data Exchange (ETDEWEB)

Mitra, Joydeep [Michigan State Univ., East Lansing, MI (United States); Ben-Idris, Mohammed [Univ. of Nevada, Reno, NV (United States); Faruque, Omar [Florida State Univ., Tallahassee, FL (United States); Backhaus, Scott [Los Alamos National Lab. (LANL), Los Alamos, NM (United States); Deb, Sidart [LCG Consulting, Los Altos, CA (United States)

2016-03-30

This report summarizes the outcome of a research project that comprised the development of a Lyapunov function based remedial action screening tool using real-time data (L-RAS). The L-RAS is an advanced computational tool that is intended to assist system operators in making real-time redispatch decisions to preserve power grid stability. The tool relies on screening contingencies using a homotopy method based on Lyapunov functions to avoid, to the extent possible, the use of time domain simulations. This enables transient stability evaluation at real-time speed without the use of massively parallel computational resources. The project combined the following components. 1. Development of a methodology for contingency screening using a homotopy method based on Lyapunov functions and real-time data. 2. Development of a methodology for recommending remedial actions based on the screening results. 3. Development of a visualization and operator interaction interface. 4. Testing of screening tool, validation of control actions, and demonstration of project outcomes on a representative real system simulated on a Real-Time Digital Simulator (RTDS) cluster. The project was led by Michigan State University (MSU), where the theoretical models including homotopy-based screening, trajectory correction using real-time data, and remedial action were developed and implemented in the form of research-grade software. Los Alamos National Laboratory (LANL) contributed to the development of energy margin sensitivity dynamics, which constituted a part of the remedial action portfolio. Florida State University (FSU) and Southern California Edison (SCE) developed a model of the SCE system that was implemented on FSU's RTDS cluster to simulate real-time data that was streamed over the internet to MSU where the L-RAS tool was executed and remedial actions were communicated back to FSU to execute stabilizing controls on the simulated system. LCG Consulting developed the visualization

Heat conduction in one-dimensional chains and nonequilibrium Lyapunov spectrum

International Nuclear Information System (INIS)

Posch, H.A.; Hoover, W.G.

1998-01-01

We define and study the heat conductivity κ and the Lyapunov spectrum for a modified 'ding-a-ling' chain undergoing steady heat flow. Free and bound particles alternate along a chain. In the present work, we use a linear gravitational potential to bind all the even-numbered particles to their lattice sites. The chain is bounded by two stochastic heat reservoirs, one hot and one cold. The Fourier conductivity of the chain decreases smoothly to a finite large-system limit. Special treatment of satellite collisions with the stochastic boundaries is required to obtain Lyapunov spectra. The summed spectra are negative, and correspond to a relatively small contraction in phase space, with the formation of a multifractal strange attractor. The largest of the Lyapunov exponents for the ding-a-ling chain appears to converge to a limiting value with increasing chain length, so that the large-system Lyapunov spectrum has a finite limit. copyright 1998 The American Physical Society

Analysis of Human Standing Balance by Largest Lyapunov Exponent

Directory of Open Access Journals (Sweden)

Kun Liu

2015-01-01

Full Text Available The purpose of this research is to analyse the relationship between nonlinear dynamic character and individuals’ standing balance by the largest Lyapunov exponent, which is regarded as a metric for assessing standing balance. According to previous study, the largest Lyapunov exponent from centre of pressure time series could not well quantify the human balance ability. In this research, two improvements were made. Firstly, an external stimulus was applied to feet in the form of continuous horizontal sinusoidal motion by a moving platform. Secondly, a multiaccelerometer subsystem was adopted. Twenty healthy volunteers participated in this experiment. A new metric, coordinated largest Lyapunov exponent was proposed, which reflected the relationship of body segments by integrating multidimensional largest Lyapunov exponent values. By using this metric in actual standing performance under sinusoidal stimulus, an obvious relationship between the new metric and the actual balance ability was found in the majority of the subjects. These results show that the sinusoidal stimulus can make human balance characteristics more obvious, which is beneficial to assess balance, and balance is determined by the ability of coordinating all body segments.

Global exponential stability of neutral high-order stochastic Hopfield neural networks with Markovian jump parameters and mixed time delays.

Science.gov (United States)

Huang, Haiying; Du, Qiaosheng; Kang, Xibing

2013-11-01

In this paper, a class of neutral high-order stochastic Hopfield neural networks with Markovian jump parameters and mixed time delays is investigated. The jumping parameters are modeled as a continuous-time finite-state Markov chain. At first, the existence of equilibrium point for the addressed neural networks is studied. By utilizing the Lyapunov stability theory, stochastic analysis theory and linear matrix inequality (LMI) technique, new delay-dependent stability criteria are presented in terms of linear matrix inequalities to guarantee the neural networks to be globally exponentially stable in the mean square. Numerical simulations are carried out to illustrate the main results. © 2013 ISA. Published by ISA. All rights reserved.

Adaptive control of nonlinear in parameters chaotic system via Lyapunov exponents placement

Energy Technology Data Exchange (ETDEWEB)

Ayati, Moosa [Department of Electrical Engineering, K.N. Toosi University of Technology, Sayyed Khandan Bridge, Shariati Street, Tehran (Iran, Islamic Republic of)], E-mail: Ayati@dena.kntu.ac.ir; Khaki-Sedigh, Ali [Department of Electrical Engineering, K.N. Toosi University of Technology, Sayyed Khandan Bridge, Shariati Street, Tehran (Iran, Islamic Republic of)], E-mail: sedigh@kntu.ac.ir

2009-08-30

This paper proposes a new method for the adaptive control of nonlinear in parameters (NLP) chaotic systems. A method based on Lagrangian of a cost function is used to identify the parameters of the system. Estimation results are used to calculate the Lyapunov exponents adaptively. Finally, the Lyapunov exponents placement method is used to assign the desired Lyapunov exponents of the closed loop system.

Adaptive control of nonlinear in parameters chaotic system via Lyapunov exponents placement

International Nuclear Information System (INIS)

Ayati, Moosa; Khaki-Sedigh, Ali

2009-01-01

This paper proposes a new method for the adaptive control of nonlinear in parameters (NLP) chaotic systems. A method based on Lagrangian of a cost function is used to identify the parameters of the system. Estimation results are used to calculate the Lyapunov exponents adaptively. Finally, the Lyapunov exponents placement method is used to assign the desired Lyapunov exponents of the closed loop system.

Fuzzy Stabilization for Nonlinear Discrete Ship Steering Stochastic Systems Subject to State Variance and Passivity Constraints

Directory of Open Access Journals (Sweden)

Wen-Jer Chang

2014-01-01

Full Text Available For nonlinear discrete-time stochastic systems, a fuzzy controller design methodology is developed in this paper subject to state variance constraint and passivity constraint. According to fuzzy model based control technique, the nonlinear discrete-time stochastic systems considered in this paper are represented by the discrete-time Takagi-Sugeno fuzzy models with multiplicative noise. Employing Lyapunov stability theory, upper bound covariance control theory, and passivity theory, some sufficient conditions are derived to find parallel distributed compensation based fuzzy controllers. In order to solve these sufficient conditions, an iterative linear matrix inequality algorithm is applied based on the linear matrix inequality technique. Finally, the fuzzy stabilization problem for nonlinear discrete ship steering stochastic systems is investigated in the numerical example to illustrate the feasibility and validity of proposed fuzzy controller design method.

Globally exponential stability of neural network with constant and variable delays

International Nuclear Information System (INIS)

Zhao Weirui; Zhang Huanshui

2006-01-01

This Letter presents new sufficient conditions of globally exponential stability of neural networks with delays. We show that these results generalize recently published globally exponential stability results. In particular, several different globally exponential stability conditions in the literatures which were proved using different Lyapunov functionals are generalized and unified by using the same Lyapunov functional and the technique of inequality of integral. A comparison between our results and the previous results admits that our results establish a new set of stability criteria for delayed neural networks. Those conditions are less restrictive than those given in the earlier references

The stability analysis of non-topological solitons in gauge theory and in electrodynamics

International Nuclear Information System (INIS)

Chakrabarti, S.

1982-08-01

The Lyapunov stability analysis of the nontopological soliton solution in the many-charge Qsub(i) Synge Model in non-Abelian SU(2)xU(1) symmetry with the presence of gauge fields is considered. It is shown that in the presence of the subsidiary condition of fixation of charges μsub(i)νsub(i)delta Qsub(i)=0 the necessary condition for stability of the soliton solution (periodic in time with parameters νsub(i)) is defined by the inequality: μsub(i,k) (deltaQsub(i) 0 /deltaνsub(k)) - νsub(i)νsub(k)<0. This condition holds for any Lagrangian density with second-order time derivatives in the presence of gauge fields. This result is extended to the stability analysis of a scalar soliton with electromagnetic field in U(1) symmetry, and it is shown that, in this case, the necessary condition reduces to deltaQsub(i)/deltaν<0. (author)

Lyapunov Exponent and Out-of-Time-Ordered Correlator's Growth Rate in a Chaotic System.

Science.gov (United States)

Rozenbaum, Efim B; Ganeshan, Sriram; Galitski, Victor

2017-02-24

It was proposed recently that the out-of-time-ordered four-point correlator (OTOC) may serve as a useful characteristic of quantum-chaotic behavior, because, in the semiclassical limit ℏ→0, its rate of exponential growth resembles the classical Lyapunov exponent. Here, we calculate the four-point correlator C(t) for the classical and quantum kicked rotor-a textbook driven chaotic system-and compare its growth rate at initial times with the standard definition of the classical Lyapunov exponent. Using both quantum and classical arguments, we show that the OTOC's growth rate and the Lyapunov exponent are, in general, distinct quantities, corresponding to the logarithm of the phase-space averaged divergence rate of classical trajectories and to the phase-space average of the logarithm, respectively. The difference appears to be more pronounced in the regime of low kicking strength K, where no classical chaos exists globally. In this case, the Lyapunov exponent quickly decreases as K→0, while the OTOC's growth rate may decrease much slower, showing a higher sensitivity to small chaotic islands in the phase space. We also show that the quantum correlator as a function of time exhibits a clear singularity at the Ehrenfest time t_{E}: transitioning from a time-independent value of t^{-1}lnC(t) at ttime at t>t_{E}. We note that the underlying physics here is the same as in the theory of weak (dynamical) localization [Aleiner and Larkin, Phys. Rev. B 54, 14423 (1996)PRBMDO0163-182910.1103/PhysRevB.54.14423; Tian, Kamenev, and Larkin, Phys. Rev. Lett. 93, 124101 (2004)PRLTAO0031-900710.1103/PhysRevLett.93.124101] and is due to a delay in the onset of quantum interference effects, which occur sharply at a time of the order of the Ehrenfest time.

Indefinite damping in mechanical systems and gyroscopic stabilization

DEFF Research Database (Denmark)

Kliem, Wolfhard; Pommer, Christian

2009-01-01

This paper deals with gyroscopic stabilization of the unstable system Mx + D(x) over dot + K-x = 0, with positive definite mass and stiffness matrices M and K, respectively, and an indefinite damping matrix D. The main question if for which skew-symmetric matrices G the system Mx (D+ G)(x) over dot...... + K-x = 0 can become stable? After investigating special cases we find an appropriat solution of the Lyapunov matrix equation for the general case. Examples show the deviation of the stability limit found by the Lyapunov method from the exact value....

On Stabilization of Nonautonomous Nonlinear Systems

International Nuclear Information System (INIS)

Bogdanov, A. Yu.

2008-01-01

The procedures to obtain the sufficient conditions of asymptotic stability for nonlinear nonstationary continuous-time systems are discussed. We consider different types of the following general controlled system: x = X(t,x,u) = F(t,x)+B(t,x)u, x(t 0 ) = x 0 . (*) The basis of investigation is limiting equations, limiting Lyapunov functions, etc. The improved concept of observability of the pair of functional matrices is presented. By these results the problem of synthesis of asymptotically stable control nonlinear nonautonomous systems (with linear parts) involving the quadratic time-dependent Lyapunov functions is solved as well as stabilizing a given unstable system with nonlinear control law.

Stabilization analysis of Euler-Bernoulli beam equation with locally distributed disturbance

Directory of Open Access Journals (Sweden)

Pengcheng HAN

2017-12-01

Full Text Available In order to enrich the system stability theory of the control theories, taking Euler-Bernoulli beam equation as the research subject, the stability of Euler-Bernoulli beam equation with locally distributed disturbance is studied. A feedback controller based on output is designed to reduce the effects of the disturbances. The well-posedness of the nonlinear closed-loop system is investigated by the theory of maximal monotone operator, namely the existence and uniqueness of solutions for the closed-loop system. An appropriate state space is established, an appropriate inner product is defined, and a non-linear operator satisfying this state space is defined. Then, the system is transformed into the form of evolution equation. Based on this, the existence and uniqueness of solutions for the closed-loop system are proved. The asymptotic stability of the system is studied by constructing an appropriate Lyapunov function, which proves the asymptotic stability of the closed-loop system. The result shows that designing proper anti-interference controller is the foundation of investigating the system stability, and the research of the stability of Euler-bernoulli beam equation with locally distributed disturbance can prove the asymptotic stability of the system. This method can be extended to study the other equations such as wave equation, Timoshenko beam equation, Schrodinger equation, etc.

Anisotropies in magnetic field evolution and local Lyapunov exponents

International Nuclear Information System (INIS)

Tang, X.Z.; Boozer, A.H.

2000-01-01

The natural occurrence of small scale structures and the extreme anisotropy in the evolution of a magnetic field embedded in a conducting flow is interpreted in terms of the properties of the local Lyapunov exponents along the various local characteristic (un)stable directions for the Lagrangian flow trajectories. The local Lyapunov exponents and the characteristic directions are functions of Lagrangian coordinates and time, which are completely determined once the flow field is specified. The characteristic directions that are associated with the spatial anisotropy of the problem, are prescribed in both Lagrangian and Eulerian frames. Coordinate transformation techniques are employed to relate the spatial distributions of the magnetic field, the induced current density, and the Lorentz force, which are usually followed in Eulerian frame, to those of the local Lyapunov exponents, which are naturally defined in Lagrangian coordinates

Exploring the Lyapunov instability properties of high-dimensional atmospheric and climate models

Science.gov (United States)

De Cruz, Lesley; Schubert, Sebastian; Demaeyer, Jonathan; Lucarini, Valerio; Vannitsem, Stéphane

2018-05-01

The stability properties of intermediate-order climate models are investigated by computing their Lyapunov exponents (LEs). The two models considered are PUMA (Portable University Model of the Atmosphere), a primitive-equation simple general circulation model, and MAOOAM (Modular class="text">Arbitrary-Order Ocean-Atmosphere Model), a quasi-geostrophic coupled ocean-class="text">atmosphere model on a β-plane. We wish to investigate the effect of the different levels of filtering on the instabilities and dynamics of the atmospheric flows. Moreover, we assess the impact of the oceanic coupling, the dissipation scheme, and the resolution on the spectra of LEs. The PUMA Lyapunov spectrum is computed for two different values of the meridional temperature gradient defining the Newtonian forcing to the temperature field. The increase in the gradient gives rise to a higher baroclinicity and stronger instabilities, corresponding to a larger dimension of the unstable manifold and a larger first LE. The Kaplan-Yorke dimension of the attractor increases as well. The convergence rate of the rate function for the large deviation law of the finite-time Lyapunov exponents (FTLEs) is fast for all exponents, which can be interpreted as resulting from the absence of a clear-cut atmospheric timescale separation in such a model. The MAOOAM spectra show that the dominant atmospheric instability is correctly represented even at low resolutions. However, the dynamics of the central manifold, which is mostly associated with the ocean dynamics, is not fully resolved because of its associated long timescales, even at intermediate orders. As expected, increasing the mechanical atmosphere-ocean coupling coefficient or introducing a turbulent diffusion parametrisation reduces the Kaplan-Yorke dimension and Kolmogorov-Sinai entropy. In all considered configurations, we are not yet in the regime in which one can robustly define large deviation laws describing the statistics of the FTLEs. This

Analytic Quasi-Perodic Cocycles with Singularities and the Lyapunov Exponent of Extended Harper's Model

Science.gov (United States)

Jitomirskaya, S.; Marx, C. A.

2012-11-01

We show how to extend (and with what limitations) Avila's global theory of analytic SL(2,C) cocycles to families of cocycles with singularities. This allows us to develop a strategy to determine the Lyapunov exponent for the extended Harper's model, for all values of parameters and all irrational frequencies. In particular, this includes the self-dual regime for which even heuristic results did not previously exist in physics literature. The extension of Avila's global theory is also shown to imply continuous behavior of the LE on the space of analytic {M_2({C})}-cocycles. This includes rational approximation of the frequency, which so far has not been available.

Fuzzy Logic Controller Stability Analysis Using a Satisfiability Modulo Theories Approach

Science.gov (United States)

Arnett, Timothy; Cook, Brandon; Clark, Matthew A.; Rattan, Kuldip

2017-01-01

While many widely accepted methods and techniques exist for validation and verification of traditional controllers, at this time no solutions have been accepted for Fuzzy Logic Controllers (FLCs). Due to the highly nonlinear nature of such systems, and the fact that developing a valid FLC does not require a mathematical model of the system, it is quite difficult to use conventional techniques to prove controller stability. Since safety-critical systems must be tested and verified to work as expected for all possible circumstances, the fact that FLC controllers cannot be tested to achieve such requirements poses limitations on the applications for such technology. Therefore, alternative methods for verification and validation of FLCs needs to be explored. In this study, a novel approach using formal verification methods to ensure the stability of a FLC is proposed. Main research challenges include specification of requirements for a complex system, conversion of a traditional FLC to a piecewise polynomial representation, and using a formal verification tool in a nonlinear solution space. Using the proposed architecture, the Fuzzy Logic Controller was found to always generate negative feedback, but inconclusive for Lyapunov stability.

Finite-Time Stability and Stabilization of Nonlinear Quadratic Systems with Jumps

Directory of Open Access Journals (Sweden)

Minsong Zhang

2014-01-01

Full Text Available This paper investigates the problems of finite-time stability and finite-time stabilization for nonlinear quadratic systems with jumps. The jump time sequences here are assumed to satisfy some given constraints. Based on Lyapunov function and a particular presentation of the quadratic terms, sufficient conditions for finite-time stability and finite-time stabilization are developed to a set containing bilinear matrix inequalities (BLIMs and linear matrix inequalities (LMIs. Numerical examples are given to illustrate the effectiveness of the proposed methodology.

Local Lyapunov exponents for dissipative continuous systems

International Nuclear Information System (INIS)

Grond, Florian; Diebner, Hans H.

2005-01-01

We analyze a recently proposed algorithm for computing Lyapunov exponents focusing on its capability to calculate reliable local values for chaotic attractors. The averaging process of local contributions to the global measure becomes interpretable, i.e. they are related to the local topological structure in phase space. We compare the algorithm with the commonly used Wolf algorithm by means of analyzing correlations between coordinates of the chaotic attractor and local values of the Lyapunov exponents. The correlations for the new algorithm turn out to be significantly stronger than those for the Wolf algorithm. Since the usage of scalar measures to capture complex structures can be questioned we discuss these entities along with a more phenomenological description of scatter plots

Handbook of functional equations stability theory

CERN Document Server

2014-01-01

This  handbook consists of seventeen chapters written by eminent scientists from the international mathematical community, who present important research works in the field of mathematical analysis and related subjects, particularly in the Ulam stability theory of functional equations. The book provides an insight into a large domain of research with emphasis to the discussion of several theories, methods and problems in approximation theory, analytic inequalities, functional analysis, computational algebra and applications.                           The notion of stability of functional equations has its origins with S. M. Ulam, who posed the fundamental problem for approximate homomorphisms in 1940 and with D. H. Hyers, Th. M. Rassias, who provided the first significant solutions for additive and linear mappings in 1941 and 1978, respectively. During the last decade the notion of stability of functional equations has evolved into a very active domain of mathematical research with...

Stability under persistent perturbation by white noise

International Nuclear Information System (INIS)

Kalyakin, L

2014-01-01

Deterministic dynamical system which has an asymptotical stable equilibrium is considered under persistent perturbation by white noise. It is well known that if the perturbation does not vanish in the equilibrium position then there is not Lyapunov's stability. The trajectories of the perturbed system diverge from the equilibrium to arbitrarily large distances with probability 1 in finite time. New concept of stability on a large time interval is discussed. The length of interval agrees the reciprocal quantity of the perturbation parameter. The measure of stability is the expectation of the square distance from the trajectory till the equilibrium position. The method of parabolic equation is applied to both estimate the expectation and prove such stability. The main breakthrough is the barrier function derived for the parabolic equation. The barrier is constructed by using the Lyapunov function of the unperturbed system

Dynamical behaviors determined by the Lyapunov function in competitive Lotka-Volterra systems

Science.gov (United States)

Tang, Ying; Yuan, Ruoshi; Ma, Yian

2013-01-01

Dynamical behaviors of the competitive Lotka-Volterra system even for 3 species are not fully understood. In this paper, we study this problem from the perspective of the Lyapunov function. We construct explicitly the Lyapunov function using three examples of the competitive Lotka-Volterra system for the whole state space: (1) the general 2-species case, (2) a 3-species model, and (3) the model of May-Leonard. The basins of attraction for these examples are demonstrated, including cases with bistability and cyclical behavior. The first two examples are the generalized gradient system, where the energy dissipation may not follow the gradient of the Lyapunov function. In addition, under a new type of stochastic interpretation, the Lyapunov function also leads to the Boltzmann-Gibbs distribution on the final steady state when multiplicative noise is added.

Stability and Control of Large-Scale Dynamical Systems A Vector Dissipative Systems Approach

CERN Document Server

Haddad, Wassim M

2011-01-01

Modern complex large-scale dynamical systems exist in virtually every aspect of science and engineering, and are associated with a wide variety of physical, technological, environmental, and social phenomena, including aerospace, power, communications, and network systems, to name just a few. This book develops a general stability analysis and control design framework for nonlinear large-scale interconnected dynamical systems, and presents the most complete treatment on vector Lyapunov function methods, vector dissipativity theory, and decentralized control architectures. Large-scale dynami

Dynamic aeroelastic stability of vertical-axis wind turbines under constant wind velocity

Science.gov (United States)

Nitzsche, Fred

1994-05-01

The flutter problem associated with the blades of a class of vertical-axis wind turbines called Darrieus is studied in detail. The spinning blade is supposed to be initially curved in a particular shape characterized by a state of pure tension at the blade cross section. From this equilibrium position a three-dimensional linear perturbation pattern is superimposed to determine the dynamic aeroelastic stability of the blade in the presence of free wind speed by means of the Floquet-Lyapunov theory for periodic systems.

Global exponential stability of periodic solution for shunting inhibitory CNNs with delays

International Nuclear Information System (INIS)

Li Yongkun; Liu Chunchao; Zhu Lifei

2005-01-01

By using the continuation theorem of coincidence degree theory and constructing suitable Lyapunov functions, we study the existence and stability of periodic solution for shunting inhibitory cellular neural networks (SICNNs) with delays x-bar ij (t)=-a ij (t)x ij (t)--bar B kl -bar Nr(i,j)B ij kl (t)f ij (x kl (t))x ij (t)--bar C kl -bar Nr(i,j)C ij kl (t)g ij (x kl (t-τ kl ))x ij (t)+L ij (t)

Some stability and boundedness criteria for a class of Volterra integro-differential systems

Directory of Open Access Journals (Sweden)

Jito Vanualailai

2002-01-01

Full Text Available Using Lyapunov and Lyapunov-like functionals, we study the stability and boundedness of the solutions of a system of Volterra integrodifferential equations. Our results, also extending some of the more well-known criteria, give new sufficient conditions for stability of the zero solution of the nonperturbed system, and prove that the same conditions for the perturbed system yield boundedness when the perturbation is $L^2$.

Inertia theorems for operator Lyapunov inequalities

NARCIS (Netherlands)

Sasane, AJ; Curtain, RF

2001-01-01

We study operator Lyapunov inequalities and equations for which the infinitesimal generator is not necessarily stable, but it satisfies the spectrum decomposition assumption and it has at most finitely many unstable eigenvalues. Moreover, the input or output operators are not necessarily bounded,

A Study of Strong Stability of Distributed Systems. Ph.D. Thesis

Science.gov (United States)

Cataltepe, Tayfun

1989-01-01

The strong stability of distributed systems is studied and the problem of characterizing strongly stable semigroups of operators associated with distributed systems is addressed. Main emphasis is on contractive systems. Three different approaches to characterization of strongly stable contractive semigroups are developed. The first one is an operator theoretical approach. Using the theory of dilations, it is shown that every strongly stable contractive semigroup is related to the left shift semigroup on an L(exp 2) space. Then, a decomposition for the state space which identifies strongly stable and unstable states is introduced. Based on this decomposition, conditions for a contractive semigroup to be strongly stable are obtained. Finally, extensions of Lyapunov's equation for distributed parameter systems are investigated. Sufficient conditions for weak and strong stabilities of uniformly bounded semigroups are obtained by relaxing the equivalent norm condition on the right hand side of the Lyanupov equation. These characterizations are then applied to the problem of feedback stabilization. First, it is shown via the state space decomposition that under certain conditions a contractive system (A,B) can be strongly stabilized by the feedback -B(*). Then, application of the extensions of the Lyapunov equation results in sufficient conditions for weak, strong, and exponential stabilizations of contractive systems by the feedback -B(*). Finally, it is shown that for a contractive system, the first derivative of x with respect to time = Ax + Bu (where B is any linear bounded operator), there is a related linear quadratic regulator problem and a corresponding steady state Riccati equation which always has a bounded nonnegative solution.

A statistical approach to estimate the LYAPUNOV spectrum in disc brake squeal

Science.gov (United States)

Oberst, S.; Lai, J. C. S.

2015-01-01

The estimation of squeal propensity of a brake system from the prediction of unstable vibration modes using the linear complex eigenvalue analysis (CEA) in the frequency domain has its fair share of successes and failures. While the CEA is almost standard practice for the automotive industry, time domain methods and the estimation of LYAPUNOV spectra have not received much attention in brake squeal analyses. One reason is the challenge in estimating the true LYAPUNOV exponents and their discrimination against spurious ones in experimental data. A novel method based on the application of the ECKMANN-RUELLE matrices is proposed here to estimate LYAPUNOV exponents by using noise in a statistical procedure. It is validated with respect to parameter variations and dimension estimates. By counting the number of non-overlapping confidence intervals for LYAPUNOV exponent distributions obtained by moving a window of increasing size over bootstrapped same-length estimates of an observation function, a dispersion measure's width is calculated and fed into a BAYESIAN beta-binomial model. Results obtained using this method for benchmark models of white and pink noise as well as the classical HENON map indicate that true LYAPUNOV exponents can be isolated from spurious ones with high confidence. The method is then applied to accelerometer and microphone data obtained from brake squeal tests. Estimated LYAPUNOV exponents indicate that the pad's out-of-plane vibration behaves quasi-periodically on the brink to chaos while the microphone's squeal signal remains periodic.

On chaos in quantum mechanics: The two meanings of sensitive dependence

International Nuclear Information System (INIS)

Ingraham, R.L.; Luna Acosta, G.A.

1993-08-01

Sensitive dependence on initial conditions, the most important signature of chaos, can mean failure of Lyapunov stability, the primary meaning adopted in dynamical systems theory, or the presence of positive Lyapunov exponents, the meaning favored in physics. These are not equivalent in general. We show that there is sensitive dependence in quantum mechanics in the sense of violation of Lyapunov stability for maps of the state vector like involving unbounded operators A. This is true even for bounded quantum systems, where the corresponding Lyapunov exponents are all zero. Experiments to reveal this sensitive dependence, a definite though unfamiliar prediction of quantum mechanics, should be devised. It may also invalidate the usual assumption of linear response theory in quantum statistical mechanics in some cases. (author) 13 refs

Stability and Control of Human Trunk Movement During Walking.

Science.gov (United States)

Wu, Q.; Sepehri, N.; Thornton-Trump, A. B.; Alexander, M.

1998-01-01

A mathematical model has been developed to study the control mechanisms of human trunk movement during walking. The trunk is modeled as a base-excited inverted pendulum with two-degrees of rotational freedom. The base point, corresponding to the bony landmark of the sacrum, can move in three-dimensional space in a general way. Since the stability of upright posture is essential for human walking, a controller has been designed such that the stability of the pendulum about the upright position is guaranteed. The control laws are developed based on Lyapunov's stability theory and include feedforward and linear feedback components. It is found that the feedforward component plays a critical role in keeping postural stability, and the linear feedback component, (resulting from viscoelastic function of the musculoskeletal system) can effectively duplicate the pattern of trunk movement. The mathematical model is validated by comparing the simulation results with those based on gait measurements performed in the Biomechanics Laboratory at the University of Manitoba.

LYAPUNOV-Based Sensor Failure Detection and Recovery for the Reverse Water Gas Shift Process

Science.gov (United States)

Haralambous, Michael G.

2002-01-01

Livingstone, a model-based AI software system, is planned for use in the autonomous fault diagnosis, reconfiguration, and control of the oxygen-producing reverse water gas shift (RWGS) process test-bed located in the Applied Chemistry Laboratory at KSC. In this report the RWGS process is first briefly described and an overview of Livingstone is given. Next, a Lyapunov-based approach for detecting and recovering from sensor failures, differing significantly from that used by Livingstone, is presented. In this new method, models used are in t e m of the defining differential equations of system components, thus differing from the qualitative, static models used by Livingstone. An easily computed scalar inequality constraint, expressed in terms of sensed system variables, is used to determine the existence of sensor failures. In the event of sensor failure, an observer/estimator is used for determining which sensors have failed. The theory underlying the new approach is developed. Finally, a recommendation is made to use the Lyapunov-based approach to complement the capability of Livingstone and to use this combination in the RWGS process.

An alternative bifurcation analysis of the Rose-Hindmarsh model

International Nuclear Information System (INIS)

Nikolov, Svetoslav

2005-01-01

The paper presents an alternative study of the bifurcation behavior of the Rose-Hindmarsh model using Lyapunov-Andronov's theory. This is done on the basis of the obtained analytical formula expressing the first Lyapunov's value (this is not Lyapunov exponent) at the boundary of stability. From the obtained results the following new conclusions are made: Transition to chaos and the occurrence of chaotic oscillations in the Rose-Hindmarsh system take place under hard stability loss

Lyapunov-based decentralized control of a rougher flotation phenomenological simulator

International Nuclear Information System (INIS)

Benaskeur, A.R.; Desbiens, A.

1999-01-01

In this paper a new approach to decentralized control of linear two-by-two plants is presented. The novelty lies in the use of a modified control function of Lyapunov and the introduction of an integral action in each manipulated variable, to ensure zero tracking errors. An appropriate choice of the regulated errors, allows the elimination of the cross terms in the obtained backstepping-based multivariable controller. It will be proven that if the H ∞ -norm of the plant interaction quotient is less than one, the centralized controller can be split up into two independent scalar output feedback regulators. Under these conditions, the global stability and zero tracking errors will still be guaranteed. The developed scheme is successfully applied to the control of a rougher flotation phenomenological simulator. (author)

M-Theory Model-Building and Proton Stability

CERN Document Server

Ellis, Jonathan Richard; Nanopoulos, Dimitri V; Ellis, John; Faraggi, Alon E.

1998-01-01

We study the problem of baryon stability in M theory, starting from realistic four-dimensional string models constructed using the free-fermion formulation of the weakly-coupled heterotic string. Suitable variants of these models manifest an enhanced custodial gauge symmetry that forbids to all orders the appearance of dangerous dimension-five baryon-decay operators. We exhibit the underlying geometric (bosonic) interpretation of these models, which have a $Z_2 \\times Z_2$ orbifold structure similar, but not identical, to the class of Calabi-Yau threefold compactifications of M and F theory investigated by Voisin and Borcea. A related generalization of their work may provide a solution to the problem of proton stability in M theory.

M-theory model-building and proton stability

International Nuclear Information System (INIS)

Ellis, J.; Faraggi, A.E.; Nanopoulos, D.V.; Houston Advanced Research Center, The Woodlands, TX; Academy of Athens

1997-09-01

The authors study the problem of baryon stability in M theory, starting from realistic four-dimensional string models constructed using the free-fermion formulation of the weakly-coupled heterotic string. Suitable variants of these models manifest an enhanced custodial gauge symmetry that forbids to all orders the appearance of dangerous dimension-five baryon-decay operators. The authors exhibit the underlying geometric (bosonic) interpretation of these models, which have a Z 2 x Z 2 orbifold structure similar, but not identical, to the class of Calabi-Yau threefold compactifications of M and F theory investigated by Voisin and Borcea. A related generalization of their work may provide a solution to the problem of proton stability in M theory

Construction of a Smooth Lyapunov Function for the Robust and Exact Second-Order Differentiator

Directory of Open Access Journals (Sweden)

Tonametl Sanchez

2016-01-01

Full Text Available Differentiators play an important role in (continuous feedback control systems. In particular, the robust and exact second-order differentiator has shown some very interesting properties and it has been used successfully in sliding mode control, in spite of the lack of a Lyapunov based procedure to design its gains. As contribution of this paper, we provide a constructive method to determine a differentiable Lyapunov function for such a differentiator. Moreover, the Lyapunov function is used to provide a procedure to design the differentiator’s parameters. Also, some sets of such parameters are provided. The determination of the positive definiteness of the Lyapunov function and negative definiteness of its derivative is converted to the problem of solving a system of inequalities linear in the parameters of the Lyapunov function candidate and also linear in the gains of the differentiator, but bilinear in both.

Exponential stability of uncertain stochastic neural networks with mixed time-delays

International Nuclear Information System (INIS)

Wang Zidong; Lauria, Stanislao; Fang Jian'an; Liu Xiaohui

2007-01-01

This paper is concerned with the global exponential stability analysis problem for a class of stochastic neural networks with mixed time-delays and parameter uncertainties. The mixed delays comprise discrete and distributed time-delays, the parameter uncertainties are norm-bounded, and the neural networks are subjected to stochastic disturbances described in terms of a Brownian motion. The purpose of the stability analysis problem is to derive easy-to-test criteria under which the delayed stochastic neural network is globally, robustly, exponentially stable in the mean square for all admissible parameter uncertainties. By resorting to the Lyapunov-Krasovskii stability theory and the stochastic analysis tools, sufficient stability conditions are established by using an efficient linear matrix inequality (LMI) approach. The proposed criteria can be checked readily by using recently developed numerical packages, where no tuning of parameters is required. An example is provided to demonstrate the usefulness of the proposed criteria

Global exponential stability of bidirectional associative memory neural networks with distributed delays

Science.gov (United States)

Song, Qiankun; Cao, Jinde

2007-05-01

A bidirectional associative memory neural network model with distributed delays is considered. By constructing a new Lyapunov functional, employing the homeomorphism theory, M-matrix theory and the inequality (a[greater-or-equal, slanted]0,bk[greater-or-equal, slanted]0,qk>0 with , and r>1), a sufficient condition is obtained to ensure the existence, uniqueness and global exponential stability of the equilibrium point for the model. Moreover, the exponential converging velocity index is estimated, which depends on the delay kernel functions and the system parameters. The results generalize and improve the earlier publications, and remove the usual assumption that the activation functions are bounded . Two numerical examples are given to show the effectiveness of the obtained results.

Three caveats for linear stability theory: Rayleigh-Benard convection

International Nuclear Information System (INIS)

Greenside, H.S.

1984-06-01

Recent theories and experiments challenge the applicability of linear stability theory near the onset of buoyancy-driven (Rayleigh-Benard) convection. This stability theory, based on small perturbations of infinite parallel rolls, is found to miss several important features of the convective flow. The reason is that the lateral boundaries have a profound influence on the possible wave numbers and flow patterns even for the largest cells studied. Also, the nonlinear growth of incoherent unstable modes distorts the rolls, leading to a spatially disordered and sometimes temporally nonperiodic flow. Finally, the relation of the skewed varicose instability to the onset of turbulence (nonperiodic time dependence) is examined. Linear stability theory may not suffice to predict the onset of time dependence in large cells close to threshold

Stability of a viral infection model with state-dependent delay, CTL and antibody immune responses

Czech Academy of Sciences Publication Activity Database

Rezunenko, Oleksandr

2017-01-01

Roč. 22, č. 4 (2017), s. 1547-1563 ISSN 1531-3492 R&D Projects: GA ČR(CZ) GA16-06678S Institutional support: RVO:67985556 Keywords : Evolution equations * Lyapunov stability * state-dependent delay * virus infection model Subject RIV: BC - Control Systems Theory OBOR OECD: Computer sciences, information science, bioinformathics (hardware development to be 2.2, social aspect to be 5.8) Impact factor: 0.994, year: 2016 http://library.utia.cas.cz/separaty/2017/AS/rezunenko-0476128.pdf

Nonlinear generalized synchronization of chaotic systems by pure error dynamics and elaborate nondiagonal Lyapunov function

International Nuclear Information System (INIS)

Ge Zhengming; Chang Chingming

2009-01-01

By applying pure error dynamics and elaborate nondiagonal Lyapunov function, the nonlinear generalized synchronization is studied in this paper. Instead of current mixed error dynamics in which master state variables and slave state variables are presented, the nonlinear generalized synchronization can be obtained by pure error dynamics without auxiliary numerical simulation. The elaborate nondiagonal Lyapunov function is applied rather than current monotonous square sum Lyapunov function deeply weakening the powerfulness of Lyapunov direct method. Both autonomous and nonautonomous double Mathieu systems are used as examples with numerical simulations.

A sampling approach to constructing Lyapunov functions for nonlinear continuous–time systems

NARCIS (Netherlands)

Bobiti, R.V.; Lazar, M.

2016-01-01

The problem of constructing a Lyapunov function for continuous-time nonlinear dynamical systems is tackled in this paper via a sampling-based approach. The main idea of the sampling-based method is to verify a Lyapunov-type inequality for a finite number of points (known state vectors) in the

Statistical-mechanical formulation of Lyapunov exponents

International Nuclear Information System (INIS)

Tanase-Nicola, Sorin; Kurchan, Jorge

2003-01-01

We show how the Lyapunov exponents of a dynamic system can, in general, be expressed in terms of the free energy of a (non-Hermitian) quantum many-body problem. This puts their study as a problem of statistical mechanics, whose intuitive concepts and techniques of approximation can hence be borrowed

Dynamics, stability, and statistics on lattices and networks

International Nuclear Information System (INIS)

Livi, Roberto

2014-01-01

These lectures aim at surveying some dynamical models that have been widely explored in the recent scientific literature as case studies of complex dynamical evolution, emerging from the spatio-temporal organization of several coupled dynamical variables. The first message is that a suitable mathematical description of such models needs tools and concepts borrowed from the general theory of dynamical systems and from out-of-equilibrium statistical mechanics. The second message is that the overall scenario is definitely reacher than the standard problems in these fields. For instance, systems exhibiting complex unpredictable evolution do not necessarily exhibit deterministic chaotic behavior (i.e., Lyapunov chaos) as it happens for dynamical models made of a few degrees of freedom. In fact, a very large number of spatially organized dynamical variables may yield unpredictable evolution even in the absence of Lyapunov instability. Such a mechanism may emerge from the combination of spatial extension and nonlinearity. Moreover, spatial extension allows one to introduce naturally disorder, or heterogeneity of the interactions as important ingredients for complex evolution. It is worth to point out that the models discussed in these lectures share such features, despite they have been inspired by quite different physical and biological problems. Along these lectures we describe also some of the technical tools employed for the study of such models, e.g., Lyapunov stability analysis, unpredictability indicators for “stable chaos,” hydrodynamic description of transport in low spatial dimension, spectral decomposition of stochastic dynamics on directed networks, etc

Critical behavior of the Lyapunov exponent in type-III intermittency

Energy Technology Data Exchange (ETDEWEB)

Alvarez-Llamoza, O. [Departamento de Fisica, FACYT, Universidad de Carabobo, Valencia (Venezuela); Centro de Fisica Fundamental, Grupo de Caos y Sistemas Complejos, Universidad de Los Andes, Merida 5251, Merida (Venezuela)], E-mail: llamoza@ula.ve; Cosenza, M.G. [Centro de Fisica Fundamental, Grupo de Caos y Sistemas Complejos, Universidad de Los Andes, Merida 5251, Merida (Venezuela); Ponce, G.A. [Departamento de Fisica, Universidad Nacional Autonoma de Honduras (Honduras); Departamento de Ciencias Naturales, Universidad Pedagogica Nacional Francisco Morazan, Tegucigalpa (Honduras)

2008-04-15

The critical behavior of the Lyapunov exponent near the transition to robust chaos via type-III intermittency is determined for a family of one-dimensional singular maps. Critical boundaries separating the region of robust chaos from the region where stable fixed points exist are calculated on the parameter space of the system. A critical exponent {beta} expressing the scaling of the Lyapunov exponent is calculated along the critical curve corresponding to the type-III intermittent transition to chaos. It is found that {beta} varies on the interval 0 {<=} {beta} < 1/2 as a function of the order of the singularity of the map. This contrasts with earlier predictions for the scaling behavior of the Lyapunov exponent in type-III intermittency. The variation of the critical exponent {beta} implies a continuous change in the nature of the transition to chaos via type-III intermittency, from a second-order, continuous transition to a first-order, discontinuous transition.

Critical behavior of the Lyapunov exponent in type-III intermittency

International Nuclear Information System (INIS)

Alvarez-Llamoza, O.; Cosenza, M.G.; Ponce, G.A.

2008-01-01

The critical behavior of the Lyapunov exponent near the transition to robust chaos via type-III intermittency is determined for a family of one-dimensional singular maps. Critical boundaries separating the region of robust chaos from the region where stable fixed points exist are calculated on the parameter space of the system. A critical exponent β expressing the scaling of the Lyapunov exponent is calculated along the critical curve corresponding to the type-III intermittent transition to chaos. It is found that β varies on the interval 0 ≤ β < 1/2 as a function of the order of the singularity of the map. This contrasts with earlier predictions for the scaling behavior of the Lyapunov exponent in type-III intermittency. The variation of the critical exponent β implies a continuous change in the nature of the transition to chaos via type-III intermittency, from a second-order, continuous transition to a first-order, discontinuous transition

Novel stability criteria for fuzzy Hopfield neural networks based on an improved homogeneous matrix polynomials technique

International Nuclear Information System (INIS)

Feng Yi-Fu; Zhang Qing-Ling; Feng De-Zhi

2012-01-01

The global stability problem of Takagi—Sugeno (T—S) fuzzy Hopfield neural networks (FHNNs) with time delays is investigated. Novel LMI-based stability criteria are obtained by using Lyapunov functional theory to guarantee the asymptotic stability of the FHNNs with less conservatism. Firstly, using both Finsler's lemma and an improved homogeneous matrix polynomial technique, and applying an affine parameter-dependent Lyapunov—Krasovskii functional, we obtain the convergent LMI-based stability criteria. Algebraic properties of the fuzzy membership functions in the unit simplex are considered in the process of stability analysis via the homogeneous matrix polynomials technique. Secondly, to further reduce the conservatism, a new right-hand-side slack variables introducing technique is also proposed in terms of LMIs, which is suitable to the homogeneous matrix polynomials setting. Finally, two illustrative examples are given to show the efficiency of the proposed approaches

Optimal control theory applied to fusion plasma thermal stabilization

International Nuclear Information System (INIS)

Sager, G.; Miley, G.; Maya, I.

1985-01-01

Many authors have investigated stability characteristics and performance of various burn control schemes. The work presented here represents the first application of optimal control theory to the problem of fusion plasma thermal stabilization. The objectives of this initial investigation were to develop analysis methods, demonstrate tractability, and present some preliminary results of optimal control theory in burn control research

Stability properties of solitary waves for fractional KdV and BBM equations

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Angulo Pava, Jaime

2018-03-01

This paper sheds new light on the stability properties of solitary wave solutions associated with Korteweg-de Vries-type models when the dispersion is very low. Using a compact, analytic approach and asymptotic perturbation theory, we establish sufficient conditions for the existence of exponentially growing solutions to the linearized problem and so a criterium of spectral instability of solitary waves is obtained for both models. Moreover, the nonlinear stability and spectral instability of the ground state solutions for both models is obtained for some specific regimen of parameters. Via a Lyapunov strategy and a variational analysis, we obtain the stability of the blow-up of solitary waves for the critical fractional KdV equation. The arguments presented in this investigation show promise for use in the study of the instability of traveling wave solutions of other nonlinear evolution equations.

Regeneration cycle and the covariant Lyapunov vectors in a minimal wall turbulence.

Science.gov (United States)

Inubushi, Masanobu; Takehiro, Shin-ichi; Yamada, Michio

2015-08-01

Considering a wall turbulence as a chaotic dynamical system, we study regeneration cycles in a minimal wall turbulence from the viewpoint of orbital instability by employing the covariant Lyapunov analysis developed by [F. Ginelli et al. Phys. Rev. Lett. 99, 130601 (2007)]. We divide the regeneration cycle into two phases and characterize them with the local Lyapunov exponents and the covariant Lyapunov vectors of the Navier-Stokes turbulence. In particular, we show numerically that phase (i) is dominated by instabilities related to the sinuous mode and the streamwise vorticity, and there is no instability in phase (ii). Furthermore, we discuss a mechanism of the regeneration cycle, making use of an energy budget analysis.

Stability in quadratic torsion theories

Energy Technology Data Exchange (ETDEWEB)

Vasilev, Teodor Borislavov; Cembranos, Jose A.R.; Gigante Valcarcel, Jorge; Martin-Moruno, Prado [Universidad Complutense de Madrid, Departamento de Fisica Teorica I, Madrid (Spain)

2017-11-15

We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when the torsion vanishes and investigating the behaviour of the vector and pseudo-vector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier. (orig.)

Stability in quadratic torsion theories

International Nuclear Information System (INIS)

Vasilev, Teodor Borislavov; Cembranos, Jose A.R.; Gigante Valcarcel, Jorge; Martin-Moruno, Prado

2017-01-01

We revisit the definition and some of the characteristics of quadratic theories of gravity with torsion. We start from a Lagrangian density quadratic in the curvature and torsion tensors. By assuming that General Relativity should be recovered when the torsion vanishes and investigating the behaviour of the vector and pseudo-vector torsion fields in the weak-gravity regime, we present a set of necessary conditions for the stability of these theories. Moreover, we explicitly obtain the gravitational field equations using the Palatini variational principle with the metricity condition implemented via a Lagrange multiplier. (orig.)

Stability Criterion of Linear Stochastic Systems Subject to Mixed H2/Passivity Performance

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Cheung-Chieh Ku

2015-01-01

Full Text Available The H2 control scheme and passivity theory are applied to investigate the stability criterion of continuous-time linear stochastic system subject to mixed performance. Based on the stochastic differential equation, the stochastic behaviors can be described as multiplicative noise terms. For the considered system, the H2 control scheme is applied to deal with the problem on minimizing output energy. And the asymptotical stability of the system can be guaranteed under desired initial conditions. Besides, the passivity theory is employed to constrain the effect of external disturbance on the system. Moreover, the Itô formula and Lyapunov function are used to derive the sufficient conditions which are converted into linear matrix inequality (LMI form for applying convex optimization algorithm. Via solving the sufficient conditions, the state feedback controller can be established such that the asymptotical stability and mixed performance of the system are achieved in the mean square. Finally, the synchronous generator system is used to verify the effectiveness and applicability of the proposed design method.

Lyapunov exponent of the random frequency oscillator: cumulant expansion approach

International Nuclear Information System (INIS)

Anteneodo, C; Vallejos, R O

2010-01-01

We consider a one-dimensional harmonic oscillator with a random frequency, focusing on both the standard and the generalized Lyapunov exponents, λ and λ* respectively. We discuss the numerical difficulties that arise in the numerical calculation of λ* in the case of strong intermittency. When the frequency corresponds to a Ornstein-Uhlenbeck process, we compute analytically λ* by using a cumulant expansion including up to the fourth order. Connections with the problem of finding an analytical estimate for the largest Lyapunov exponent of a many-body system with smooth interactions are discussed.

Stability and Linear Quadratic Differential Games of Discrete-Time Markovian Jump Linear Systems with State-Dependent Noise

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Huiying Sun

2014-01-01

Full Text Available We mainly consider the stability of discrete-time Markovian jump linear systems with state-dependent noise as well as its linear quadratic (LQ differential games. A necessary and sufficient condition involved with the connection between stochastic Tn-stability of Markovian jump linear systems with state-dependent noise and Lyapunov equation is proposed. And using the theory of stochastic Tn-stability, we give the optimal strategies and the optimal cost values for infinite horizon LQ stochastic differential games. It is demonstrated that the solutions of infinite horizon LQ stochastic differential games are concerned with four coupled generalized algebraic Riccati equations (GAREs. Finally, an iterative algorithm is presented to solve the four coupled GAREs and a simulation example is given to illustrate the effectiveness of it.

Global exponential stability of periodic solution for shunting inhibitory CNNs with delays

Energy Technology Data Exchange (ETDEWEB)

Li Yongkun [Department of Mathematics, Yunnan University, Kunming, Yunnan 650091 (China)]. E-mail: yklie@ynu.edu.cn; Liu Chunchao [Department of Mathematics, Yunnan University, Kunming, Yunnan 650091 (China); Zhu Lifei [Department of Mathematics, Yunnan University, Kunming, Yunnan 650091 (China)

2005-03-28

By using the continuation theorem of coincidence degree theory and constructing suitable Lyapunov functions, we study the existence and stability of periodic solution for shunting inhibitory cellular neural networks (SICNNs) with delays x-bar {sub ij}(t)=-a{sub ij}(t)x{sub ij}(t)--bar B{sup kl}-bar Nr(i,j)B{sub ij}{sup kl}(t)f{sub ij}(x{sub kl}(t))x{sub ij}(t)--bar C{sup kl}-bar Nr(i,j)C{sub ij}{sup kl}(t)g{sub ij}(x{sub kl}(t-{tau}{sub kl}))x{sub ij}(t)+L{sub ij}(t)

Lyapunov-based distributed control of the safety-factor profile in a tokamak plasma

International Nuclear Information System (INIS)

Bribiesca Argomedo, Federico; Witrant, Emmanuel; Prieur, Christophe; Brémond, Sylvain; Nouailletas, Rémy; Artaud, Jean-François

2013-01-01

A real-time model-based controller is developed for the tracking of the distributed safety-factor profile in a tokamak plasma. Using relevant physical models and simplifying assumptions, theoretical stability and robustness guarantees were obtained using a Lyapunov function. This approach considers the couplings between the poloidal flux diffusion equation, the time-varying temperature profiles and an independent total plasma current control. The actuator chosen for the safety-factor profile tracking is the lower hybrid current drive, although the results presented can be easily extended to any non-inductive current source. The performance and robustness of the proposed control law is evaluated with a physics-oriented simulation code on Tore Supra experimental test cases. (paper)

Global pulse synchronization of chaotic oscillators through fast-switching: theory and experiments

International Nuclear Information System (INIS)

Porfiri, Maurizio; Fiorilli, Francesca

2009-01-01

We study pulse synchronization of chaotic systems in master-slave configuration. The slave system is unidirectionally coupled to the master system through an intermittent linear error feedback coupling, whose gain matrix periodically switches among a finite set of constant matrices. Using Lyapunov-stability theory, fast-switching techniques, and the concept of matrix measure, we derive sufficient conditions for global synchronization. The derived conditions are specialized to the case of Chua's circuits. An inductorless realization of coupled Chua's circuits is developed to illustrate the effectiveness of the proposed approach.

Stability of Almost Periodic Solution for a General Class of Discontinuous Neural Networks with Mixed Time-Varying Delays

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Yingwei Li

2013-01-01

Full Text Available The global exponential stability issues are considered for almost periodic solution of the neural networks with mixed time-varying delays and discontinuous neuron activations. Some sufficient conditions for the existence, uniqueness, and global exponential stability of almost periodic solution are achieved in terms of certain linear matrix inequalities (LMIs, by applying differential inclusions theory, matrix inequality analysis technique, and generalized Lyapunov functional approach. In addition, the existence and asymptotically almost periodic behavior of the solution of the neural networks are also investigated under the framework of the solution in the sense of Filippov. Two simulation examples are given to illustrate the validity of the theoretical results.

International Congress NONLINEAR DYNAMICAL ANALYSIS 2007 dedicated to the 150th Anniversary of Academician A. M. Lyapunov

Science.gov (United States)

2010-05-14

Mikhailovich Lyapunov is discussed. Main attention is focused on the first Lyapunov method. LYAPUNOV BUNDLES IN CYCLIC FEEDBACK SYSTEMS WITH DELAYS George ...Lyapunov frequently discussed this problem with Henry Poincare (1854-1912) and George Darwin (1845 - 1912). They both considered the "pear-form" figure as... Cantor -type set. Neither can the existence of such systems be excluded. The results we present are discussed in a joint paper with K. Bjerkloev. МЕТОДЫ А.М

Generalized Momentum Control of the Spin-Stabilized Magnetospheric Multiscale Formation

Science.gov (United States)

Queen, Steven Z.; Shah, Neerav; Benegalrao, Suyog S.; Blackman, Kathie

2015-01-01

The Magnetospheric Multiscale (MMS) mission consists of four identically instrumented, spin-stabilized observatories elliptically orbiting the Earth in a tetrahedron formation. The on-board attitude control system adjusts the angular momentum of the system using a generalized thruster-actuated control system that simultaneously manages precession, nutation and spin. Originally developed using Lyapunov control-theory with rate-feedback, a published algorithm has been augmented to provide a balanced attitude/rate response using a single weighting parameter. This approach overcomes an orientation sign-ambiguity in the existing formulation, and also allows for a smoothly tuned-response applicable to both a compact/agile spacecraft, as well as one with large articulating appendages.

Robust Stability for Nonlinear Systems with Time-Varying Delay and Uncertainties via the H∞ Quasi-Sliding Mode Control

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Yi-You Hou

2014-01-01

Full Text Available This paper considers the problem of the robust stability for the nonlinear system with time-varying delay and parameters uncertainties. Based on the H∞ theorem, Lyapunov-Krasovskii theory, and linear matrix inequality (LMI optimization technique, the H∞ quasi-sliding mode controller and switching function are developed such that the nonlinear system is asymptotically stable in the quasi-sliding mode and satisfies the disturbance attenuation (H∞-norm performance. The effectiveness and accuracy of the proposed methods are shown in numerical simulations.

Stability of a nonlinear second order equation under parametric bounded noise excitation

International Nuclear Information System (INIS)

Wiebe, Richard; Xie, Wei-Chau

2016-01-01

The motivation for the following work is a structural column under dynamic axial loads with both deterministic (harmonic transmitted forces from the surrounding structure) and random (wind and/or earthquake) loading components. The bounded noise used herein is a sinusoid with an argument composed of a random (Wiener) process deviation about a mean frequency. By this approach, a noise parameter may be used to investigate the behavior through the spectrum from simple harmonic forcing, to a bounded random process with very little harmonic content. The stability of both the trivial and non-trivial stationary solutions of an axially-loaded column (which is modeled as a second order nonlinear equation) under parametric bounded noise excitation is investigated by use of Lyapunov exponents. Specifically the effect of noise magnitude, amplitude of the forcing, and damping on stability of a column is investigated. First order averaging is employed to obtain analytical approximations of the Lyapunov exponents of the trivial solution. For the non-trivial stationary solution however, the Lyapunov exponents are obtained via Monte Carlo simulation as the stability equations become analytically intractable. (paper)

Methodological remarks on contraction theory

DEFF Research Database (Denmark)

Jouffroy, Jerome; Slotine, Jean-Jacques E.

Because contraction analysis stems from a differential and incremental framework, the nature and methodology of contraction-based proofs are significantly different from those of their Lyapunov-based counterparts. This paper specifically studies this issue, and illustrates it by revisiting some c...... classical examples traditionally addressed using Lyapunov theory. Even in these cases, contraction tools can often yield significantly simplified analysis. The examples include adaptive control, robotics, and a proof of convergence of the deterministic Extended Kalman Filter....

Globally Asymptotic Stability of Stochastic Nonlinear Systems with Time-Varying Delays via Output Feedback Control

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Mingzhu Song

2016-01-01

Full Text Available We address the problem of globally asymptotic stability for a class of stochastic nonlinear systems with time-varying delays. By the backstepping method and Lyapunov theory, we design a linear output feedback controller recursively based on the observable linearization for a class of stochastic nonlinear systems with time-varying delays to guarantee that the closed-loop system is globally asymptotically stable in probability. In particular, we extend the deterministic nonlinear system to stochastic nonlinear systems with time-varying delays. Finally, an example and its simulations are given to illustrate the theoretical results.

On some properties of the discrete Lyapunov exponent

International Nuclear Information System (INIS)

Amigo, Jose M.; Kocarev, Ljupco; Szczepanski, Janusz

2008-01-01

One of the possible by-products of discrete chaos is the application of its tools, in particular of the discrete Lyapunov exponent, to cryptography. In this Letter we explore this question in a very general setting

Lyapunov Based Estimation of Flight Stability Boundary under Icing Conditions

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Binbin Pei

2017-01-01

Full Text Available Current fight boundary of the envelope protection in icing conditions is usually defined by the critical values of state parameters; however, such method does not take the interrelationship of each parameter and the effect of the external disturbance into consideration. This paper proposes constructing the stability boundary of the aircraft in icing conditions through analyzing the region of attraction (ROA around the equilibrium point. Nonlinear icing effect model is proposed according to existing wind tunnel test results. On this basis, the iced polynomial short period model can be deduced further to obtain the stability boundary under icing conditions using ROA analysis. Simulation results for a series of icing severity demonstrate that, regardless of the icing severity, the boundary of the calculated ROA can be treated as an estimation of the stability boundary around an equilibrium point. The proposed methodology is believed to be a promising way for ROA analysis and stability boundary construction of the aircraft in icing conditions, and it will provide theoretical support for multiple boundary protection of icing tolerant flight.

Novel criteria for global exponential periodicity and stability of recurrent neural networks with time-varying delays

International Nuclear Information System (INIS)

Song Qiankun

2008-01-01

In this paper, the global exponential periodicity and stability of recurrent neural networks with time-varying delays are investigated by applying the idea of vector Lyapunov function, M-matrix theory and inequality technique. We assume neither the global Lipschitz conditions on these activation functions nor the differentiability on these time-varying delays, which were needed in other papers. Several novel criteria are found to ascertain the existence, uniqueness and global exponential stability of periodic solution for recurrent neural network with time-varying delays. Moreover, the exponential convergence rate index is estimated, which depends on the system parameters. Some previous results are improved and generalized, and an example is given to show the effectiveness of our method

Detection of the onset of numerical chaotic instabilities by lyapunov exponents

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Alicia Serfaty De Markus

2001-01-01

Full Text Available It is commonly found in the fixed-step numerical integration of nonlinear differential equations that the size of the integration step is opposite related to the numerical stability of the scheme and to the speed of computation. We present a procedure that establishes a criterion to select the largest possible step size before the onset of chaotic numerical instabilities, based upon the observation that computational chaos does not occur in a smooth, continuous way, but rather abruptly, as detected by examining the largest Lyapunov exponent as a function of the step size. For completeness, examination of the bifurcation diagrams with the step reveals the complexity imposed by the algorithmic discretization, showing the robustness of a scheme to numerical instabilities, illustrated here for explicit and implicit Euler schemes. An example of numerical suppression of chaos is also provided.

Global stability and existence of periodic solutions of discrete delayed cellular neural networks

International Nuclear Information System (INIS)

Li Yongkun

2004-01-01

We use the continuation theorem of coincidence degree theory and Lyapunov functions to study the existence and stability of periodic solutions for the discrete cellular neural networks (CNNs) with delays xi(n+1)=xi(n)e-bi(n)h+θi(h)-bar j=1maij(n)fj(xj(n))+θi(h)-bar j=1mbij(n)fj(xj(n- τij(n)))+θi(h)Ii(n),i=1,2,...,m. We obtain some sufficient conditions to ensure that for the networks there exists a unique periodic solution, and all its solutions converge to such a periodic solution

Improved Criteria on Delay-Dependent Stability for Discrete-Time Neural Networks with Interval Time-Varying Delays

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O. M. Kwon

2012-01-01

Full Text Available The purpose of this paper is to investigate the delay-dependent stability analysis for discrete-time neural networks with interval time-varying delays. Based on Lyapunov method, improved delay-dependent criteria for the stability of the networks are derived in terms of linear matrix inequalities (LMIs by constructing a suitable Lyapunov-Krasovskii functional and utilizing reciprocally convex approach. Also, a new activation condition which has not been considered in the literature is proposed and utilized for derivation of stability criteria. Two numerical examples are given to illustrate the effectiveness of the proposed method.

Stability in higher-derivative matter fields theories

International Nuclear Information System (INIS)

Tretyakov, Petr V.

2016-01-01

We discuss possible instabilities in higher-derivative matter field theories. These theories have two free parameters β 1 and β 4 . By using a dynamical system approach we explicitly demonstrate that for the stability of Minkowski space in an expanding universe we need the condition β 4 < 0. By using the quantum field theory approach we also find an additional restriction for the parameters, β 1 > -(1)/(3)β 4 , which is needed to avoid a tachyon-like instability. (orig.)

A method for determining the non-existence of a common quadratic Lyapunov function for switched linear systems based on particle swarm optimisation

Czech Academy of Sciences Publication Activity Database

Duarte-Mermoud, M.A.; Ordonez-Hurtado, R.H.; Zagalak, Petr

2012-01-01

Roč. 43, č. 11 (2012), s. 2015-2029 ISSN 0020-7721 R&D Projects: GA ČR(CZ) GAP103/12/2431 Institutional support: RVO:67985556 Keywords : Switched linear systems * Lyapunov function * particle swarm optimization Subject RIV: BC - Control Systems Theory Impact factor: 1.305, year: 2012 http://library.utia.cas.cz/separaty/2012/AS/zagalak-0382169.pdf

Adaptive Integral Sliding Mode Stabilization of Nonholonomic Drift-Free Systems

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Waseem Abbasi

2016-01-01

Full Text Available This article presents adaptive integral sliding mode control algorithm for the stabilization of nonholonomic drift-free systems. First the system is transformed, by using input transform, into a special structure containing a nominal part and some unknown terms which are computed adaptively. The transformed system is then stabilized using adaptive integral sliding mode control. The stabilizing controller for the transformed system is constructed that consists of the nominal control plus a compensator control. The compensator control and the adaptive laws are derived on the basis of Lyapunov stability theory. The proposed control algorithm is applied to three different nonholonomic drift-free systems: the unicycle model, the front wheel car model, and the mobile robot with trailer model. The controllability Lie algebra of the unicycle model contains Lie brackets of depth one, the model of a front wheel car contains Lie brackets of depths one and two, and the model of a mobile robot with trailer contains Lie brackets of depths one, two, and three. The effectiveness of the proposed control algorithm is verified through numerical simulations.

New delay-dependent absolute stability criteria for Lur'e systems with time-varying delay

Science.gov (United States)

Chen, Yonggang; Bi, Weiping; Li, Wenlin

2011-07-01

In this article, the absolute stability problem is investigated for Lur'e systems with time-varying delay and sector-bounded nonlinearity. By employing the delay fractioning idea, the new augmented Lyapunov functional is first constructed. Then, by introducing some slack matrices and by reserving the useful term when estimating the upper bound of the derivative of Lyapunov functional, the new delay-dependent absolute stability criteria are derived in terms of linear matrix inequalities. Several numerical examples are presented to show the effectiveness and the less conservativeness of the proposed method.

Multiscale Lyapunov exponent for 2-microlocal functions

International Nuclear Information System (INIS)

Dhifaoui, Zouhaier; Kortas, Hedi; Ammou, Samir Ben

2009-01-01

The Lyapunov exponent is an important indicator of chaotic dynamics. Using wavelet analysis, we define a multiscale representation of this exponent which we demonstrate the scale-wise dependence for functions belonging to C x 0 s,s ' spaces. An empirical study involving simulated processes and financial time series corroborates the theoretical findings.

Fluctuating interaction network and time-varying stability of a natural fish community

Science.gov (United States)

Ushio, Masayuki; Hsieh, Chih-Hao; Masuda, Reiji; Deyle, Ethan R.; Ye, Hao; Chang, Chun-Wei; Sugihara, George; Kondoh, Michio

2018-02-01

Ecological theory suggests that large-scale patterns such as community stability can be influenced by changes in interspecific interactions that arise from the behavioural and/or physiological responses of individual species varying over time. Although this theory has experimental support, evidence from natural ecosystems is lacking owing to the challenges of tracking rapid changes in interspecific interactions (known to occur on timescales much shorter than a generation time) and then identifying the effect of such changes on large-scale community dynamics. Here, using tools for analysing nonlinear time series and a 12-year-long dataset of fortnightly collected observations on a natural marine fish community in Maizuru Bay, Japan, we show that short-term changes in interaction networks influence overall community dynamics. Among the 15 dominant species, we identify 14 interspecific interactions to construct a dynamic interaction network. We show that the strengths, and even types, of interactions change with time; we also develop a time-varying stability measure based on local Lyapunov stability for attractor dynamics in non-equilibrium nonlinear systems. We use this dynamic stability measure to examine the link between the time-varying interaction network and community stability. We find seasonal patterns in dynamic stability for this fish community that broadly support expectations of current ecological theory. Specifically, the dominance of weak interactions and higher species diversity during summer months are associated with higher dynamic stability and smaller population fluctuations. We suggest that interspecific interactions, community network structure and community stability are dynamic properties, and that linking fluctuating interaction networks to community-level dynamic properties is key to understanding the maintenance of ecological communities in nature.

pth moment exponential stability of stochastic memristor-based bidirectional associative memory (BAM) neural networks with time delays.

Science.gov (United States)

Wang, Fen; Chen, Yuanlong; Liu, Meichun

2018-02-01

Stochastic memristor-based bidirectional associative memory (BAM) neural networks with time delays play an increasingly important role in the design and implementation of neural network systems. Under the framework of Filippov solutions, the issues of the pth moment exponential stability of stochastic memristor-based BAM neural networks are investigated. By using the stochastic stability theory, Itô's differential formula and Young inequality, the criteria are derived. Meanwhile, with Lyapunov approach and Cauchy-Schwarz inequality, we derive some sufficient conditions for the mean square exponential stability of the above systems. The obtained results improve and extend previous works on memristor-based or usual neural networks dynamical systems. Four numerical examples are provided to illustrate the effectiveness of the proposed results. Copyright © 2017 Elsevier Ltd. All rights reserved.

Collisionless two-fluid theory of toroidal ηi stability

International Nuclear Information System (INIS)

Mondt, J.; Weiland, J.

1989-01-01

A collisionless two-fluid theory based on a fourteen-moment generalization of the 'double-adiabatic' equations is developed to lowest order in the Larmor radius parameter, and applied to derive the toroidal η i stability boundary for all values of the ratio of the density gradient scale length divided by the field curvature length. The present model is an improvement over existing collisional two-fluid models in view of the collisionless nature of the η i instability, while retaining the advantage over kinetic theory of the practability of mode-coupling simulations. The linear stability boundary, linear growth rate and real frequency agree fairly accurately with draft-kinetic theory

Controlled test for predictive power of Lyapunov exponents: their inability to predict epileptic seizures.

Science.gov (United States)

Lai, Ying-Cheng; Harrison, Mary Ann F; Frei, Mark G; Osorio, Ivan

2004-09-01

Lyapunov exponents are a set of fundamental dynamical invariants characterizing a system's sensitive dependence on initial conditions. For more than a decade, it has been claimed that the exponents computed from electroencephalogram (EEG) or electrocorticogram (ECoG) signals can be used for prediction of epileptic seizures minutes or even tens of minutes in advance. The purpose of this paper is to examine the predictive power of Lyapunov exponents. Three approaches are employed. (1) We present qualitative arguments suggesting that the Lyapunov exponents generally are not useful for seizure prediction. (2) We construct a two-dimensional, nonstationary chaotic map with a parameter slowly varying in a range containing a crisis, and test whether this critical event can be predicted by monitoring the evolution of finite-time Lyapunov exponents. This can thus be regarded as a "control test" for the claimed predictive power of the exponents for seizure. We find that two major obstacles arise in this application: statistical fluctuations of the Lyapunov exponents due to finite time computation and noise from the time series. We show that increasing the amount of data in a moving window will not improve the exponents' detective power for characteristic system changes, and that the presence of small noise can ruin completely the predictive power of the exponents. (3) We report negative results obtained from ECoG signals recorded from patients with epilepsy. All these indicate firmly that, the use of Lyapunov exponents for seizure prediction is practically impossible as the brain dynamical system generating the ECoG signals is more complicated than low-dimensional chaotic systems, and is noisy. Copyright 2004 American Institute of Physics

Robust stability of bidirectional associative memory neural networks with time delays

Science.gov (United States)

Park, Ju H.

2006-01-01

Based on the Lyapunov Krasovskii functionals combined with linear matrix inequality approach, a novel stability criterion is proposed for asymptotic stability of bidirectional associative memory neural networks with time delays. A novel delay-dependent stability criterion is given in terms of linear matrix inequalities, which can be solved easily by various optimization algorithms.

Robust stability of bidirectional associative memory neural networks with time delays

International Nuclear Information System (INIS)

Park, Ju H.

2006-01-01

Based on the Lyapunov-Krasovskii functionals combined with linear matrix inequality approach, a novel stability criterion is proposed for asymptotic stability of bidirectional associative memory neural networks with time delays. A novel delay-dependent stability criterion is given in terms of linear matrix inequalities, which can be solved easily by various optimization algorithms

On the relation between Lyapunov exponents and exponential decay of correlations

International Nuclear Information System (INIS)

Slipantschuk, Julia; Bandtlow, Oscar F; Just, Wolfram

2013-01-01

Chaotic dynamics with sensitive dependence on initial conditions may result in exponential decay of correlation functions. We show that for one-dimensional interval maps the corresponding quantities, that is, Lyapunov exponents and exponential decay rates, are related. More specifically, for piecewise linear expanding Markov maps observed via piecewise analytic functions, we show that the decay rate is bounded above by twice the Lyapunov exponent, that is, we establish lower bounds for the subleading eigenvalue of the corresponding Perron–Frobenius operator. In addition, we comment on similar relations for general piecewise smooth expanding maps. (paper)

Global asymptotic stability to a generalized Cohen-Grossberg BAM neural networks of neutral type delays.

Science.gov (United States)

Zhang, Zhengqiu; Liu, Wenbin; Zhou, Dongming

2012-01-01

In this paper, we first discuss the existence of a unique equilibrium point of a generalized Cohen-Grossberg BAM neural networks of neutral type delays by means of the Homeomorphism theory and inequality technique. Then, by applying the existence result of an equilibrium point and constructing a Lyapunov functional, we study the global asymptotic stability of the equilibrium solution to the above Cohen-Grossberg BAM neural networks of neutral type. In our results, the hypothesis for boundedness in the existing paper, which discussed Cohen-Grossberg neural networks of neutral type on the activation functions, are removed. Finally, we give an example to demonstrate the validity of our global asymptotic stability result for the above neural networks. Copyright © 2011 Elsevier Ltd. All rights reserved.

Behaviour of Lyapunov exponents near crisis points in the dissipative standard map

Science.gov (United States)

Pompe, B.; Leven, R. W.

1988-11-01

We numerically study the behaviour of the largest Lyapunov characteristic exponent λ1 in dependence on a control parameter in the 2D standard map with dissipation. In order to investigate the system's motion in parameter intervals slightly above crisis points we introduce "partial" Lyapunov exponents which characterize the average exponential divergence of nearby orbits on a semi-attractor at a boundary crisis and on distinct parts of a "large" chaotic attractor near an interior crisis. In the former case we find no significant difference between λ1 in the pre-crisis regime and the partial Lyapunov exponent describing transient chaotic motions slightly above the crisis. For the latter case we give a quantitative description of the drastic increase of λ1. Moreover, a formula which connects the critical exponent of a chaotic transient above a boundary crisis with a pointwise dimension is derived.

Parallel Optimization of Polynomials for Large-scale Problems in Stability and Control

Science.gov (United States)

Kamyar, Reza

In this thesis, we focus on some of the NP-hard problems in control theory. Thanks to the converse Lyapunov theory, these problems can often be modeled as optimization over polynomials. To avoid the problem of intractability, we establish a trade off between accuracy and complexity. In particular, we develop a sequence of tractable optimization problems --- in the form of Linear Programs (LPs) and/or Semi-Definite Programs (SDPs) --- whose solutions converge to the exact solution of the NP-hard problem. However, the computational and memory complexity of these LPs and SDPs grow exponentially with the progress of the sequence - meaning that improving the accuracy of the solutions requires solving SDPs with tens of thousands of decision variables and constraints. Setting up and solving such problems is a significant challenge. The existing optimization algorithms and software are only designed to use desktop computers or small cluster computers --- machines which do not have sufficient memory for solving such large SDPs. Moreover, the speed-up of these algorithms does not scale beyond dozens of processors. This in fact is the reason we seek parallel algorithms for setting-up and solving large SDPs on large cluster- and/or super-computers. We propose parallel algorithms for stability analysis of two classes of systems: 1) Linear systems with a large number of uncertain parameters; 2) Nonlinear systems defined by polynomial vector fields. First, we develop a distributed parallel algorithm which applies Polya's and/or Handelman's theorems to some variants of parameter-dependent Lyapunov inequalities with parameters defined over the standard simplex. The result is a sequence of SDPs which possess a block-diagonal structure. We then develop a parallel SDP solver which exploits this structure in order to map the computation, memory and communication to a distributed parallel environment. Numerical tests on a supercomputer demonstrate the ability of the algorithm to

Present status of mirror stability theory

International Nuclear Information System (INIS)

Baldwin, D.E.; Berk, H.L.; Byers, J.A.

1976-01-01

A status report of microinstability as it applies to 2XIIB and MX theory for mirror machines is presented. It is shown that quasilinear computations reproduce many of the parameters observed in the 2XIIB experiment. In regard to large mirror machines, there are presented detailed calculations of the linear theory of the drift cyclotron loss-cone mode, with inhomogeneous geometry and nonlinear diffusive effects. Further, the stability of a mirror machine to the Alfven ion-cyclotron instability is assessed, and the Baldwin-Callen diffusion is estimated for a spatially varying plasma

Predicting Traffic Flow in Local Area Networks by the Largest Lyapunov Exponent

Directory of Open Access Journals (Sweden)

Yan Liu

2016-01-01

Full Text Available The dynamics of network traffic are complex and nonlinear, and chaotic behaviors and their prediction, which play an important role in local area networks (LANs, are studied in detail, using the largest Lyapunov exponent. With the introduction of phase space reconstruction based on the time sequence, the high-dimensional traffic is projected onto the low dimension reconstructed phase space, and a reduced dynamic system is obtained from the dynamic system viewpoint. Then, a numerical method for computing the largest Lyapunov exponent of the low-dimensional dynamic system is presented. Further, the longest predictable time, which is related to chaotic behaviors in the system, is studied using the largest Lyapunov exponent, and the Wolf method is used to predict the evolution of the traffic in a local area network by both Dot and Interval predictions, and a reliable result is obtained by the presented method. As the conclusion, the results show that the largest Lyapunov exponent can be used to describe the sensitivity of the trajectory in the reconstructed phase space to the initial values. Moreover, Dot Prediction can effectively predict the flow burst. The numerical simulation also shows that the presented method is feasible and efficient for predicting the complex dynamic behaviors in LAN traffic, especially for congestion and attack in networks, which are the main two complex phenomena behaving as chaos in networks.

Finite-time synchronization of Lorenz chaotic systems: theory and circuits

International Nuclear Information System (INIS)

Louodop, Patrick; Fotsin, Hilaire; Kountchou, Michaux; Bowong, Samuel

2013-01-01

This paper addresses the problem of finite-time master–slave synchronization of Lorenz chaotic systems from a control theoretic point of view. We propose a family of feedback couplings which accomplish the synchronization of Lorenz chaotic systems based on Lyapunov stability theory. These feedback couplings are based on non-periodic functions. A finite horizon can be arbitrarily established by ensuring that chaos synchronization is achieved at established time. An advantage is that some of the proposed feedback couplings are simple and easy to implement. Both mathematical investigations and numerical simulations followed by a Pspice experiment are presented to show the feasibility of the proposed method. (paper)

Fuzzy wavelet plus a quantum neural network as a design base for power system stability enhancement.

Science.gov (United States)

Ganjefar, Soheil; Tofighi, Morteza; Karami, Hamidreza

2015-11-01

In this study, we introduce an indirect adaptive fuzzy wavelet neural controller (IAFWNC) as a power system stabilizer to damp inter-area modes of oscillations in a multi-machine power system. Quantum computing is an efficient method for improving the computational efficiency of neural networks, so we developed an identifier based on a quantum neural network (QNN) to train the IAFWNC in the proposed scheme. All of the controller parameters are tuned online based on the Lyapunov stability theory to guarantee the closed-loop stability. A two-machine, two-area power system equipped with a static synchronous series compensator as a series flexible ac transmission system was used to demonstrate the effectiveness of the proposed controller. The simulation and experimental results demonstrated that the proposed IAFWNC scheme can achieve favorable control performance. Copyright © 2015 Elsevier Ltd. All rights reserved.

Control Strategy of an Impulse Turbine for an Oscillating Water Column-Wave Energy Converter in Time-Domain Using Lyapunov Stability Method

Directory of Open Access Journals (Sweden)

Seung Kwan Song

2016-10-01

Full Text Available We present two control strategies for an oscillating water column-wave energy converter (OWC-WEC in the time domain. We consider a fixed OWC-WEC on the open sea with an impulse turbine module. This system mainly consists of a chamber, turbine and electric generator. For the time domain analysis, all of the conversion stages considering mutualities among them should be analyzed based on the Newtonian mechanics. According to the analysis of Newtonian mechanics, the hydrodynamics of wave energy absorption in the chamber and the turbine aerodynamic performance are directly coupled and share the internal air pressure term via the incompressible air assumption. The turbine aerodynamics and the dynamics of the electric generator are connected by torque load through the rotor shaft, which depends on an electric terminal load that acts as a control input. The proposed control strategies are an instant maximum turbine efficiency tracking control and a constant angular velocity of the turbine rotor control methods. Both are derived by Lyapunov stability analysis. Numerical simulations are carried out under irregular waves with various heights and periods in the time domain, and the results with the controllers are analyzed. We then compare these results with simulations carried out in the absence of the control strategy in order to prove the performance of the controllers.

Modulational estimate for the maximal Lyapunov exponent in Fermi-Pasta-Ulam chains

Science.gov (United States)

Dauxois, Thierry; Ruffo, Stefano; Torcini, Alessandro

1997-12-01

In the framework of the Fermi-Pasta-Ulam (FPU) model, we show a simple method to give an accurate analytical estimation of the maximal Lyapunov exponent at high energy density. The method is based on the computation of the mean value of the modulational instability growth rates associated to unstable modes. Moreover, we show that the strong stochasticity threshold found in the β-FPU system is closely related to a transition in tangent space, the Lyapunov eigenvector being more localized in space at high energy.

Vacuum stability of asymptotically safe gauge-Yukawa theories

DEFF Research Database (Denmark)

Litim, Daniel F.; Mojaza, Matin; Sannino, Francesco

2016-01-01

We study the phase diagram and the stability of the ground state for certain four-dimensional gauge-Yukawa theories whose high-energy behaviour is controlled by an interacting fixed point. We also provide analytical and numerical results for running couplings, their crossover scales, the separatr......, and the Coleman-Weinberg effective potential. Classical and quantum stability of the vacuum is established....

Ultraviolet stability of three-dimensional lattice pure gauge field theories

International Nuclear Information System (INIS)

Balaban, T.

1985-01-01

We prove the ultraviolet stability for three-dimensional lattice gauge field theories. We consider only the Wilson lattice approximation for pure Yang-Mills field theories. The proof is based on results of the previous papers on renormalization group method for lattice gauge theories. (orig.)

Pramana – Journal of Physics | Indian Academy of Sciences

Indian Academy of Sciences (India)

... which is an important issue. By utilizing rigorous mathematical theory, sufficient condition is drawn for the stability of error dynamics based on Lyapunov stability theory. Theoretical results are supported with the numerical simulations. The complexity of this methodology is useful to strengthen the security of communication ...

Exponential stability of switched linear systems with time-varying delay

Directory of Open Access Journals (Sweden)

Satiracoo Pairote

2007-11-01

Full Text Available We use a Lyapunov-Krasovskii functional approach to establish the exponential stability of linear systems with time-varying delay. Our delay-dependent condition allows to compute simultaneously the two bounds that characterize the exponential stability rate of the solution. A simple procedure for constructing switching rule is also presented.

Global stability of stochastic high-order neural networks with discrete and distributed delays

International Nuclear Information System (INIS)

Wang Zidong; Fang Jianan; Liu Xiaohui

2008-01-01

High-order neural networks can be considered as an expansion of Hopfield neural networks, and have stronger approximation property, faster convergence rate, greater storage capacity, and higher fault tolerance than lower-order neural networks. In this paper, the global asymptotic stability analysis problem is considered for a class of stochastic high-order neural networks with discrete and distributed time-delays. Based on an Lyapunov-Krasovskii functional and the stochastic stability analysis theory, several sufficient conditions are derived, which guarantee the global asymptotic convergence of the equilibrium point in the mean square. It is shown that the stochastic high-order delayed neural networks under consideration are globally asymptotically stable in the mean square if two linear matrix inequalities (LMIs) are feasible, where the feasibility of LMIs can be readily checked by the Matlab LMI toolbox. It is also shown that the main results in this paper cover some recently published works. A numerical example is given to demonstrate the usefulness of the proposed global stability criteria

Improved Polynomial Fuzzy Modeling and Controller with Stability Analysis for Nonlinear Dynamical Systems

Directory of Open Access Journals (Sweden)

Hamed Kharrati

2012-01-01

Full Text Available This study presents an improved model and controller for nonlinear plants using polynomial fuzzy model-based (FMB systems. To minimize mismatch between the polynomial fuzzy model and nonlinear plant, the suitable parameters of membership functions are determined in a systematic way. Defining an appropriate fitness function and utilizing Taylor series expansion, a genetic algorithm (GA is used to form the shape of membership functions in polynomial forms, which are afterwards used in fuzzy modeling. To validate the model, a controller based on proposed polynomial fuzzy systems is designed and then applied to both original nonlinear plant and fuzzy model for comparison. Additionally, stability analysis for the proposed polynomial FMB control system is investigated employing Lyapunov theory and a sum of squares (SOS approach. Moreover, the form of the membership functions is considered in stability analysis. The SOS-based stability conditions are attained using SOSTOOLS. Simulation results are also given to demonstrate the effectiveness of the proposed method.

Improved Stabilization Conditions for Nonlinear Systems with Input and State Delays via T-S Fuzzy Model

Directory of Open Access Journals (Sweden)

Chang Che

2018-01-01

Full Text Available This paper focuses on the problem of nonlinear systems with input and state delays. The considered nonlinear systems are represented by Takagi-Sugeno (T-S fuzzy model. A new state feedback control approach is introduced for T-S fuzzy systems with input delay and state delays. A new Lyapunov-Krasovskii functional is employed to derive less conservative stability conditions by incorporating a recently developed Wirtinger-based integral inequality. Based on the Lyapunov stability criterion, a series of linear matrix inequalities (LMIs are obtained by using the slack variables and integral inequality, which guarantees the asymptotic stability of the closed-loop system. Several numerical examples are given to show the advantages of the proposed results.

New prediction of chaotic time series based on local Lyapunov exponent

International Nuclear Information System (INIS)

Zhang Yong

2013-01-01

A new method of predicting chaotic time series is presented based on a local Lyapunov exponent, by quantitatively measuring the exponential rate of separation or attraction of two infinitely close trajectories in state space. After reconstructing state space from one-dimensional chaotic time series, neighboring multiple-state vectors of the predicting point are selected to deduce the prediction formula by using the definition of the local Lyapunov exponent. Numerical simulations are carried out to test its effectiveness and verify its higher precision over two older methods. The effects of the number of referential state vectors and added noise on forecasting accuracy are also studied numerically. (general)

Robust H∞ Control for Singular Time-Delay Systems via Parameterized Lyapunov Functional Approach

Directory of Open Access Journals (Sweden)

Li-li Liu

2014-01-01

Full Text Available A new version of delay-dependent bounded real lemma for singular systems with state delay is established by parameterized Lyapunov-Krasovskii functional approach. In order to avoid generating nonconvex problem formulations in control design, a strategy that introduces slack matrices and decouples the system matrices from the Lyapunov-Krasovskii parameter matrices is used. Examples are provided to demonstrate that the results in this paper are less conservative than the existing corresponding ones in the literature.

ORIGINAL ARTICLE Stability Analysis of Delayed Cournot Model in ...

African Journals Online (AJOL)

HP

and Lyapunov method of nonlinear stability analysis are employed. It is ascertained ... and the rival player makes decision without delay, it leads to instability of the dynamic system at ... phenomena such as economic growth, prediction and ...

Lyapunov, singular and bred vectors in a multi-scale system: an empirical exploration of vectors related to instabilities

International Nuclear Information System (INIS)

Norwood, Adrienne; Kalnay, Eugenia; Ide, Kayo; Yang, Shu-Chih; Wolfe, Christopher

2013-01-01

imitating the tropical El Niño–Southern Oscillation. The bred vectors are able to separate the fast and slow modes of growth through appropriate selection of the breeding perturbation size and rescaling interval. The Lyapunov vectors are able to successfully separate the fast ‘extratropical atmosphere’, but are unable to completely decouple the ‘tropical atmosphere’ from the ‘ocean’. This leads to ‘coupled’ Lyapunov vectors that are mainly useful in the (slow) ‘ocean’ system, but are still affected by changes in the (fast) ‘tropical’ system. The singular vectors are excellent in capturing the fast modes, but are unable to capture the slow modes of growth. The dissimilar behavior of the three types of vectors leads to a degradation in the similarities of the subspaces they inhabit and affects their relative ability of representing the coupled modes. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (paper)

An equivalent condition for stability properties of Lotka-Volterra systems

International Nuclear Information System (INIS)

Chu Tianguang

2007-01-01

We give a solvable Lie algebraic condition for the equivalence of four typical stability notions (asymptotic stability, D-stability, total stability, and Volterra-Lyapunov stability) concerning Lotka-Volterra systems. Our approach makes use of the decomposition of the interaction matrix into symmetric and skew-symmetric parts, which may be related to the cooperative and competitive interaction pattern of a Lotka-Volterra system. The present result covers a known condition and can yield a larger set of interaction matrices for equivalence of the stability properties

Effect of asynchronous updating on the stability of cellular automata

International Nuclear Information System (INIS)

Baetens, J.M.; Van der Weeën, P.; De Baets, B.

2012-01-01

Highlights: ► An upper bound on the Lyapunov exponent of asynchronously updated CA is established. ► The employed update method has repercussions on the stability of CAs. ► A decision on the employed update method should be taken with care. ► Substantial discrepancies arise between synchronously and asynchronously updated CA. ► Discrepancies between different asynchronous update schemes are less pronounced. - Abstract: Although cellular automata (CAs) were conceptualized as utter discrete mathematical models in which the states of all their spatial entities are updated simultaneously at every consecutive time step, i.e. synchronously, various CA-based models that rely on so-called asynchronous update methods have been constructed in order to overcome the limitations that are tied up with the classical way of evolving CAs. So far, only a few researchers have addressed the consequences of this way of updating on the evolved spatio-temporal patterns, and the reachable stationary states. In this paper, we exploit Lyapunov exponents to determine to what extent the stability of the rules within a family of totalistic CAs is affected by the underlying update method. For that purpose, we derive an upper bound on the maximum Lyapunov exponent of asynchronously iterated CAs, and show its validity, after which we present a comparative study between the Lyapunov exponents obtained for five different update methods, namely one synchronous method and four well-established asynchronous methods. It is found that the stability of CAs is seriously affected if one of the latter methods is employed, whereas the discrepancies arising between the different asynchronous methods are far less pronounced and, finally, we discuss the repercussions of our findings on the development of CA-based models.

Using machine learning to replicate chaotic attractors and calculate Lyapunov exponents from data

Science.gov (United States)

Pathak, Jaideep; Lu, Zhixin; Hunt, Brian R.; Girvan, Michelle; Ott, Edward

2017-12-01

We use recent advances in the machine learning area known as "reservoir computing" to formulate a method for model-free estimation from data of the Lyapunov exponents of a chaotic process. The technique uses a limited time series of measurements as input to a high-dimensional dynamical system called a "reservoir." After the reservoir's response to the data is recorded, linear regression is used to learn a large set of parameters, called the "output weights." The learned output weights are then used to form a modified autonomous reservoir designed to be capable of producing an arbitrarily long time series whose ergodic properties approximate those of the input signal. When successful, we say that the autonomous reservoir reproduces the attractor's "climate." Since the reservoir equations and output weights are known, we can compute the derivatives needed to determine the Lyapunov exponents of the autonomous reservoir, which we then use as estimates of the Lyapunov exponents for the original input generating system. We illustrate the effectiveness of our technique with two examples, the Lorenz system and the Kuramoto-Sivashinsky (KS) equation. In the case of the KS equation, we note that the high dimensional nature of the system and the large number of Lyapunov exponents yield a challenging test of our method, which we find the method successfully passes.

Extending the length and time scales of Gram–Schmidt Lyapunov vector computations

Energy Technology Data Exchange (ETDEWEB)

Costa, Anthony B., E-mail: acosta@northwestern.edu [Department of Chemistry, Northwestern University, Evanston, IL 60208 (United States); Green, Jason R., E-mail: jason.green@umb.edu [Department of Chemistry, Northwestern University, Evanston, IL 60208 (United States); Department of Chemistry, University of Massachusetts Boston, Boston, MA 02125 (United States)

2013-08-01

Lyapunov vectors have found growing interest recently due to their ability to characterize systems out of thermodynamic equilibrium. The computation of orthogonal Gram–Schmidt vectors requires multiplication and QR decomposition of large matrices, which grow as N{sup 2} (with the particle count). This expense has limited such calculations to relatively small systems and short time scales. Here, we detail two implementations of an algorithm for computing Gram–Schmidt vectors. The first is a distributed-memory message-passing method using Scalapack. The second uses the newly-released MAGMA library for GPUs. We compare the performance of both codes for Lennard–Jones fluids from N=100 to 1300 between Intel Nahalem/Infiniband DDR and NVIDIA C2050 architectures. To our best knowledge, these are the largest systems for which the Gram–Schmidt Lyapunov vectors have been computed, and the first time their calculation has been GPU-accelerated. We conclude that Lyapunov vector calculations can be significantly extended in length and time by leveraging the power of GPU-accelerated linear algebra.

Edge state preparation in a one-dimensional lattice by quantum Lyapunov control

International Nuclear Information System (INIS)

Zhao, X L; Shi, Z C; Qin, M; Yi, X X

2017-01-01

Quantum Lyapunov control uses a feedback control methodology to determine control fields applied to control quantum systems in an open-loop way. In this work, we employ two Lyapunov control schemes to prepare an edge state for a fermionic chain consisting of cold atoms loaded in an optical lattice. Such a chain can be described by the Harper model. Corresponding to the two schemes, two types of quantum Lyapunov functions are considered. The results show that both the schemes are effective at preparing the edge state within a wide range of parameters. We found that the edge state can be prepared with high fidelity even if there are moderate fluctuations of on-site or hopping potentials. Both control schemes can be extended to similar chains (3 m + d , d = 2) of different lengths. Since a regular amplitude control field is easier to apply in practice, an amplitude-modulated control field is used to replace the unmodulated one. Such control approaches provide tools to explore the edge states of one-dimensional topological materials. (paper)

Extending the length and time scales of Gram–Schmidt Lyapunov vector computations

International Nuclear Information System (INIS)

Costa, Anthony B.; Green, Jason R.

2013-01-01

Lyapunov vectors have found growing interest recently due to their ability to characterize systems out of thermodynamic equilibrium. The computation of orthogonal Gram–Schmidt vectors requires multiplication and QR decomposition of large matrices, which grow as N 2 (with the particle count). This expense has limited such calculations to relatively small systems and short time scales. Here, we detail two implementations of an algorithm for computing Gram–Schmidt vectors. The first is a distributed-memory message-passing method using Scalapack. The second uses the newly-released MAGMA library for GPUs. We compare the performance of both codes for Lennard–Jones fluids from N=100 to 1300 between Intel Nahalem/Infiniband DDR and NVIDIA C2050 architectures. To our best knowledge, these are the largest systems for which the Gram–Schmidt Lyapunov vectors have been computed, and the first time their calculation has been GPU-accelerated. We conclude that Lyapunov vector calculations can be significantly extended in length and time by leveraging the power of GPU-accelerated linear algebra

Global exponential stability for nonautonomous cellular neural networks with delays

International Nuclear Information System (INIS)

Zhang Qiang; Wei Xiaopeng; Xu Jin

2006-01-01

In this Letter, by utilizing Lyapunov functional method and Halanay inequalities, we analyze global exponential stability of nonautonomous cellular neural networks with delay. Several new sufficient conditions ensuring global exponential stability of the network are obtained. The results given here extend and improve the earlier publications. An example is given to demonstrate the effectiveness of the obtained results

Neural networks for tracking of unknown SISO discrete-time nonlinear dynamic systems.

Science.gov (United States)

Aftab, Muhammad Saleheen; Shafiq, Muhammad

2015-11-01

This article presents a Lyapunov function based neural network tracking (LNT) strategy for single-input, single-output (SISO) discrete-time nonlinear dynamic systems. The proposed LNT architecture is composed of two feedforward neural networks operating as controller and estimator. A Lyapunov function based back propagation learning algorithm is used for online adjustment of the controller and estimator parameters. The controller and estimator error convergence and closed-loop system stability analysis is performed by Lyapunov stability theory. Moreover, two simulation examples and one real-time experiment are investigated as case studies. The achieved results successfully validate the controller performance. Copyright © 2015 ISA. Published by Elsevier Ltd. All rights reserved.

Local Dynamic Stability Assessment of Motion Impaired Elderly Using Electronic Textile Pants.

Science.gov (United States)

Liu, Jian; Lockhart, Thurmon E; Jones, Mark; Martin, Tom

2008-10-01

A clear association has been demonstrated between gait stability and falls in the elderly. Integration of wearable computing and human dynamic stability measures into home automation systems may help differentiate fall-prone individuals in a residential environment. The objective of the current study was to evaluate the capability of a pair of electronic textile (e-textile) pants system to assess local dynamic stability and to differentiate motion-impaired elderly from their healthy counterparts. A pair of e-textile pants comprised of numerous e-TAGs at locations corresponding to lower extremity joints was developed to collect acceleration, angular velocity and piezoelectric data. Four motion-impaired elderly together with nine healthy individuals (both young and old) participated in treadmill walking with a motion capture system simultaneously collecting kinematic data. Local dynamic stability, characterized by maximum Lyapunov exponent, was computed based on vertical acceleration and angular velocity at lower extremity joints for the measurements from both e-textile and motion capture systems. Results indicated that the motion-impaired elderly had significantly higher maximum Lyapunov exponents (computed from vertical acceleration data) than healthy individuals at the right ankle and hip joints. In addition, maximum Lyapunov exponents assessed by the motion capture system were found to be significantly higher than those assessed by the e-textile system. Despite the difference between these measurement techniques, attaching accelerometers at the ankle and hip joints was shown to be an effective sensor configuration. It was concluded that the e-textile pants system, via dynamic stability assessment, has the potential to identify motion-impaired elderly.

Electroweak vacuum stability in the Higgs-Dilaton theory

Energy Technology Data Exchange (ETDEWEB)

Shkerin, A. [Institute of Physics, Ecole Polytechnique Fédérale de Lausanne (EPFL),CH-1015, Lausanne (Switzerland); Institute for Nuclear Research of the Russian Academy of Sciences,60th October Anniversary prospect 7a, 117312, Moscow (Russian Federation)

2017-05-30

We study the stability of the Electroweak (EW) vacuum in a scale-invariant extension of the Standard Model and General Relativity, known as a Higgs-Dilaton theory. The safety of the EW vacuum against possible transition towards another vacuum is a necessary condition for the model to be phenomenologically acceptable. We find that, within a wide range of parameters of the theory, the decay rate is significantly suppressed compared to that of the Standard Model. We also discuss properties of a tunneling solution that are specific to the Higgs-Dilaton theory.

Stochastic Stability of Endogenous Growth: Theory and Applications

OpenAIRE

Boucekkine, Raouf; Pintus, Patrick; Zou, Benteng

2015-01-01

We examine the issue of stability of stochastic endogenous growth. First, stochastic stability concepts are introduced and applied to stochastic linear homogenous differen- tial equations to which several stochastic endogenous growth models reduce. Second, we apply the mathematical theory to two models, starting with the stochastic AK model. It’s shown that in this case exponential balanced paths, which characterize optimal trajectories in the absence of uncertainty, are not robust to uncerta...

Robust flow stability: Theory, computations and experiments in near wall turbulence

Science.gov (United States)

Bobba, Kumar Manoj

Helmholtz established the field of hydrodynamic stability with his pioneering work in 1868. From then on, hydrodynamic stability became an important tool in understanding various fundamental fluid flow phenomena in engineering (mechanical, aeronautics, chemical, materials, civil, etc.) and science (astrophysics, geophysics, biophysics, etc.), and turbulence in particular. However, there are many discrepancies between classical hydrodynamic stability theory and experiments. In this thesis, the limitations of traditional hydrodynamic stability theory are shown and a framework for robust flow stability theory is formulated. A host of new techniques like gramians, singular values, operator norms, etc. are introduced to understand the role of various kinds of uncertainty. An interesting feature of this framework is the close interplay between theory and computations. It is shown that a subset of Navier-Stokes equations are globally, non-nonlinearly stable for all Reynolds number. Yet, invoking this new theory, it is shown that these equations produce structures (vortices and streaks) as seen in the experiments. The experiments are done in zero pressure gradient transiting boundary layer on a flat plate in free surface tunnel. Digital particle image velocimetry, and MEMS based laser Doppler velocimeter and shear stress sensors have been used to make quantitative measurements of the flow. Various theoretical and computational predictions are in excellent agreement with the experimental data. A closely related topic of modeling, simulation and complexity reduction of large mechanics problems with multiple spatial and temporal scales is also studied. A nice method that rigorously quantifies the important scales and automatically gives models of the problem to various levels of accuracy is introduced. Computations done using spectral methods are presented.

Atmospheric stability modelling for nuclear emergency response systems using fuzzy set theory

International Nuclear Information System (INIS)

Walle, B. van de; Ruan, D.; Govaerts, P.

1993-01-01

A new approach to Pasquill stability classification is developed using fuzzy set theory, taking into account the natural continuity of the atmospheric stability and providing means to analyse the obtained stability classes. (2 figs.)

Differential algebras with remainder and rigorous proofs of long-term stability

International Nuclear Information System (INIS)

Berz, Martin

1997-01-01

It is shown how in addition to determining Taylor maps of general optical systems, it is possible to obtain rigorous interval bounds for the remainder term of the n-th order Taylor expansion. To this end, the three elementary operations of addition, multiplication, and differentiation in the Differential Algebraic approach are augmented by suitable interval operations in such a way that a remainder bound of the sum, product, and derivative is obtained from the Taylor polynomial and remainder bound of the operands. The method can be used to obtain bounds for the accuracy with which a Taylor map represents the true map of the particle optical system. In a more general sense, it is also useful for a variety of other numerical problems, including rigorous global optimization of highly complex functions. Combined with methods to obtain pseudo-invariants of repetitive motion and extensions of the Lyapunov- and Nekhoroshev stability theory, the latter can be used to guarantee stability for storage rings and other weakly nonlinear systems

Stability analysis for cellular neural networks with variable delays

International Nuclear Information System (INIS)

Zhang Qiang; Wei Xiaopeng; Xu Jin

2006-01-01

Some sufficient conditions for the global exponential stability of cellular neural networks with variable delay are obtained by means of a method based on delay differential inequality. The method, which does not make use of Lyapunov functionals, is simple and effective for the stability analysis of neural networks with delay. Some previously established results in the literature are shown to be special cases of the presented result

Stability of large scale interconnected dynamical systems

International Nuclear Information System (INIS)

Akpan, E.P.

1993-07-01

Large scale systems modelled by a system of ordinary differential equations are considered and necessary and sufficient conditions are obtained for the uniform asymptotic connective stability of the systems using the method of cone-valued Lyapunov functions. It is shown that this model significantly improves the existing models. (author). 9 refs

Almost sure exponential stability of stochastic fuzzy cellular neural networks with delays

International Nuclear Information System (INIS)

Zhao Hongyong; Ding Nan; Chen Ling

2009-01-01

This paper is concerned with the problem of exponential stability analysis for fuzzy cellular neural network with delays. By constructing suitable Lyapunov functional and using stochastic analysis we present some sufficient conditions ensuring almost sure exponential stability for the network. Moreover, an example is given to demonstrate the advantages of our method.

Hyperchaos of four state autonomous system with three positive Lyapunov exponents

International Nuclear Information System (INIS)

Ge Zhengming; Yang, C-H.

2009-01-01

This Letter gives the results of numerical simulations of Quantum Cellular Neural Network (Quantum-CNN) autonomous system with four state variables. Three positive Lyapunov exponents confirm hyperchaotic nature of its dynamics

Linear and nonlinear stability criteria for compressible MHD flows in a gravitational field

Science.gov (United States)

Moawad, S. M.; Moawad

2013-10-01

The equilibrium and stability properties of ideal magnetohydrodynamics (MHD) of compressible flow in a gravitational field with a translational symmetry are investigated. Variational principles for the steady-state equations are formulated. The MHD equilibrium equations are obtained as critical points of a conserved Lyapunov functional. This functional consists of the sum of the total energy, the mass, the circulation along field lines (cross helicity), the momentum, and the magnetic helicity. In the unperturbed case, the equilibrium states satisfy a nonlinear second-order partial differential equation (PDE) associated with hydrodynamic Bernoulli law. The PDE can be an elliptic or a parabolic equation depending on increasing the poloidal flow speed. Linear and nonlinear Lyapunov stability conditions under translational symmetric perturbations are established for the equilibrium states.

Breaking Dense Structures: Proving Stability of Densely Structured Hybrid Systems

Directory of Open Access Journals (Sweden)

Eike Möhlmann

2015-06-01

Full Text Available Abstraction and refinement is widely used in software development. Such techniques are valuable since they allow to handle even more complex systems. One key point is the ability to decompose a large system into subsystems, analyze those subsystems and deduce properties of the larger system. As cyber-physical systems tend to become more and more complex, such techniques become more appealing. In 2009, Oehlerking and Theel presented a (de-composition technique for hybrid systems. This technique is graph-based and constructs a Lyapunov function for hybrid systems having a complex discrete state space. The technique consists of (1 decomposing the underlying graph of the hybrid system into subgraphs, (2 computing multiple local Lyapunov functions for the subgraphs, and finally (3 composing the local Lyapunov functions into a piecewise Lyapunov function. A Lyapunov function can serve multiple purposes, e.g., it certifies stability or termination of a system or allows to construct invariant sets, which in turn may be used to certify safety and security. In this paper, we propose an improvement to the decomposing technique, which relaxes the graph structure before applying the decomposition technique. Our relaxation significantly reduces the connectivity of the graph by exploiting super-dense switching. The relaxation makes the decomposition technique more efficient on one hand and on the other allows to decompose a wider range of graph structures.

Stabilization of nonlinear systems using sampled-data output-feedback fuzzy controller based on polynomial-fuzzy-model-based control approach.

Science.gov (United States)

Lam, H K

2012-02-01

This paper investigates the stability of sampled-data output-feedback (SDOF) polynomial-fuzzy-model-based control systems. Representing the nonlinear plant using a polynomial fuzzy model, an SDOF fuzzy controller is proposed to perform the control process using the system output information. As only the system output is available for feedback compensation, it is more challenging for the controller design and system analysis compared to the full-state-feedback case. Furthermore, because of the sampling activity, the control signal is kept constant by the zero-order hold during the sampling period, which complicates the system dynamics and makes the stability analysis more difficult. In this paper, two cases of SDOF fuzzy controllers, which either share the same number of fuzzy rules or not, are considered. The system stability is investigated based on the Lyapunov stability theory using the sum-of-squares (SOS) approach. SOS-based stability conditions are obtained to guarantee the system stability and synthesize the SDOF fuzzy controller. Simulation examples are given to demonstrate the merits of the proposed SDOF fuzzy control approach.

Asymptotic stability results for retarded differential systems | Igobi ...

African Journals Online (AJOL)

... matrices are used in formulating a Lyapunov functional. The introduction of convex set segment of a symmetric matrix is explored to establish boundedness of the first derivative of the formulated functional. The integral-differential equation is utilized in computing the maximum delay interval for the system to attain stability.

Stability of Rotor Systems: A Complex Modelling Approach

DEFF Research Database (Denmark)

Kliem, Wolfhard; Pommer, Christian; Stoustrup, Jakob

1996-01-01

A large class of rotor systems can be modelled by a complex matrix differential equation of secondorder. The angular velocity of the rotor plays the role of a parameter. We apply the Lyapunov matrix equation in a complex setting and prove two new stability results which are compared...

Lyapunov exponent and criticality in the Hamiltonian mean field model

Science.gov (United States)

Filho, L. H. Miranda; Amato, M. A.; Rocha Filho, T. M.

2018-03-01

We investigate the dependence of the largest Lyapunov exponent (LLE) of an N-particle self-gravitating ring model at equilibrium with respect to the number of particles and its dependence on energy. This model has a continuous phase-transition from a ferromagnetic to homogeneous phase, and we numerically confirm with large scale simulations the existence of a critical exponent associated to the LLE, although at variance with the theoretical estimate. The existence of strong chaos in the magnetized state evidenced by a positive Lyapunov exponent is explained by the coupling of individual particle oscillations to the diffusive motion of the center of mass of the system and also results in a change of the scaling of the LLE with the number of particles. We also discuss thoroughly for the model the validity and limits of the approximations made by a geometrical model for their analytic estimate.

Stabilization and tracking controller for a class of nonlinear discrete-time systems

International Nuclear Information System (INIS)

Sharma, B.B.; Kar, I.N.

2011-01-01

Highlights: → We present recursive design of stabilizing controller for nonlinear discrete-time systems. → Problem of stabilizing and tracking control of single link manipulator system is addressed. → We extend the proposed results to output tracking problems. → The proposed methodology is applied satisfactorily to discrete-time chaotic maps. - Abstract: In this paper, stabilization and tracking control problem for parametric strict feedback class of discrete time systems is addressed. Recursive design of control function based on contraction theory framework is proposed instead of traditional Lyapunov based method. Explicit structure of controller is derived for the addressed class of nonlinear discrete-time systems. Conditions for exponential stability of system states are derived in terms of controller parameters. At each stage of recursive procedure a specific structure of Jacobian matrix is ensured so as to satisfy conditions of stability. The closed loop dynamics in this case remains nonlinear in nature. The proposed algorithm establishes global stability results in quite a simple manner as it does not require formulation of error dynamics. Problem of stabilization and output tracking control in case of single link manipulator system with actuator dynamics is analyzed using the proposed strategy. The proposed results are further extended to stabilization of discrete time chaotic systems. Numerical simulations presented in the end show the effectiveness of the proposed approach.

Stability analysis of linear switching systems with time delays

International Nuclear Information System (INIS)

Li Ping; Zhong Shouming; Cui Jinzhong

2009-01-01

The issue of stability analysis of linear switching system with discrete and distributed time delays is studied in this paper. An appropriate switching rule is applied to guarantee the stability of the whole switching system. Our results use a Riccati-type Lyapunov functional under a condition on the time delay. So, switching systems with mixed delays are developed. A numerical example is given to illustrate the effectiveness of our results.

MPC for LPV Systems Based on Parameter-Dependent Lyapunov Function with Perturbation on Control Input Strategy

Directory of Open Access Journals (Sweden)

Pornchai Bumroongsri

2012-04-01

Full Text Available In this paper, the model predictive control (MPC algorithm for linear parameter varying (LPV systems is proposed. The proposed algorithm consists of two steps. The first step is derived by using parameter-dependent Lyapunov function and the second step is derived by using the perturbation on control input strategy. In order to achieve good control performance, the bounds on the rate of variation of the parameters are taken into account in the controller synthesis. An overall algorithm is proved to guarantee robust stability. The controller design is illustrated with two case studies of continuous stirred-tank reactors. Comparisons with other MPC algorithms for LPV systems have been undertaken. The results show that the proposed algorithm can achieve better control performance.

Lyapunov functions for a dengue disease transmission model

International Nuclear Information System (INIS)

Tewa, Jean Jules; Dimi, Jean Luc; Bowong, Samuel

2009-01-01

In this paper, we study a model for the dynamics of dengue fever when only one type of virus is present. For this model, Lyapunov functions are used to show that when the basic reproduction ratio is less than or equal to one, the disease-free equilibrium is globally asymptotically stable, and when it is greater than one there is an endemic equilibrium which is also globally asymptotically stable.

Lyapunov functions for a dengue disease transmission model

Energy Technology Data Exchange (ETDEWEB)

Tewa, Jean Jules [Department of Mathematics, Faculty of Science, University of Yaounde I, P.O. Box 812, Yaounde (Cameroon)], E-mail: tewa@univ-metz.fr; Dimi, Jean Luc [Department of Mathematics, Faculty of Science, University Marien Ngouabi, P.O. Box 69, Brazzaville (Congo, The Democratic Republic of the)], E-mail: jldimi@yahoo.fr; Bowong, Samuel [Department of Mathematics and Computer Science, Faculty of Science, University of Douala, P.O. Box 24157, Douala (Cameroon)], E-mail: samuelbowong@yahoo.fr

2009-01-30

In this paper, we study a model for the dynamics of dengue fever when only one type of virus is present. For this model, Lyapunov functions are used to show that when the basic reproduction ratio is less than or equal to one, the disease-free equilibrium is globally asymptotically stable, and when it is greater than one there is an endemic equilibrium which is also globally asymptotically stable.

Stabilization with guaranteed safety using Control Lyapunov–Barrier Function

NARCIS (Netherlands)

Romdlony, Muhammad Zakiyullah; Jayawardhana, Bayu

2016-01-01

We propose a novel nonlinear control method for solving the problem of stabilization with guaranteed safety for nonlinear systems. The design is based on the merging of the well-known Control Lyapunov Function (CLF) and the recent concept of Control Barrier Function (CBF). The proposed control

Stability, causality, and hyperbolicity in Carter's ''regular'' theory of relativistic heat-conducting fluids

International Nuclear Information System (INIS)

Olson, T.S.; Hiscock, W.A.

1990-01-01

Stability and causality are studied for linear perturbations about equilibrium in Carter's ''regular'' theory of relativistic heat-conducting fluids. The ''regular'' theory, when linearized around an equilibrium state having vanishing expansion and shear, is shown to be equivalent to the inviscid limit of the linearized Israel-Stewart theory of relativistic dissipative fluids for a particular choice of the second-order coefficients β 1 and γ 2 . A set of stability conditions is determined for linear perturbations of a general inviscid Israel-Stewart fluid using a monotonically decreasing energy functional. It is shown that, as in the viscous case, stability implies that the characteristic velocities are subluminal and that perturbations obey hyperbolic equations. The converse theorem is also true. We then apply this analysis to a nonrelativistic Boltzmann gas and to a strongly degenerate free Fermi gas in the ''regular'' theory. Carter's ''regular'' theory is shown to be incapable of correctly describing the nonrelativistic Boltzmann gas and the degenerate Fermi gas (at all temperatures)

A remark on the stability and boundedness criteria in retarded Volterra integro-differential equations

Directory of Open Access Journals (Sweden)

Cemil Tunç

2017-10-01

Full Text Available In this article, the authors obtain some clear assumptions for the asymptotic stability (AS and boundedness (B of solutions of non-linear retarded Volterra integro-differential equations (VIDEs of first order by constructing a new Lyapunov functional (LF. The results obtained are new and differ from those found in the literature, and they also contain and improve a result found in the literature under more less restrictive conditions. We establish an example and give a discussion to indicate the applicability of the weaker conditions obtained. We also employ MATLAB-Simulink to display the behaviors of the orbits of the (VIDEs considered. Keywords: Nonlinear, Volterra integro-differential equations, First order, Asymptotic stability, Boundedness, Lyapunov functional, MSC: 34D05, 34K20, 45J05

Lyapunov exponent as a metric for assessing the dynamic content and predictability of large-eddy simulations

Science.gov (United States)

Nastac, Gabriel; Labahn, Jeffrey W.; Magri, Luca; Ihme, Matthias

2017-09-01

Metrics used to assess the quality of large-eddy simulations commonly rely on a statistical assessment of the solution. While these metrics are valuable, a dynamic measure is desirable to further characterize the ability of a numerical simulation for capturing dynamic processes inherent in turbulent flows. To address this issue, a dynamic metric based on the Lyapunov exponent is proposed which assesses the growth rate of the solution separation. This metric is applied to two turbulent flow configurations: forced homogeneous isotropic turbulence and a turbulent jet diffusion flame. First, it is shown that, despite the direct numerical simulation (DNS) and large-eddy simulation (LES) being high-dimensional dynamical systems with O (107) degrees of freedom, the separation growth rate qualitatively behaves like a lower-dimensional dynamical system, in which the dimension of the Lyapunov system is substantially smaller than the discretized dynamical system. Second, a grid refinement analysis of each configuration demonstrates that as the LES filter width approaches the smallest scales of the system the Lyapunov exponent asymptotically approaches a plateau. Third, a small perturbation is superimposed onto the initial conditions of each configuration, and the Lyapunov exponent is used to estimate the time required for divergence, thereby providing a direct assessment of the predictability time of simulations. By comparing inert and reacting flows, it is shown that combustion increases the predictability of the turbulent simulation as a result of the dilatation and increased viscosity by heat release. The predictability time is found to scale with the integral time scale in both the reacting and inert jet flows. Fourth, an analysis of the local Lyapunov exponent is performed to demonstrate that this metric can also determine flow-dependent properties, such as regions that are sensitive to small perturbations or conditions of large turbulence within the flow field. Finally

Stability Analysis and Stabilization of T-S Fuzzy Delta Operator Systems with Time-Varying Delay via an Input-Output Approach

Directory of Open Access Journals (Sweden)

Zhixiong Zhong

2013-01-01

Full Text Available The stability analysis and stabilization of Takagi-Sugeno (T-S fuzzy delta operator systems with time-varying delay are investigated via an input-output approach. A model transformation method is employed to approximate the time-varying delay. The original system is transformed into a feedback interconnection form which has a forward subsystem with constant delays and a feedback one with uncertainties. By applying the scaled small gain (SSG theorem to deal with this new system, and based on a Lyapunov Krasovskii functional (LKF in delta operator domain, less conservative stability analysis and stabilization conditions are obtained. Numerical examples are provided to illustrate the advantages of the proposed method.

The brief time-reversibility of the local Lyapunov exponents for a small chaotic Hamiltonian system

International Nuclear Information System (INIS)

Waldner, Franz; Hoover, William G.; Hoover, Carol G.

2014-01-01

Highlights: •We consider the local Lyapunov spectrum for a four-dimensional Hamilton system. •Its stable periodic motion can be reversed for long times. •In the chaotic motion, time reversal occurs only for a short time. •Perturbations will change this short unstable case into a different stable case. •These observations might relate chaos to the Second Law of Thermodynamics. - Abstract: We consider the local (instantaneous) Lyapunov spectrum for a four-dimensional Hamiltonian system. Its stable periodic motion can be reversed for long times. Its unstable chaotic motion, with two symmetric pairs of exponents, cannot. In the latter case reversal occurs for more than a thousand fourth-order Runge–Kutta time steps, followed by a transition to a new set of paired Lyapunov exponents, unrelated to those seen in the forward time direction. The relation of the observed chaotic dynamics to the Second Law of Thermodynamics is discussed

Computation of the Lyapunov exponents in the compass-gait model under OGY control via a hybrid Poincaré map

International Nuclear Information System (INIS)

Gritli, Hassène; Belghith, Safya

2015-01-01

Highlights: • A numerical calculation method of the Lyapunov exponents in the compass-gait model under OGY control is proposed. • A new linearization method of the impulsive hybrid dynamics around a one-periodic hybrid limit cycle is achieved. • We develop a simple analytical expression of a controlled hybrid Poincaré map. • A dimension reduction of the hybrid Poincaré map is realized. • We describe the numerical computation procedure of the Lyapunov exponents via the designed hybrid Poincaré map. - Abstract: This paper aims at providing a numerical calculation method of the spectrum of Lyapunov exponents in a four-dimensional impulsive hybrid nonlinear dynamics of a passive compass-gait model under the OGY control approach by means of a controlled hybrid Poincaré map. We present a four-dimensional simplified analytical expression of such hybrid map obtained by linearizing the uncontrolled impulsive hybrid nonlinear dynamics around a desired one-periodic passive hybrid limit cycle. In order to compute the spectrum of Lyapunov exponents, a dimension reduction of the controlled hybrid Poincaré map is realized. The numerical calculation of the spectrum of Lyapunov exponents using the reduced-dimension controlled hybrid Poincaré map is given in detail. In order to show the effectiveness of the developed method, the spectrum of Lyapunov exponents is calculated as the slope (bifurcation) parameter varies and hence used to predict the walking dynamics behavior of the compass-gait model under the OGY control.

Complex dynamics of a new 3D Lorenz-type autonomous chaotic ...

Indian Academy of Sciences (India)

Newautonomous chaotic system; chaotic attractors; Lyapunov stability theory; ultimate ... College of Mathematics and Statistics, Chongqing Technology and Business ... College of Electronic and Information Engineering, Southwest University, ...

Hyperbolicity and integral expression of the Lyapunov exponents for linear cocycles

Science.gov (United States)

Dai, Xiongping

Consider in this paper a linear skew-product system (θ,Θ) :T×W×R→W×R; (t,w,x)↦(tw,Θ(t,w)ṡx) where T=R or Z, and θ :(t,w)↦tw is a topological dynamical system on a compact metrizable space W, and where Θ(t,w)∈GL(n,R) satisfies the cocycle condition based on θ and is continuously differentiable in t if T=R. We show that 'semi λ-exponential dichotomy' of (θ,Θ) implies ' λ-exponential dichotomy.' Precisely, if Θ has no Lyapunov exponent λ and is almost uniformly λ-contracting along the λ-stable direction E(w;λ) and if dimE(w;λ) is constant a.e., then Θ is almost λ-exponentially dichotomous. To prove this, we first use Liao's spectrum theorem, which gives integral expression of the Lyapunov exponents, and then use the semi-uniform ergodic theorem by Sturman and Stark, which allows one to derive uniform estimates from nonuniform ones. As a consequence, we obtain the open-and-dense hyperbolicity of eventual GL(2,R)-cocycles based on a uniquely ergodic endomorphism, and of GL(2,R)-cocycles based on a uniquely ergodic equi-continuous endomorphism, respectively. On the other hand, in the sense of C-topology we obtain the density of SL(2,R)-cocycles having positive Lyapunov exponent based on a minimal subshift satisfying the Boshernitzan condition.

Improved result on stability analysis of discrete stochastic neural networks with time delay

International Nuclear Information System (INIS)

Wu Zhengguang; Su Hongye; Chu Jian; Zhou Wuneng

2009-01-01

This Letter investigates the problem of exponential stability for discrete stochastic time-delay neural networks. By defining a novel Lyapunov functional, an improved delay-dependent exponential stability criterion is established in terms of linear matrix inequality (LMI) approach. Meanwhile, the computational complexity of the newly established stability condition is reduced because less variables are involved. Numerical example is given to illustrate the effectiveness and the benefits of the proposed method.

Robust uniform persistence in discrete and continuous dynamical systems using Lyapunov exponents.

Science.gov (United States)

Salceanu, Paul L

2011-07-01

This paper extends the work of Salceanu and Smith [12, 13] where Lyapunov exponents were used to obtain conditions for uniform persistence ina class of dissipative discrete-time dynamical systems on the positive orthant of R(m), generated by maps. Here a united approach is taken, for both discrete and continuous time, and the dissipativity assumption is relaxed. Sufficient conditions are given for compact subsets of an invariant part of the boundary of R(m+) to be robust uniform weak repellers. These conditions require Lyapunov exponents be positive on such sets. It is shown how this leads to robust uniform persistence. The results apply to the investigation of robust uniform persistence of the disease in host populations, as shown in an application.

Design of Connectivity Preserving Flocking Using Control Lyapunov Function

OpenAIRE

Erfianto, Bayu; Bambang, Riyanto T.; Hindersah, Hilwadi; Muchtadi-Alamsyah, Intan

2016-01-01

This paper investigates cooperative flocking control design with connectivity preserving mechanism. During flocking, interagent distance is measured to determine communication topology of the flocks. Then, cooperative flocking motion is built based on cooperative artificial potential field with connectivity preserving mechanism to achieve the common flocking objective. The flocking control input is then obtained by deriving cooperative artificial potential field using control Lyapunov functio...

ON THE BOUNDEDNESS AND THE STABILITY OF SOLUTION TO THIRD ORDER NON-LINEAR DIFFERENTIAL EQUATIONS

Institute of Scientific and Technical Information of China (English)

无

2008-01-01

In this paper we investigate the global asymptotic stability,boundedness as well as the ultimate boundedness of solutions to a general third order nonlinear differential equation,using complete Lyapunov function.

Phase stability of random brasses: pseudopotential theory revisited

International Nuclear Information System (INIS)

Rahman, S.M.M.

1987-06-01

We review the theoretical development concerning the phase stability of random brasses. The introductory discussion of the subject embraces the rules of metallurgy in general, but we emphasize on the roles of electron-per-atom ratio in the major bulk of our discussion. Starting from the so-called rigid-band model the discussion goes up to the recent higher-order pseudopotential theory. The theoretical refinements within the pseudopotential framework are discussed briefly. The stability criteria of the random phases are analysed both in the static lattice and dynamic lattice approximations. (author). 71 refs, figs and tabs

Stability and chaos of LMSER PCA learning algorithm

International Nuclear Information System (INIS)

Lv Jiancheng; Y, Zhang

2007-01-01

LMSER PCA algorithm is a principal components analysis algorithm. It is used to extract principal components on-line from input data. The algorithm has both stability and chaotic dynamic behavior under some conditions. This paper studies the local stability of the LMSER PCA algorithm via a corresponding deterministic discrete time system. Conditions for local stability are derived. The paper also explores the chaotic behavior of this algorithm. It shows that the LMSER PCA algorithm can produce chaos. Waveform plots, Lyapunov exponents and bifurcation diagrams are presented to illustrate the existence of chaotic behavior of this algorithm

Preservation of stability and synchronization in nonlinear systems

International Nuclear Information System (INIS)

Fernandez-Anaya, G.; Flores-Godoy, J.J.; Femat, R.; Alvarez-Ramirez, J.J.

2007-01-01

Preservation of stability in the presence of structural and/or parametric changes is an important issue in the study of dynamical systems. A specific case is the synchronization of chaos in complex networks where synchronization should be preserved in spite of changes in the network parameters and connectivity. In this work, a methodology to establish conditions for preservation of stability in a class of dynamical system is given in terms of Lyapunov methods. The idea is to construct a group of dynamical transformations under which stability is retained along certain manifolds. Some synchronization examples illustrate the results

Preservation of stability and synchronization in nonlinear systems

Energy Technology Data Exchange (ETDEWEB)

Fernandez-Anaya, G. [Departamento de Fisica y Matematicas, Universidad Iberoamericana, Prol. Paseo de la Reforma 880, Lomas de Santa Fe, Mexico, D.F. 01210 (Mexico)], E-mail: guillermo.fernandez@uia.mx; Flores-Godoy, J.J. [Departamento de Fisica y Matematicas, Universidad Iberoamericana, Prol. Paseo de la Reforma 880, Lomas de Santa Fe, Mexico, D.F. 01210 (Mexico)], E-mail: job.flores@uia.mx; Femat, R. [Division de Matematicas Aplicadas y Sistemas Computacionales, IPICyT, Camino a la Presa San Jose 2055, Col. Lomas 4a. seccion, San Luis Potosi, San Luis Potosi 78216 (Mexico)], E-mail: rfemat@ipicyt.edu.mx; Alvarez-Ramirez, J.J. [Ingenieria de Procesos e Hidraulica, Universidad Autonoma Metropolitana-Iztapalapa, Av. San Rafael Atlixco 186, Col. Vicentina, Mexico, D.F. 09340 (Mexico)], E-mail: jjar@xanum.uam.mx

2007-11-12

Preservation of stability in the presence of structural and/or parametric changes is an important issue in the study of dynamical systems. A specific case is the synchronization of chaos in complex networks where synchronization should be preserved in spite of changes in the network parameters and connectivity. In this work, a methodology to establish conditions for preservation of stability in a class of dynamical system is given in terms of Lyapunov methods. The idea is to construct a group of dynamical transformations under which stability is retained along certain manifolds. Some synchronization examples illustrate the results.

Integrator backstepping using contraction theory: a brief technological note

DEFF Research Database (Denmark)

Jouffroy, Jerome; Lottin, Jacques

While the use of Lyapunov function candidates for integrator backstepping has been extensively studied in the literature, little research has been conducted regarding the applicability of the so-called incremental stability approaches. This note addresses the problem of the use of an incremental ...

Espectro de Lyapunov de un Oscilador Colpitts en Base Común

Directory of Open Access Journals (Sweden)

Camilo Andrés Florez

2013-09-01

Full Text Available En el presente documento se presenta la definición de exponentes de Lyapunov de un sistema autónomo no lineal de tiempo continuo y una técnica recomendada para medir dicho conjunto de exponentes (espectro, con la finalidad de detectar la existencia de ciclos límites o de caos en un circuito oscilador Colpitts implementado con un transistor BJT. A partir del modelo de Ebers-Möll del transistor BJT se derivaron las ecuaciones de estado que rigen al circuito, luego se adoptó un caso numérico de estudio, y mediante el uso de un programa de simulación matemática se aplicó la metodología propuesta para determinar el espectro de Lyapunov del oscilador. Los resultados obtenidos evidencian la existencia de caos para algunos conjuntos de valores de los parámetros del circuito.

On a program manifold's stability of one contour automatic control systems

Science.gov (United States)

Zumatov, S. S.

2017-12-01

Methodology of analysis of stability is expounded to the one contour systems automatic control feedback in the presence of non-linearities. The methodology is based on the use of the simplest mathematical models of the nonlinear controllable systems. Stability of program manifolds of one contour automatic control systems is investigated. The sufficient conditions of program manifold's absolute stability of one contour automatic control systems are obtained. The Hurwitz's angle of absolute stability was determined. The sufficient conditions of program manifold's absolute stability of control systems by the course of plane in the mode of autopilot are obtained by means Lyapunov's second method.

Generalized Synchronization of Nonlinear Chaotic Systems through Natural Bioinspired Controlling Strategy

Directory of Open Access Journals (Sweden)

Shih-Yu Li

2015-01-01

Full Text Available A novel bioinspired control strategy design is proposed for generalized synchronization of nonlinear chaotic systems, combining the bioinspired stability theory, fuzzy modeling, and a novel, simple-form Lyapunov control function design of derived high efficient, heuristic and bioinspired controllers. Three main contributions are concluded: (1 apply the bioinspired stability theory to further analyze the stability of fuzzy error systems; the high performance of controllers has been shown in previous study by Li and Ge 2009, (2 a new Lyapunov control function based on bioinspired stability theory is designed to achieve synchronization without using traditional LMI method, which is a simple linear homogeneous function of states and the process of designing controller to synchronize two fuzzy chaotic systems becomes much simpler, and (3 three different situations of synchronization are proposed; classical master and slave Lorenz systems, slave Chen’s system, and Rossler’s system as functional system are illustrated to further show the effectiveness and feasibility of our novel strategy. The simulation results show that our novel control strategy can be applied to different and complicated control situations with high effectiveness.

Nonlinear stability of Gardner breathers

Science.gov (United States)

Alejo, Miguel A.

2018-01-01

We show that breather solutions of the Gardner equation, a natural generalization of the KdV and mKdV equations, are H2 (R) stable. Through a variational approach, we characterize Gardner breathers as minimizers of a new Lyapunov functional and we study the associated spectral problem, through (i) the analysis of the spectrum of explicit linear systems (spectral stability), and (ii) controlling degenerated directions by using low regularity conservation laws.

Intelligent robust control law for induction motors based on field-oriented control theory

Energy Technology Data Exchange (ETDEWEB)

Barambones, O.; Alcorta, P.; Sevillano, G.; Garrido, A.; Garrido, I. [Univ. del Pais Vasco, Bilbao (Spain). Dpto. Ingenieri a de Sistemas y Automatica

2009-07-01

A sensorless adaptive control law was developed to improve the trajectory tracking performance of induction motors. The law used an integral sliding mode algorithm to avoid the necessity of calculating an upper bound for system uncertainties. The vector control theory was used to develop the induction motor drives. The sliding mode control law incorporated an adaptive switching gain and included a method of estimating rotor speeds. Rotor speed estimation errors were presented as a first order simple function based on the difference between real stator currents and estimated stator currents. The Lyapunov stability theory was used to analyze the controller under different load disturbances and parameter uncertainties. Results of the study showed that the control signal of the scheme was smaller than signals obtained using traditional variable structure control schemes. It was concluded that speed tracking objectives can be obtained under various parameter and torque uncertainties. 9 refs., 7 figs.

Lyapunov stability of large systems of van der Pol-like oscillators and connection with turbulence and fluctuations spectra

International Nuclear Information System (INIS)

Tasso, H.

1993-04-01

For a system of van der Pol-like oscillators, Lyapunov functions valid in the greater part of phase space are given. They allow a finite region of attraction to be defined. Any attractor has to be within the rigorously estimated bounds. Under a special choice of the interaction matrices the attractive region can be squeezed to zero. In this case the asymptotic behaviour is given by a conservative system of nonlinear oscillators which acts as attractor. Though this system does not possess, in general, a Hamiltonian formulation, Gibbs statistics is possible due to the proof of a Liouville theorem and the existence of a positive invariant or 'shell' condition. The 'canonical' distribution on the attractor is remarkably simple despite nonlinearities. Finally the connection of the van der Pol-like system and of the attractive region with turbulence and fluctuation spectra in fluids and plasmas is discussed. (orig.)

Stability of abstract nonlinear nonautonomous differential-delay equations with unbounded history-responsive operators

Science.gov (United States)

Gil', M. I.

2005-08-01

We consider a class of nonautonomous functional-differential equations in a Banach space with unbounded nonlinear history-responsive operators, which have the local Lipshitz property. Conditions for the boundedness of solutions, Lyapunov stability, absolute stability and input-output one are established. Our approach is based on a combined usage of properties of sectorial operators and spectral properties of commuting operators.

Nonlinear stability research on the hydraulic system of double-side rolling shear

Science.gov (United States)

Wang, Jun; Huang, Qingxue; An, Gaocheng; Qi, Qisong; Sun, Binyu

2015-10-01

This paper researches the stability of the nonlinear system taking the hydraulic system of double-side rolling shear as an example. The hydraulic system of double-side rolling shear uses unsymmetrical electro-hydraulic proportional servo valve to control the cylinder with single piston rod, which can make best use of the space and reduce reversing shock. It is a typical nonlinear structure. The nonlinear state-space equations of the unsymmetrical valve controlling cylinder system are built first, and the second Lyapunov method is used to evaluate its stability. Second, the software AMEsim is applied to simulate the nonlinear system, and the results indicate that the system is stable. At last, the experimental results show that the system unsymmetrical valve controlling the cylinder with single piston rod is stable and conforms to what is deduced by theoretical analysis and simulation. The construction and application of Lyapunov function not only provide the theoretical basis for using of unsymmetrical valve controlling cylinder with single piston rod but also develop a new thought for nonlinear stability evaluation.

NL(q) Theory: A Neural Control Framework with Global Asymptotic Stability Criteria.

Science.gov (United States)

Vandewalle, Joos; De Moor, Bart L.R.; Suykens, Johan A.K.

1997-06-01

In this paper a framework for model-based neural control design is presented, consisting of nonlinear state space models and controllers, parametrized by multilayer feedforward neural networks. The models and closed-loop systems are transformed into so-called NL(q) system form. NL(q) systems represent a large class of nonlinear dynamical systems consisting of q layers with alternating linear and static nonlinear operators that satisfy a sector condition. For such NL(q)s sufficient conditions for global asymptotic stability, input/output stability (dissipativity with finite L(2)-gain) and robust stability and performance are presented. The stability criteria are expressed as linear matrix inequalities. In the analysis problem it is shown how stability of a given controller can be checked. In the synthesis problem two methods for neural control design are discussed. In the first method Narendra's dynamic backpropagation for tracking on a set of specific reference inputs is modified with an NL(q) stability constraint in order to ensure, e.g., closed-loop stability. In a second method control design is done without tracking on specific reference inputs, but based on the input/output stability criteria itself, within a standard plant framework as this is done, for example, in H( infinity ) control theory and &mgr; theory. Copyright 1997 Elsevier Science Ltd.

On the stability of the asymptotically free scalar field theories

Energy Technology Data Exchange (ETDEWEB)

Shalaby, A M. [Department of Mathematics, Statistics and Physics, College of Arts and Sciences, Qatar University, Doha (Qatar); Physics Department, Faculty of Science, Mansoura University, Egypt. amshalab@qu.edu.qa (Egypt)

2015-03-30

Asymptotic freedom plays a vital role in our understanding of the theory of particle interactions. To have this property, one has to resort to a Non-abelian gauge theory with the number of colors equal to or greater than three (QCD). However, recent studies have shown that simple scalar field theories can possess this interesting property. These theories have non-Hermitian effective field forms but their classical potentials are bounded from above. In this work, we shall address the stability of the vacua of the bounded from above (−Φ{sup 4+n}) scalar field theories. Moreover, we shall cover the effect of the distribution of the Stokes wedges in the complex Φ-plane on the features of the vacuum condensate within these theories.

Complexity dynamics and Hopf bifurcation analysis based on the first Lyapunov coefficient about 3D IS-LM macroeconomics system

Science.gov (United States)

Ma, Junhai; Ren, Wenbo; Zhan, Xueli

2017-04-01

Based on the study of scholars at home and abroad, this paper improves the three-dimensional IS-LM model in macroeconomics, analyzes the equilibrium point of the system and stability conditions, focuses on the parameters and complex dynamic characteristics when Hopf bifurcation occurs in the three-dimensional IS-LM macroeconomics system. In order to analyze the stability of limit cycles when Hopf bifurcation occurs, this paper further introduces the first Lyapunov coefficient to judge the limit cycles, i.e. from a practical view of the business cycle. Numerical simulation results show that within the range of most of the parameters, the limit cycle of 3D IS-LM macroeconomics is stable, that is, the business cycle is stable; with the increase of the parameters, limit cycles becomes unstable, and the value range of the parameters in this situation is small. The research results of this paper have good guide significance for the analysis of macroeconomics system.

Advanced Lyapunov control of a novel laser beam tracking system

Science.gov (United States)

Nikulin, Vladimir V.; Sofka, Jozef; Skormin, Victor A.

2005-05-01

Laser communication systems developed for mobile platforms, such as satellites, aircraft, and terrain vehicles, require fast wide-range beam-steering devices to establish and maintain a communication link. Conventionally, the low-bandwidth, high-steering-range part of the beam-positioning task is performed by gimbals that inherently constitutes the system bottleneck in terms of reliability, accuracy and dynamic performance. Omni-WristTM, a novel robotic sensor mount capable of carrying a payload of 5 lb and providing a full 180-deg hemisphere of azimuth/declination motion is known to be free of most of the deficiencies of gimbals. Provided with appropriate controls, it has the potential to become a new generation of gimbals systems. The approach we demonstrate describes an adaptive controller enabling Omni-WristTM to be utilized as a part of a laser beam positioning system. It is based on a Lyapunov function that ensures global asymptotic stability of the entire system while achieving high tracking accuracy. The proposed scheme is highly robust, does not require knowledge of complex system dynamics, and facilitates independent control of each channel by full decoupling of the Omni-WristTM dynamics. We summarize the basic algorithm and demonstrate the results obtained in the simulation environment.

Global robust stability of delayed recurrent neural networks

International Nuclear Information System (INIS)

Cao Jinde; Huang Deshuang; Qu Yuzhong

2005-01-01

This paper is concerned with the global robust stability of a class of delayed interval recurrent neural networks which contain time-invariant uncertain parameters whose values are unknown but bounded in given compact sets. A new sufficient condition is presented for the existence, uniqueness, and global robust stability of equilibria for interval neural networks with time delays by constructing Lyapunov functional and using matrix-norm inequality. An error is corrected in an earlier publication, and an example is given to show the effectiveness of the obtained results

Lyapunov exponents for infinite dimensional dynamical systems

Science.gov (United States)

Mhuiris, Nessan Mac Giolla

1987-01-01

Classically it was held that solutions to deterministic partial differential equations (i.e., ones with smooth coefficients and boundary data) could become random only through one mechanism, namely by the activation of more and more of the infinite number of degrees of freedom that are available to such a system. It is only recently that researchers have come to suspect that many infinite dimensional nonlinear systems may in fact possess finite dimensional chaotic attractors. Lyapunov exponents provide a tool for probing the nature of these attractors. This paper examines how these exponents might be measured for infinite dimensional systems.

Global chaos synchronization of coupled parametrically excited ...

Indian Academy of Sciences (India)

In this paper, we study the synchronization behaviour of two linearly coupled parametrically excited chaotic pendula. The stability of the synchronized state is examined using Lyapunov stability theory and linear matrix inequality (LMI); and some sufficient criteria for global asymptotic synchronization are derived from which ...

Stability analysis of impulsive parabolic complex networks

Energy Technology Data Exchange (ETDEWEB)

Wang Jinliang, E-mail: wangjinliang1984@yahoo.com.cn [Science and Technology on Aircraft Control Laboratory, School of Automation Science and Electrical Engineering, Beihang University, XueYuan Road, No. 37, HaiDian District, Beijing 100191 (China); Wu Huaining [Science and Technology on Aircraft Control Laboratory, School of Automation Science and Electrical Engineering, Beihang University, XueYuan Road, No. 37, HaiDian District, Beijing 100191 (China)

2011-11-15

Highlights: > Two impulsive parabolic complex network models are proposed. > The global exponential stability of impulsive parabolic complex networks are considered. > The robust global exponential stability of impulsive parabolic complex networks are considered. - Abstract: In the present paper, two kinds of impulsive parabolic complex networks (IPCNs) are considered. In the first one, all nodes have the same time-varying delay. In the second one, different nodes have different time-varying delays. Using the Lyapunov functional method combined with the inequality techniques, some global exponential stability criteria are derived for the IPCNs. Furthermore, several robust global exponential stability conditions are proposed to take uncertainties in the parameters of the IPCNs into account. Finally, numerical simulations are presented to illustrate the effectiveness of the results obtained here.

Stability analysis of impulsive parabolic complex networks

International Nuclear Information System (INIS)

Wang Jinliang; Wu Huaining

2011-01-01

Highlights: → Two impulsive parabolic complex network models are proposed. → The global exponential stability of impulsive parabolic complex networks are considered. → The robust global exponential stability of impulsive parabolic complex networks are considered. - Abstract: In the present paper, two kinds of impulsive parabolic complex networks (IPCNs) are considered. In the first one, all nodes have the same time-varying delay. In the second one, different nodes have different time-varying delays. Using the Lyapunov functional method combined with the inequality techniques, some global exponential stability criteria are derived for the IPCNs. Furthermore, several robust global exponential stability conditions are proposed to take uncertainties in the parameters of the IPCNs into account. Finally, numerical simulations are presented to illustrate the effectiveness of the results obtained here.

Introduction to linear systems of differential equations

CERN Document Server

Adrianova, L Ya

1995-01-01

The theory of linear systems of differential equations is one of the cornerstones of the whole theory of differential equations. At its root is the concept of the Lyapunov characteristic exponent. In this book, Adrianova presents introductory material and further detailed discussions of Lyapunov exponents. She also discusses the structure of the space of solutions of linear systems. Classes of linear systems examined are from the narrowest to widest: 1)�autonomous, 2)�periodic, 3)�reducible to autonomous, 4)�nearly reducible to autonomous, 5)�regular. In addition, Adrianova considers the following: stability of linear systems and the influence of perturbations of the coefficients on the stability the criteria of uniform stability and of uniform asymptotic stability in terms of properties of the solutions several estimates of the growth rate of solutions of a linear system in terms of its coefficients How perturbations of the coefficients change all the elements of the spectrum of the system is defin...

Stability Analysis of Fractional-Order Nonlinear Systems with Delay

Directory of Open Access Journals (Sweden)

Yu Wang

2014-01-01

Full Text Available Stability analysis of fractional-order nonlinear systems with delay is studied. We propose the definition of Mittag-Leffler stability of time-delay system and introduce the fractional Lyapunov direct method by using properties of Mittag-Leffler function and Laplace transform. Then some new sufficient conditions ensuring asymptotical stability of fractional-order nonlinear system with delay are proposed firstly. And the application of Riemann-Liouville fractional-order systems is extended by the fractional comparison principle and the Caputo fractional-order systems. Numerical simulations of an example demonstrate the universality and the effectiveness of the proposed method.

Stabilization of Neutral Systems with Saturating Actuators

Directory of Open Access Journals (Sweden)

F. El Haoussi

2012-01-01

to determine stabilizing state-feedback controllers with large domain of attraction, expressed as linear matrix inequalities, readily implementable using available numerical tools and with tuning parameters that make possible to select the most adequate solution. These conditions are derived by using a Lyapunov-Krasovskii functional on the vertices of the polytopic description of the actuator saturations. Numerical examples demonstrate the effectiveness of the proposed technique.

Lyapunov-based control of limit cycle oscillations in uncertain aircraft systems

Science.gov (United States)

Bialy, Brendan

Store-induced limit cycle oscillations (LCO) affect several fighter aircraft and is expected to remain an issue for next generation fighters. LCO arises from the interaction of aerodynamic and structural forces, however the primary contributor to the phenomenon is still unclear. The practical concerns regarding this phenomenon include whether or not ordnance can be safely released and the ability of the aircrew to perform mission-related tasks while in an LCO condition. The focus of this dissertation is the development of control strategies to suppress LCO in aircraft systems. The first contribution of this work (Chapter 2) is the development of a controller consisting of a continuous Robust Integral of the Sign of the Error (RISE) feedback term with a neural network (NN) feedforward term to suppress LCO behavior in an uncertain airfoil system. The second contribution of this work (Chapter 3) is the extension of the development in Chapter 2 to include actuator saturation. Suppression of LCO behavior is achieved through the implementation of an auxiliary error system that features hyperbolic functions and a saturated RISE feedback control structure. Due to the lack of clarity regarding the driving mechanism behind LCO, common practice in literature and in Chapters 2 and 3 is to replicate the symptoms of LCO by including nonlinearities in the wing structure, typically a nonlinear torsional stiffness. To improve the accuracy of the system model a partial differential equation (PDE) model of a flexible wing is derived (see Appendix F) using Hamilton's principle. Chapters 4 and 5 are focused on developing boundary control strategies for regulating the bending and twisting deformations of the derived model. The contribution of Chapter 4 is the construction of a backstepping-based boundary control strategy for a linear PDE model of an aircraft wing. The backstepping-based strategy transforms the original system to a exponentially stable system. A Lyapunov-based stability

Novel results for global robust stability of delayed neural networks

International Nuclear Information System (INIS)

Yucel, Eylem; Arik, Sabri

2009-01-01

This paper investigates the global robust convergence properties of continuous-time neural networks with discrete time delays. By employing suitable Lyapunov functionals, some sufficient conditions for the existence, uniqueness and global robust asymptotic stability of the equilibrium point are derived. The conditions can be easily verified as they can be expressed in terms of the network parameters only. Some numerical examples are also given to compare our results with previous robust stability results derived in the literature.

New stability and boundedness results to Volterra integro-differential equations with delay

Directory of Open Access Journals (Sweden)

Cemil Tunç

2016-04-01

Full Text Available In this paper, we consider a certain non-linear Volterra integro-differential equations with delay. We study stability and boundedness of solutions. The technique of proof involves defining suitable Lyapunov functionals. Our results improve and extend the results obtained in literature.

State feedback integral control for a rotary direct drive servo valve using a Lyapunov function approach.

Science.gov (United States)

Yu, Jue; Zhuang, Jian; Yu, Dehong

2015-01-01

This paper concerns a state feedback integral control using a Lyapunov function approach for a rotary direct drive servo valve (RDDV) while considering parameter uncertainties. Modeling of this RDDV servovalve reveals that its mechanical performance is deeply influenced by friction torques and flow torques; however, these torques are uncertain and mutable due to the nature of fluid flow. To eliminate load resistance and to achieve satisfactory position responses, this paper develops a state feedback control that integrates an integral action and a Lyapunov function. The integral action is introduced to address the nonzero steady-state error; in particular, the Lyapunov function is employed to improve control robustness by adjusting the varying parameters within their value ranges. This new controller also has the advantages of simple structure and ease of implementation. Simulation and experimental results demonstrate that the proposed controller can achieve higher control accuracy and stronger robustness. Copyright © 2014 ISA. Published by Elsevier Ltd. All rights reserved.

On exponential stability of bidirectional associative memory neural networks with time-varying delays

International Nuclear Information System (INIS)

Park, Ju H.; Lee, S.M.; Kwon, O.M.

2009-01-01

For bidirectional associate memory neural networks with time-varying delays, the problems of determining the exponential stability and estimating the exponential convergence rate are investigated by employing the Lyapunov functional method and linear matrix inequality (LMI) technique. A novel criterion for the stability, which give information on the delay-dependent property, is derived. A numerical example is given to demonstrate the effectiveness of the obtained results.

A tutorial on incremental stability analysis using contraction theory

DEFF Research Database (Denmark)

Jouffroy, Jerome; Fossen, Thor I.

2010-01-01

This paper introduces a methodology for dierential nonlinear stability analysis using contraction theory (Lohmiller and Slotine, 1998). The methodology includes four distinct steps: the descriptions of two systems to be compared (the plant and the observer in the case of observer convergence...... on several simple examples....

On global stability criterion for neural networks with discrete and distributed delays

International Nuclear Information System (INIS)

Park, Ju H.

2006-01-01

Based on the Lyapunov functional stability analysis for differential equations and the linear matrix inequality (LMI) optimization approach, a new delay-dependent criterion for neural networks with discrete and distributed delays is derived to guarantee global asymptotic stability. The criterion is expressed in terms of LMIs, which can be solved easily by various convex optimization algorithms. Some numerical examples are given to show the effectiveness of proposed method

Stability analysis of nonlinear systems with slope restricted nonlinearities.

Science.gov (United States)

Liu, Xian; Du, Jiajia; Gao, Qing

2014-01-01

The problem of absolute stability of Lur'e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP) lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results.

Stability Analysis of Nonlinear Systems with Slope Restricted Nonlinearities

Directory of Open Access Journals (Sweden)

Xian Liu

2014-01-01

Full Text Available The problem of absolute stability of Lur’e systems with sector and slope restricted nonlinearities is revisited. Novel time-domain and frequency-domain criteria are established by using the Lyapunov method and the well-known Kalman-Yakubovich-Popov (KYP lemma. The criteria strengthen some existing results. Simulations are given to illustrate the efficiency of the results.

Periodic oscillation and exponential stability of delayed CNNs

Science.gov (United States)

Cao, Jinde

2000-05-01

Both the global exponential stability and the periodic oscillation of a class of delayed cellular neural networks (DCNNs) is further studied in this Letter. By applying some new analysis techniques and constructing suitable Lyapunov functionals, some simple and new sufficient conditions are given ensuring global exponential stability and the existence of periodic oscillatory solution of DCNNs. These conditions can be applied to design globally exponentially stable DCNNs and periodic oscillatory DCNNs and easily checked in practice by simple algebraic methods. These play an important role in the design and applications of DCNNs.

Quantum resource theory of non-stabilizer states in the one-shot regime

Science.gov (United States)

Ahmadi, Mehdi; Dang, Hoan; Gour, Gilad; Sanders, Barry

Universal quantum computing is known to be impossible using only stabilizer states and stabilizer operations. However, addition of non-stabilizer states (also known as magic states) to quantum circuits enables us to achieve universality. The resource theory of non-stablizer states aims at quantifying the usefulness of non-stabilizer states. Here, we focus on a fundamental question in this resource theory in the so called single-shot regime: Given two resource states, is there a free quantum channel that will (approximately or exactly) convert one to the other?. To provide an answer, we phrase the question as a semidefinite program with constraints on the Choi matrix of the corresponding channel. Then, we use the semidefinite version of the Farkas lemma to derive the necessary and sufficient conditions for the conversion between two arbitrary resource states via a free quantum channel. BCS appreciates financial support from Alberta Innovates, NSERC, China's 1000 Talent Plan and the Institute for Quantum Information and Matter.

A new criterion on the global exponential stability for cellular neural networks with multiple time-varying delays

International Nuclear Information System (INIS)

Jiang Haijun; Teng Zhidong

2005-01-01

In this Letter, based on the Lyapunov stability theorem as well as some facts about the positive definiteness and inequality of matrices, a new sufficient condition to ensure the global exponential stability of equilibrium point for autonomous delayed CNNs is obtained. This condition is less restrictive than given in the earlier references

Dynamic behaviours and control of fractional-order memristor-based ...

Indian Academy of Sciences (India)

Dynamics of fractional-order memristor circuit system and its control are investigated in this paper. With the help of stability theory of fractional-order systems, stability of its equilibrium points is analysed. Then, the chaotic behaviours are validated using phase portraits, the Lyapunov exponents and bifurcation diagrams with ...

The adaptive synchronization of fractional-order Liu chaotic system ...

Indian Academy of Sciences (India)

In this paper, the chaos control and the synchronization of two fractional-order Liu chaotic systems with unknown parameters are studied. According to the Lyapunov stabilization theory and the adaptive control theorem, the adaptive control rule is obtained for the described error dynamic stabilization. Using the adaptive rule ...

Delay-dependent stability of neural networks of neutral type with time delay in the leakage term

International Nuclear Information System (INIS)

Li, Xiaodi; Cao, Jinde

2010-01-01

This paper studies the global asymptotic stability of neural networks of neutral type with mixed delays. The mixed delays include constant delay in the leakage term (i.e. 'leakage delay'), time-varying delays and continuously distributed delays. Based on the topological degree theory, Lyapunov method and linear matrix inequality (LMI) approach, some sufficient conditions are derived ensuring the existence, uniqueness and global asymptotic stability of the equilibrium point, which are dependent on both the discrete and distributed time delays. These conditions are expressed in terms of LMI and can be easily checked by the MATLAB LMI toolbox. Even if there is no leakage delay, the obtained results are less restrictive than some recent works. It can be applied to neural networks of neutral type with activation functions without assuming their boundedness, monotonicity or differentiability. Moreover, the differentiability of the time-varying delay in the non-neutral term is removed. Finally, two numerical examples are given to show the effectiveness of the proposed method

Lyapunov based control of hybrid energy storage system in electric vehicles

DEFF Research Database (Denmark)

El Fadil, H.; Giri, F.; Guerrero, Josep M.

2012-01-01

This paper deals with a Lyapunov based control principle in a hybrid energy storage system for electric vehicle. The storage system consists on fuel cell (FC) as a main power source and a supercapacitor (SC) as an auxiliary power source. The power stage of energy conversion consists on a boost...

Methods of solving of the optimal stabilization problem for stationary smooth control systems. Part I

Directory of Open Access Journals (Sweden)

G. Kondrat'ev

1999-10-01

Full Text Available In this article some ideas of Hamilton mechanics and differential-algebraic Geometry are used to exact definition of the potential function (Bellman-Lyapunov function in the optimal stabilization problem of smooth finite-dimensional systems.

Global stability of the coexistence equilibrium for a general class of models of facultative mutualism

Czech Academy of Sciences Publication Activity Database

Maxin, D.; Georgescu, P.; Sega, L.; Berec, Luděk

2017-01-01

Roč. 11, č. 1 (2017), s. 339-364 ISSN 1751-3758 Institutional support: RVO:60077344 Keywords : mutualistic interaction * global stability * Lyapunov functional Subject RIV: EH - Ecology, Behaviour OBOR OECD: Ecology Impact factor: 1.279, year: 2016

Theory and modelling of nanocarbon phase stability.

Energy Technology Data Exchange (ETDEWEB)

Barnard, A. S.

2006-01-01

The transformation of nanodiamonds into carbon-onions (and vice versa) has been observed experimentally and has been modeled computationally at various levels of sophistication. Also, several analytical theories have been derived to describe the size, temperature and pressure dependence of this phase transition. However, in most cases a pure carbon-onion or nanodiamond is not the final product. More often than not an intermediary is formed, known as a bucky-diamond, with a diamond-like core encased in an onion-like shell. This has prompted a number of studies investigating the relative stability of nanodiamonds, bucky-diamonds, carbon-onions and fullerenes, in various size regimes. Presented here is a review outlining results of numerous theoretical studies examining the phase diagrams and phase stability of carbon nanoparticles, to clarify the complicated relationship between fullerenic and diamond structures at the nanoscale.

Stability of biogenic metal(loid) nanomaterials related to the colloidal stabilization theory of chemical nanostructures.

Science.gov (United States)

Piacenza, Elena; Presentato, Alessandro; Turner, Raymond J

2018-02-25

In the last 15 years, the exploitation of biological systems (i.e. plants, bacteria, mycelial fungi, yeasts, and algae) to produce metal(loid) (Me)-based nanomaterials has been evaluated as eco-friendly and a cost-effective alternative to the chemical synthesis processes. Although the biological mechanisms of biogenic Me-nanomaterial (Bio-Me-nanomaterials) production are not yet completely elucidated, a key advantage of such bio-nanostructures over those chemically synthesized is related to their natural thermodynamic stability, with several studies ascribed to the presence of an organic layer surrounding these Bio-Me-nanostructures. Different macromolecules (e.g. proteins, peptides, lipids, DNA, and polysaccharides) or secondary metabolites (e.g. flavonoids, terpenoids, glycosides, organic acids, and alkaloids) naturally produced by organisms have been indicated as main contributors to the stabilization of Bio-Me-nanostructures. Nevertheless, the chemical-physical mechanisms behind the ability of these molecules in providing stability to Bio-Me-nanomaterials are unknown. In this context, transposing the stabilization theory of chemically synthesized Me-nanomaterials (Ch-Me-nanomaterials) to biogenic materials can be used towards a better comprehension of macromolecules and secondary metabolites role as stabilizing agents of Bio-Me-nanomaterials. According to this theory, nanomaterials are generally featured by high thermodynamic instability in suspension, due to their high surface area and surface energy. This feature leads to the necessity to stabilize chemical nanostructures, even during or directly after their synthesis, through the development of (i) electrostatic, (ii) steric, or (iii) electrosteric interactions occurring between molecules and nanomaterials in suspension. Based on these three mechanisms, this review is focused on parallels between the stabilization of biogenic or chemical nanomaterials, suggesting which chemical-physical mechanisms may be

Quantum control theory and applications: A survey

OpenAIRE

Dong, Daoyi; Petersen, Ian R

2009-01-01

This paper presents a survey on quantum control theory and applications from a control systems perspective. Some of the basic concepts and main developments (including open-loop control and closed-loop control) in quantum control theory are reviewed. In the area of open-loop quantum control, the paper surveys the notion of controllability for quantum systems and presents several control design strategies including optimal control, Lyapunov-based methodologies, variable structure control and q...

Design of stability-guaranteed fuzzy logic controller for nuclear steam generators

International Nuclear Information System (INIS)

Cho, B.H.; No, H.C.

1996-01-01

A fuzzy logic controller (FLC) and a fuzzy logic filter (FLF), which have a special type of fuzzifier, inference engine, and defuzzifier, are applied to the water level control of a nuclear steam generator (S/G). It is shown that arbitrary two-input, single-output linear controllers can be adequately expressed by this FLC. A procedure to construct stability-guaranteed FLC rules is proposed. It contains the following steps: (1) the stable sector of linear feedback gains is obtained from the suboptimal concept based on LQR theory and the Lyapunov's stability criteria; (2) the stable sector of linear gains is mapped into two linear rule tables that are used as limits for the FLC rules; and (3) the construction of an FLC rule table is done by choosing certain rules that lie between these limits. This type of FLC guarantees asymptotic stability of the control system. The FLF generates a feedforward signal of S/G feedwater from the steam flow measurement using a fuzzy concept. Through computer simulation, it is found that the FLC with the FLF works better than a well-tuned PID controller with variable gains to reduce swell/shrink phenomena, especially for the water level deviation and abrupt steam flow disturbances that are typical in the existing power plants

Lyapunov-Based Control Scheme for Single-Phase Grid-Connected PV Central Inverters

NARCIS (Netherlands)

Meza, C.; Biel, D.; Jeltsema, D.; Scherpen, J. M. A.

A Lyapunov-based control scheme for single-phase single-stage grid-connected photovoltaic central inverters is presented. Besides rendering the closed-loop system globally stable, the designed controller is able to deal with the system uncertainty that depends on the solar irradiance. A laboratory

Improving Delay-Range-Dependent Stability Condition for Systems with Interval Time-Varying Delay

Directory of Open Access Journals (Sweden)

Wei Qian

2013-01-01

Full Text Available This paper discusses the delay-range-dependent stability for systems with interval time-varying delay. Through defining the new Lyapunov-Krasovskii functional and estimating the derivative of the LKF by introducing new vectors, using free matrices and reciprocally convex approach, the new delay-range-dependent stability conditions are obtained. Two well-known examples are given to illustrate the less conservatism of the proposed theoretical results.

On the Lyapunov stability of a plane parallel convective flow of a binary mixture

Directory of Open Access Journals (Sweden)

Giuseppe Mulone

1991-05-01

Full Text Available The nonlinear stability of plane parallel convective flows of a binary fluid mixture in the Oberbeck-Boussinesq scheme is studied in the stress-free boundary case. Nonlinear stability conditions independent of Reynolds number are proved.

Reliability of Lyapunov characteristic exponents computed by the two-particle method

Science.gov (United States)

Mei, Lijie; Huang, Li

2018-03-01

For highly complex problems, such as the post-Newtonian formulation of compact binaries, the two-particle method may be a better, or even the only, choice to compute the Lyapunov characteristic exponent (LCE). This method avoids the complex calculations of variational equations compared with the variational method. However, the two-particle method sometimes provides spurious estimates to LCEs. In this paper, we first analyze the equivalence in the definition of LCE between the variational and two-particle methods for Hamiltonian systems. Then, we develop a criterion to determine the reliability of LCEs computed by the two-particle method by considering the magnitude of the initial tangent (or separation) vector ξ0 (or δ0), renormalization time interval τ, machine precision ε, and global truncation error ɛT. The reliable Lyapunov characteristic indicators estimated by the two-particle method form a V-shaped region, which is restricted by d0, ε, and ɛT. Finally, the numerical experiments with the Hénon-Heiles system, the spinning compact binaries, and the post-Newtonian circular restricted three-body problem strongly support the theoretical results.

The stability of a class of synchronous generator damping model

Science.gov (United States)

Liu, Jun

2018-03-01

Electricity is indispensable to modern society and the most convenient energy, it can be easily transformed into other forms of energy, has been widely used in engineering, transportation and so on, this paper studied the generator model with damping machine, using the Lyapunov function method, we obtain sufficient conditions for the asymptotic stability of the model.

Delay-slope-dependent stability results of recurrent neural networks.

Science.gov (United States)

Li, Tao; Zheng, Wei Xing; Lin, Chong

2011-12-01

By using the fact that the neuron activation functions are sector bounded and nondecreasing, this brief presents a new method, named the delay-slope-dependent method, for stability analysis of a class of recurrent neural networks with time-varying delays. This method includes more information on the slope of neuron activation functions and fewer matrix variables in the constructed Lyapunov-Krasovskii functional. Then some improved delay-dependent stability criteria with less computational burden and conservatism are obtained. Numerical examples are given to illustrate the effectiveness and the benefits of the proposed method.

Global Asymptotic Stability of Switched Neural Networks with Delays

Directory of Open Access Journals (Sweden)

Zhenyu Lu

2015-01-01

Full Text Available This paper investigates the global asymptotic stability of a class of switched neural networks with delays. Several new criteria ensuring global asymptotic stability in terms of linear matrix inequalities (LMIs are obtained via Lyapunov-Krasovskii functional. And here, we adopt the quadratic convex approach, which is different from the linear and reciprocal convex combinations that are extensively used in recent literature. In addition, the proposed results here are very easy to be verified and complemented. Finally, a numerical example is provided to illustrate the effectiveness of the results.

Equilibrium and stability of relativistic stars in extended theories of gravity

Energy Technology Data Exchange (ETDEWEB)

Wojnar, Aneta [Maria Curie-Sklodowska University, Institute of Physics, Lublin (Poland); Univ. di Monte S. Angelo, Napoli (Italy); Universita' di Napoli Federico II, Complesso Universitario di Monte S. Angelo, Dipartimento di Fisica ' ' E. Pancini' ' , Naples (Italy); INFN, Napoli (Italy); Velten, Hermano [Universidade Federal do Espirito Santo (UFES), Vitoria (Brazil)

2016-12-15

We study static, spherically symmetric equilibrium configurations in extended theories of gravity (ETG) following the notation introduced by Capozziello et al. We calculate the differential equations for the stellar structure in such theories in a very generic form i.e., the Tolman-Oppenheimer-Volkoff generalization for any ETG is introduced. Stability analysis is also investigated with special focus on the particular example of scalar-tensor gravity. (orig.)

Construction of the Lyapunov Spectrum in a Chaotic System Displaying Phase Synchronization

Energy Technology Data Exchange (ETDEWEB)

Carlo, Leonardo De, E-mail: neoleodeo@gmail.com [Gran Sasso Science Institute (GSSI) (Italy); Gentile, Guido, E-mail: gentile@mat.uniroma3.it; Giuliani, Alessandro, E-mail: giuliani@mat.uniroma3.it [Università degli Studi Roma Tre, Dipartimento di Matematica e Fisica (Italy)

2016-06-15

We consider a three-dimensional chaotic system consisting of the suspension of Arnold’s cat map coupled with a clock via a weak dissipative interaction. We show that the coupled system displays a synchronization phenomenon, in the sense that the relative phase between the suspension flow and the clock locks to a special value, thus making the motion fall onto a lower dimensional attractor. More specifically, we construct the attractive invariant manifold, of dimension smaller than three, using a convergent perturbative expansion. Moreover, we compute via convergent series the Lyapunov exponents, including notably the central one. The result generalizes a previous construction of the attractive invariant manifold in a similar but simpler model. The main novelty of the current construction relies in the computation of the Lyapunov spectrum, which consists of non-trivial analytic exponents. Some conjectures about a possible smoothening transition of the attractor as the coupling is increased are also discussed.

Delay-Dependent Stability Criterion for Bidirectional Associative Memory Neural Networks with Interval Time-Varying Delays

Science.gov (United States)

Park, Ju H.; Kwon, O. M.

In the letter, the global asymptotic stability of bidirectional associative memory (BAM) neural networks with delays is investigated. The delay is assumed to be time-varying and belongs to a given interval. A novel stability criterion for the stability is presented based on the Lyapunov method. The criterion is represented in terms of linear matrix inequality (LMI), which can be solved easily by various optimization algorithms. Two numerical examples are illustrated to show the effectiveness of our new result.

Periodicity and global exponential stability of generalized Cohen-Grossberg neural networks with discontinuous activations and mixed delays.

Science.gov (United States)

Wang, Dongshu; Huang, Lihong

2014-03-01

In this paper, we investigate the periodic dynamical behaviors for a class of general Cohen-Grossberg neural networks with discontinuous right-hand sides, time-varying and distributed delays. By means of retarded differential inclusions theory and the fixed point theorem of multi-valued maps, the existence of periodic solutions for the neural networks is obtained. After that, we derive some sufficient conditions for the global exponential stability and convergence of the neural networks, in terms of nonsmooth analysis theory with generalized Lyapunov approach. Without assuming the boundedness (or the growth condition) and monotonicity of the discontinuous neuron activation functions, our results will also be valid. Moreover, our results extend previous works not only on discrete time-varying and distributed delayed neural networks with continuous or even Lipschitz continuous activations, but also on discrete time-varying and distributed delayed neural networks with discontinuous activations. We give some numerical examples to show the applicability and effectiveness of our main results. Copyright © 2013 Elsevier Ltd. All rights reserved.

Globally exponential stability condition of a class of neural networks with time-varying delays

International Nuclear Information System (INIS)

Liao, T.-L.; Yan, J.-J.; Cheng, C.-J.; Hwang, C.-C.

2005-01-01

In this Letter, the globally exponential stability for a class of neural networks including Hopfield neural networks and cellular neural networks with time-varying delays is investigated. Based on the Lyapunov stability method, a novel and less conservative exponential stability condition is derived. The condition is delay-dependent and easily applied only by checking the Hamiltonian matrix with no eigenvalues on the imaginary axis instead of directly solving an algebraic Riccati equation. Furthermore, the exponential stability degree is more easily assigned than those reported in the literature. Some examples are given to demonstrate validity and excellence of the presented stability condition herein

Some new results on stability and synchronization for delayed inertial neural networks based on non-reduced order method.

Science.gov (United States)

Li, Xuanying; Li, Xiaotong; Hu, Cheng

2017-12-01

In this paper, without transforming the second order inertial neural networks into the first order differential systems by some variable substitutions, asymptotic stability and synchronization for a class of delayed inertial neural networks are investigated. Firstly, a new Lyapunov functional is constructed to directly propose the asymptotic stability of the inertial neural networks, and some new stability criteria are derived by means of Barbalat Lemma. Additionally, by designing a new feedback control strategy, the asymptotic synchronization of the addressed inertial networks is studied and some effective conditions are obtained. To reduce the control cost, an adaptive control scheme is designed to realize the asymptotic synchronization. It is noted that the dynamical behaviors of inertial neural networks are directly analyzed in this paper by constructing some new Lyapunov functionals, this is totally different from the traditional reduced-order variable substitution method. Finally, some numerical simulations are given to demonstrate the effectiveness of the derived theoretical results. Copyright © 2017 Elsevier Ltd. All rights reserved.

Abstraction of continuous dynamical systems utilizing lyapunov functions

DEFF Research Database (Denmark)

Sloth, Christoffer; Wisniewski, Rafael

2010-01-01

This paper considers the development of a method for abstracting continuous dynamical systems by timed automata. The method is based on partitioning the state space of dynamical systems with invariant sets, which form cells representing locations of the timed automata. To enable verification...... of the dynamical system based on the abstraction, conditions for obtaining sound, complete, and refinable abstractions are set up. It is proposed to partition the state space utilizing sub-level sets of Lyapunov functions, since they are positive invariant sets. The existence of sound abstractions for Morse......-Smale systems and complete and refinable abstractions for linear systems are shown....

Bifurcation and stability in Yang-Mills theory with sources

International Nuclear Information System (INIS)

Jackiw, R.

1979-06-01

A lecture is presented in which some recent work on solutions to classical Yang-Mills theory is discussed. The investigations summarized include the field equations with static, external sources. A pattern allowing a comprehensive description of the solutions and stability in dynamical systems are covered. A list of open questions and problems for further research is given. 20 references

Chaos synchronization and parameter identification of three time scales brushless DC motor system

International Nuclear Information System (INIS)

Ge, Z.-M.; Cheng, J.-W.

2005-01-01

Chaotic anticontrol and chaos synchronization of brushless DC motor system are studied in this paper. Nondimensional dynamic equations of three time scale brushless DC motor system are presented. Using numerical results, such as phase diagram, bifurcation diagram, and Lyapunov exponent, periodic and chaotic motions can be observed. Then, chaos synchronization of two identical systems via additional inputs and Lyapunov stability theory are studied. And further, the parameter of the system is traced via adaptive control and random optimization method

Global exponential stability for discrete-time neural networks with variable delays

International Nuclear Information System (INIS)

Chen Wuhua; Lu Xiaomei; Liang Dongying

2006-01-01

This Letter provides new exponential stability criteria for discrete-time neural networks with variable delays. The main technique is to reduce exponential convergence estimation of the neural network solution to that of one component of the corresponding solution by constructing Lyapunov function based on M-matrix. By introducing the tuning parameter diagonal matrix, the delay-independent and delay-dependent exponential stability conditions have been unified in the same mathematical formula. The effectiveness of the new results are illustrated by three examples

Tumour chemotherapy strategy based on impulse control theory.

Science.gov (United States)

Ren, Hai-Peng; Yang, Yan; Baptista, Murilo S; Grebogi, Celso

2017-03-06

Chemotherapy is a widely accepted method for tumour treatment. A medical doctor usually treats patients periodically with an amount of drug according to empirical medicine guides. From the point of view of cybernetics, this procedure is an impulse control system, where the amount and frequency of drug used can be determined analytically using the impulse control theory. In this paper, the stability of a chemotherapy treatment of a tumour is analysed applying the impulse control theory. The globally stable condition for prescription of a periodic oscillatory chemotherapeutic agent is derived. The permanence of the solution of the treatment process is verified using the Lyapunov function and the comparison theorem. Finally, we provide the values for the strength and the time interval that the chemotherapeutic agent needs to be applied such that the proposed impulse chemotherapy can eliminate the tumour cells and preserve the immune cells. The results given in the paper provide an analytical formula to guide medical doctors to choose the theoretical minimum amount of drug to treat the cancer and prevent harming the patients because of over-treating.This article is part of the themed issue 'Horizons of cybernetical physics'. © 2017 The Author(s).

Global exponential stability for reaction-diffusion recurrent neural networks with multiple time varying delays

International Nuclear Information System (INIS)

Lou, X.; Cui, B.

2008-01-01

In this paper we consider the problem of exponential stability for recurrent neural networks with multiple time varying delays and reaction-diffusion terms. The activation functions are supposed to be bounded and globally Lipschitz continuous. By means of Lyapunov functional, sufficient conditions are derived, which guarantee global exponential stability of the delayed neural network. Finally, a numerical example is given to show the correctness of our analysis. (author)

Razumikhin-Type Stability Criteria for Differential Equations with Delayed Impulses.

Science.gov (United States)

Wang, Qing; Zhu, Quanxin

2013-01-01

This paper studies stability problems of general impulsive differential equations where time delays occur in both differential and difference equations. Based on the method of Lyapunov functions, Razumikhin technique and mathematical induction, several stability criteria are obtained for differential equations with delayed impulses. Our results show that some systems with delayed impulses may be exponentially stabilized by impulses even if the system matrices are unstable. Some less restrictive sufficient conditions are also given to keep the good stability property of systems subject to certain type of impulsive perturbations. Examples with numerical simulations are discussed to illustrate the theorems. Our results may be applied to complex problems where impulses depend on both current and past states.

Razumikhin-type stability criteria for differential equations with delayed impulses

Directory of Open Access Journals (Sweden)

Qing Wang

2013-01-01

Full Text Available This paper studies stability problems of general impulsive differential equations where time delays occur in both differential and difference equations. Based on the method of Lyapunov functions, Razumikhin technique and mathematical induction, several stability criteria are obtained for differential equations with delayed impulses. Our results show that some systems with delayed impulses may be exponentially stabilized by impulses even if the system matrices are unstable. Some less restrictive sufficient conditions are also given to keep the good stability property of systems subject to certain type of impulsive perturbations. Examples with numerical simulations are discussed to illustrate the theorems. Our results may be applied to complex problems where impulses depend on both current and past states.

Application of linearized model to the stability analysis of the pressurized water reactor

International Nuclear Information System (INIS)

Li Haipeng; Huang Xiaojin; Zhang Liangju

2008-01-01

A Linear Time-Invariant model of the Pressurized Water Reactor is formulated through the linearization of the nonlinear model. The model simulation results show that the linearized model agrees well with the nonlinear model under small perturbation. Based upon the Lyapunov's First Method, the linearized model is applied to the stability analysis of the Pressurized Water Reactor. The calculation results show that the methodology of linearization to stability analysis is conveniently feasible. (authors)

Stability of the Einstein static universe in modified theories of gravity

OpenAIRE

Boehmer, Christian G.; Hollenstein, Lukas; Lobo, Francisco S. N.; Seahra, Sanjeev S.

2010-01-01

We present a brief overview of the stability analysis of the Einstein static universe in various modified theories of gravity, like f(R) gravity, Gauss-Bonnet or f(G) gravity, and Horava-Lifshitz gravity.

On asymptotic solutions of Regge field theory in zero transverse dimensions

International Nuclear Information System (INIS)

Bondarenko, S.; Horwitz, L.; Levitan, J.; Yahalom, A.

2013-01-01

An investigation of dynamical properties of solutions of a toy model of interacting Pomerons with triple vertex in zero transverse dimension is performed. Stable points and corresponding solutions at the limit of large rapidity are studied in the framework of a given model. It is shown that, at large rapidity, the “fan” amplitude is also a leading solution for the full RFT-0 (Regge Field Theory in zero transverse dimensions) Hamiltonian with both vertices of Pomeron splitting and merging included. An analytical form of the symmetrical solution of the equations of motion at high energy is obtained as well. For the solutions we have found, the scattering amplitude at large values of rapidity is calculated. Stability of the solutions is investigated by Lyapunov functions and the presence of closed cycles in solutions is demonstrated by the new method

Adiabatic invariants and asymptotic behavior of Lyapunov exponents of the Schrodinger equation

International Nuclear Information System (INIS)

Delyon, F.; Foulon, P.

1986-01-01

We give an upper bound for the high-energy behavior of the Lyapunov exponent of the one-dimensional Schrodinger equation. We relate this behavior to the diffrentiability properties of the potential. As an application, this result provides an upper bound for the asymptotic length of the gaps of the Schrodinger equation

A novel double-convection chaotic attractor, its adaptive control and circuit simulation

Science.gov (United States)

Mamat, M.; Vaidyanathan, S.; Sambas, A.; Mujiarto; Sanjaya, W. S. M.; Subiyanto

2018-03-01

A 3-D novel double-convection chaotic system with three nonlinearities is proposed in this research work. The dynamical properties of the new chaotic system are described in terms of phase portraits, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, stability analysis of equilibria, etc. Adaptive control and synchronization of the new chaotic system with unknown parameters are achieved via nonlinear controllers and the results are established using Lyapunov stability theory. Furthermore, an electronic circuit realization of the new 3-D novel chaotic system is presented in detail. Finally, the circuit experimental results of the 3-D novel chaotic attractor show agreement with the numerical simulations.

Robust stability analysis of large power systems using the structured singular value theory

Energy Technology Data Exchange (ETDEWEB)

Castellanos, R.; Sarmiento, H. [Instituto de Investigaciones Electricas, Cuernavaca, Morelos (Mexico); Messina, A.R. [Cinvestav, Graduate Program in Electrical Engineering, Guadalajara, Jalisco (Mexico)

2005-07-01

This paper examines the application of structured singular value (SSV) theory to analyse robust stability of complex power systems with respect to a set of structured uncertainties. Based on SSV theory and the frequency sweep method, techniques for robust analysis of large-scale power systems are developed. The main interest is focused on determining robust stability for varying operating conditions and uncertainties in the structure of the power system. The applicability of the proposed techniques is verified through simulation studies on a large-scale power system. In particular, results for the system are considered for a wide range of uncertainties of operating conditions. Specifically, the developed technique is used to estimate the effect of variations in the parameters of a major system inter-tie on the nominal stability of a critical inter-area mode. (Author)

Characterization of coherent structures in three-dimensional turbulent flows using the finite-size Lyapunov exponent

International Nuclear Information System (INIS)

Bettencourt, João H; López, Cristóbal; Hernández-García, Emilio

2013-01-01

In this paper, we use the finite-size Lyapunov exponent (FSLE) to characterize Lagrangian coherent structures in three-dimensional (3D) turbulent flows. Lagrangian coherent structures act as the organizers of transport in fluid flows and are crucial to understand their stirring and mixing properties. Generalized maxima (ridges) of the FSLE fields are used to locate these coherent structures. 3D FSLE fields are calculated in two phenomenologically distinct turbulent flows: a wall-bounded flow (channel flow) and a regional oceanic flow obtained by the numerical solution of the primitive equations where two-dimensional (2D) turbulence dominates. In the channel flow, autocorrelations of the FSLE field show that the structure is substantially different from the near wall to the mid-channel region and relates well to the more widely studied Eulerian coherent structure of the turbulent channel flow. The ridges of the FSLE field have complex shapes due to the 3D character of the turbulent fluctuations. In the oceanic flow, strong horizontal stirring is present and the flow regime is similar to that of 2D turbulence where the domain is populated by coherent eddies that interact strongly. This in turn results in the presence of high FSLE lines throughout the domain leading to strong non-local mixing. The ridges of the FSLE field are quasi-vertical surfaces, indicating that the horizontal dynamics dominates the flow. Indeed, due to rotation and stratification, vertical motions in the ocean are much less intense than horizontal ones. This suppression is absent in the channel flow, as the 3D character of the FSLE ridges shows. This article is part of a special issue of Journal of Physics A: Mathematical and Theoretical devoted to ‘Lyapunov analysis: from dynamical systems theory to applications’. (paper)

Stability Analysis of Neural Networks-Based System Identification

Directory of Open Access Journals (Sweden)

Talel Korkobi

2008-01-01

Full Text Available This paper treats some problems related to nonlinear systems identification. A stability analysis neural network model for identifying nonlinear dynamic systems is presented. A constrained adaptive stable backpropagation updating law is presented and used in the proposed identification approach. The proposed backpropagation training algorithm is modified to obtain an adaptive learning rate guarantying convergence stability. The proposed learning rule is the backpropagation algorithm under the condition that the learning rate belongs to a specified range defining the stability domain. Satisfying such condition, unstable phenomena during the learning process are avoided. A Lyapunov analysis leads to the computation of the expression of a convenient adaptive learning rate verifying the convergence stability criteria. Finally, the elaborated training algorithm is applied in several simulations. The results confirm the effectiveness of the CSBP algorithm.

On the asymptotic stability of nonlinear mechanical switched systems

Science.gov (United States)

Platonov, A. V.

2018-05-01

Some classes of switched mechanical systems with dissipative and potential forces are considered. The case, where either dissipative or potential forces are essentially nonlinear, is studied. It is assumed that the zero equilibrium position of the system is asymptotically stable at least for one operating mode. We will look for sufficient conditions which guarantee the preservation of asymptotic stability of the equilibrium position under the switching of modes. The Lyapunov direct method is used. A Lyapunov function for considered system is constructed, which satisfies the differential inequality of special form for every operating mode. This inequality is nonlinear for the chosen mode with asymptotically stable equilibrium position, and it is linear for the rest modes. The correlations between the intervals of activity of the pointed mode and the intervals of activity of the rest modes are obtained which guarantee the required properties.

? and ? nonquadratic stabilisation of discrete-time Takagi-Sugeno systems based on multi-instant fuzzy Lyapunov functions

Science.gov (United States)

Tognetti, Eduardo S.; Oliveira, Ricardo C. L. F.; Peres, Pedro L. D.

2015-01-01

The problem of state feedback control design for discrete-time Takagi-Sugeno (TS) (T-S) fuzzy systems is investigated in this paper. A Lyapunov function, which is quadratic in the state and presents a multi-polynomial dependence on the fuzzy weighting functions at the current and past instants of time, is proposed.This function contains, as particular cases, other previous Lyapunov functions already used in the literature, being able to provide less conservative conditions of control design for TS fuzzy systems. The structure of the proposed Lyapunov function also motivates the design of a new stabilising compensator for Takagi-Sugeno fuzzy systems. The main novelty of the proposed state feedback control law is that the gain is composed of matrices with multi-polynomial dependence on the fuzzy weighting functions at a set of past instants of time, including the current one. The conditions for the existence of a stabilising state feedback control law that minimises an upper bound to the ? or ? norms are given in terms of linear matrix inequalities. Numerical examples show that the approach can be less conservative and more efficient than other methods available in the literature.

Hopf bifurcations, Lyapunov exponents and control of chaos for a class of centrifugal flywheel governor system

International Nuclear Information System (INIS)

Zhang Jiangang; Li Xianfeng; Chu Yandong; Yu Jianning; Chang Yingxiang

2009-01-01

In this paper, complex dynamical behavior of a class of centrifugal flywheel governor system is studied. These systems have a rich variety of nonlinear behavior, which are investigated here by numerically integrating the Lagrangian equations of motion. A tiny change in parameters can lead to an enormous difference in the long-term behavior of the system. Bubbles of periodic orbits may also occur within the bifurcation sequence. Hyperchaotic behavior is also observed in cases where two of the Lyapunov exponents are positive, one is zero, and one is negative. The routes to chaos are analyzed using Poincare maps, which are found to be more complicated than those of nonlinear rotational machines. Periodic and chaotic motions can be clearly distinguished by all of the analytical tools applied here, namely Poincare sections, bifurcation diagrams, Lyapunov exponents, and Lyapunov dimensions. This paper proposes a parametric open-plus-closed-loop approach to controlling chaos, which is capable of switching from chaotic motion to any desired periodic orbit. The theoretical work and numerical simulations of this paper can be extended to other systems. Finally, the results of this paper are of practical utility to designers of rotational machines.

Tree-level stability without spacetime fermions: novel examples in string theory

International Nuclear Information System (INIS)

Israel, Dan; Niarchos, Vasilis

2007-01-01

Is perturbative stability intimately tied with the existence of spacetime fermions in string theory in more than two dimensions? Type 0'B string theory in ten-dimensional flat space is a rare example of a non-tachyonic, non-supersymmetric string theory with a purely bosonic closed string spectrum. However, all known type 0' constructions exhibit massless NSNS tadpoles signaling the fact that we are not expanding around a true vacuum of the theory. In this note, we are searching for perturbatively stable examples of type 0' string theory without massless tadpoles in backgrounds with a spatially varying dilaton. We present two examples with this property in non-critical string theories that exhibit four- and six-dimensional Poincare invariance. We discuss the D-branes that can be embedded in this context and the type of gauge theories that can be constructed in this manner. We also comment on the embedding of these non-critical models in critical string theories and their holographic (Little String Theory) interpretation and propose a general conjecture for the role of asymptotic supersymmetry in perturbative string theory

Delay-Dependent Exponential Stability for Discrete-Time BAM Neural Networks with Time-Varying Delays

Directory of Open Access Journals (Sweden)

Yonggang Chen

2008-01-01

Full Text Available This paper considers the delay-dependent exponential stability for discrete-time BAM neural networks with time-varying delays. By constructing the new Lyapunov functional, the improved delay-dependent exponential stability criterion is derived in terms of linear matrix inequality (LMI. Moreover, in order to reduce the conservativeness, some slack matrices are introduced in this paper. Two numerical examples are presented to show the effectiveness and less conservativeness of the proposed method.

Stabilization of discrete-time LTI positive systems

Directory of Open Access Journals (Sweden)

Krokavec Dušan

2017-12-01

Full Text Available The paper mitigates the existing conditions reported in the previous literature for control design of discrete-time linear positive systems. Incorporating an associated structure of linear matrix inequalities, combined with the Lyapunov inequality guaranteing asymptotic stability of discrete-time positive system structures, new conditions are presented with which the state-feedback controllers and the system state observers can be designed. Associated solutions of the proposed design conditions are illustrated by numerical illustrative examples.

Robust stabilization control based on guardian maps theory for a longitudinal model of hypersonic vehicle.

Science.gov (United States)

Liu, Yanbin; Liu, Mengying; Sun, Peihua

2014-01-01

A typical model of hypersonic vehicle has the complicated dynamics such as the unstable states, the nonminimum phases, and the strong coupling input-output relations. As a result, designing a robust stabilization controller is essential to implement the anticipated tasks. This paper presents a robust stabilization controller based on the guardian maps theory for hypersonic vehicle. First, the guardian maps theories are provided to explain the constraint relations between the open subsets of complex plane and the eigenvalues of the state matrix of closed-loop control system. Then, a general control structure in relation to the guardian maps theories is proposed to achieve the respected design demands. Furthermore, the robust stabilization control law depending on the given general control structure is designed for the longitudinal model of hypersonic vehicle. Finally, a simulation example is provided to verify the effectiveness of the proposed methods.

A training rule which guarantees finite-region stability for a class of closed-loop neural-network control systems.

Science.gov (United States)

Kuntanapreeda, S; Fullmer, R R

1996-01-01

A training method for a class of neural network controllers is presented which guarantees closed-loop system stability. The controllers are assumed to be nonlinear, feedforward, sampled-data, full-state regulators implemented as single hidden-layer neural networks. The controlled systems must be locally hermitian and observable. Stability of the closed-loop system is demonstrated by determining a Lyapunov function, which can be used to identify a finite stability region about the regulator point.

Nonlinear Lyapunov-based boundary control of distributed heat transfer mechanisms in membrane distillation plant

KAUST Repository

Eleiwi, Fadi; Laleg-Kirati, Taous-Meriem

2015-01-01

This paper presents a nonlinear Lyapunov-based boundary control for the temperature difference of a membrane distillation boundary layers. The heat transfer mechanisms inside the process are modeled with a 2D advection-diffusion equation. The model

First Integrals of Evolution Systems and Nonlinear Stability of Stationary Solutions for the Ideal Atmospheric, Oceanic Hydrodynamical and Plasma Models

International Nuclear Information System (INIS)

Gordin, V.A.

1998-01-01

First integral of the systems of nonlinear equations governing the behaviour of atmospheric, oceanic and MHD plasma models are determined. The Lyapunov stability conditions for the solutions under small initial disturbances are analyzed. (author)

Stabilization of exact nonlinear Timoshenko beams in space by boundary feedback

Science.gov (United States)

Do, K. D.

2018-05-01

Boundary feedback controllers are designed to stabilize Timoshenko beams with large translational and rotational motions in space under external disturbances. The exact nonlinear partial differential equations governing motion of the beams are derived and used in the control design. The designed controllers guarantee globally practically asymptotically (and locally practically exponentially) stability of the beam motions at the reference state. The control design, well-posedness and stability analysis are based on various relationships between the earth-fixed and body-fixed coordinates, Sobolev embeddings, and a Lyapunov-type theorem developed to study well-posedness and stability for a class of evolution systems in Hilbert space. Simulation results are included to illustrate the effectiveness of the proposed control design.

Anti-Synchronization of Chaotic Systems via Adaptive Sliding Mode Control

International Nuclear Information System (INIS)

Jawaada, Wafaa; Noorani, M. S. M.; Al-Sawalha, M. Mossa

2012-01-01

An anti-synchronization scheme is proposed to achieve the anti-synchronization behavior between chaotic systems with fully unknown parameters. A sliding surface and an adaptive sliding mode controller are designed to gain the anti-synchronization. The stability of the error dynamics is proven theoretically using the Lyapunov stability theory. Finally numerical results are presented to justify the theoretical analysis

Advanced nonlinear theory: Long-term stability at the SSC

International Nuclear Information System (INIS)

Heifets, S.

1987-01-01

This paper discussed the long-term stability of the particle beams in the Superconducting Super Collider. In particular the dynamics of a single particle beam is considered in depth. The topics of this paper include: the Hamiltonian of this particle approach, perturbation theory, canonical transformations, interaction of the resonances, structure of the phase space, synchro-Betatron oscillations, modulation diffusion and noise-resonance interaction. 36 refs

Limitations of Evolutionary Theory in Explaining Marital Satisfaction and Stability of Couple Relationships

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Victoria Cabrera García

2014-01-01

Full Text Available The explanation of marital satisfaction and stability in trajectories of couple relationships has been the central interest in different studies (Karney, Bradbury. & Johnson, 1999; Sabatelli & Ripoll, 2004; Schoebi, Karney & Bradbury, 2012. However, there are still several questions and unknown aspects surrounding the topic. Within this context, the present reflection seeks to analyze whether the principles of Evolutionary Theory suffice to explain three marital trajectories in terms of satisfaction and stability. With this in mind, we have included other explanations proposed by the Psychosocial Theory that Evolutionary Theory does not refer to in order to better understand mating behavior. Moreover, other factors that could account for satisfied and stable relationships were analyzed. Suggestions for future investigations include the analysis of other marital trajectories that may or may not end in separation or divorce but are not included in this article.

Stability analysis of delayed genetic regulatory networks with stochastic disturbances

Energy Technology Data Exchange (ETDEWEB)

Zhou Qi, E-mail: zhouqilhy@yahoo.com.c [School of Automation, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu (China); Xu Shengyuan [School of Automation, Nanjing University of Science and Technology, Nanjing 210094, Jiangsu (China); Chen Bing [Institute of Complexity Science, Qingdao University, Qingdao 266071, Shandong (China); Li Hongyi [Space Control and Inertial Technology Research Center, Harbin Institute of Technology, Harbin 150001 (China); Chu Yuming [Department of Mathematics, Huzhou Teacher' s College, Huzhou 313000, Zhejiang (China)

2009-10-05

This Letter considers the problem of stability analysis of a class of delayed genetic regulatory networks with stochastic disturbances. The delays are assumed to be time-varying and bounded. By utilizing Ito's differential formula and Lyapunov-Krasovskii functionals, delay-range-dependent and rate-dependent (rate-independent) stability criteria are proposed in terms of linear matrices inequalities. An important feature of the proposed results is that all the stability conditions are dependent on the upper and lower bounds of the delays. Another important feature is that the obtained stability conditions are less conservative than certain existing ones in the literature due to introducing some appropriate free-weighting matrices. A simulation example is employed to illustrate the applicability and effectiveness of the proposed methods.

Optimal Sliding Mode Controllers for Attitude Stabilization of Flexible Spacecraft

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Chutiphon Pukdeboon

2011-01-01

Full Text Available The robust optimal attitude control problem for a flexible spacecraft is considered. Two optimal sliding mode control laws that ensure the exponential convergence of the attitude control system are developed. Integral sliding mode control (ISMC is applied to combine the first-order sliding mode with optimal control and is used to control quaternion-based spacecraft attitude manoeuvres with external disturbances and an uncertainty inertia matrix. For the optimal control part the state-dependent Riccati equation (SDRE and optimal Lyapunov techniques are employed to solve the infinite-time nonlinear optimal control problem. The second method of Lyapunov is used to guarantee the stability of the attitude control system under the action of the proposed control laws. An example of multiaxial attitude manoeuvres is presented and simulation results are included to verify the usefulness of the developed controllers.

Impulsive effects on global asymptotic stability of delay BAM neural networks

International Nuclear Information System (INIS)

Chen Jun; Cui Baotong

2008-01-01

Based on the proper Lyapunov functions and the Jacobsthal liner inequality, some sufficient conditions are presented in this paper for global asymptotic stability of delay bidirectional associative memory neural networks with impulses. The obtained results are independently of the delay parameters and can be easily verified. Also, some remarks and an illustrative example are given to demonstrate the effectiveness of the obtained results

Stability of EBT of guiding-centre fluid theory

International Nuclear Information System (INIS)

Miller, R.L.

1981-01-01

The stability of the hot-electron annulus in the ELMO Bumpy Torus (EBT) is not yet completely understood despite considerable attention. Most stability studies have dealt with localized analysis of simplified models in which the actual magnetic configuration is replaced by a straight-line slab with a gravity to emulate the effects of curvature and gradients in the actual magnetic field. Here, a more realistic geometry, a 'bumpy' cylinder with a 2:1 magnetic mirror ratio, is considered and the response of the hot-electron rings to various non-local perturbations, specifying only the mode number in the ignorable co-ordinate, is examined. Guiding-centre theory (with psub(perpendicular) > psub(parallel)) is used and the second variation in the plasma energy (σW) using a finite-element representation to identify the least stable mode for the plasma is studied. All the equilibria that are examined are found to be unstable for all poloidal mode numbers m>=1, with growth rates increasing with increasing ring beta, plasma beta, and poloidal mode number. It is concluded that two-fluid and/or kinetic effects are required to explain the observed global stability of EBT-I. (author)

Tutorial on Feedback Control of Flows, Part I: Stabilization of Fluid Flows in Channels and Pipes

Directory of Open Access Journals (Sweden)

Ole M. Aamo

2002-07-01

Full Text Available The field of flow control has picked up pace over the past decade or so, on the promise of real-time distributed control on turbulent scales being realizable in the near future. This promise is due to the micromachining technology that emerged in the 1980s and developed at an amazing speed through the 1990s. In lab experiments, so called micro-electro-mechanical systems (MEMS that incorporate the entire detection-decision-actuation process on a single chip, have been batch processed in large numbers and assembled into flexible skins for gluing onto body-fluid interfaces for drag reduction purposes. Control of fluid flows span a wide variety of specialities. In Part I of this tutorial, we focus on the problem of reducing drag in channel and pipe flows by stabilizing the parabolic equilibrium profile using boundary feedback control. The control strategics used for this problem include classical control, based on the Nyquist criteria, and various optimal control techniques (H2, H-Infinity, as well as applications of Lyapunov stability theory.

Determining the Lyapunov Spectrum of Continuous-Time 1D and 2D Multiscroll Chaotic Oscillators via the Solution of m-PWL Variational Equations

Directory of Open Access Journals (Sweden)

Jesus Manuel Munoz-Pacheco

2013-01-01

Full Text Available An algorithm to compute the Lyapunov exponents of piecewise linear function-based multidirectional multiscroll chaotic oscillators is reported. Based on the m regions in the piecewise linear functions, the suggested algorithm determines the individual expansion rate of Lyapunov exponents from m-piecewise linear variational equations and their associated m-Jacobian matrices whose entries remain constant during all computation cycles. Additionally, by considering OpAmp-based chaotic oscillators, we study the impact of two analog design procedures on the magnitude of Lyapunov exponents. We focus on analyzing variations of both frequency bandwidth and voltage/current dynamic range of the chaotic signals at electronic system level. As a function of the design parameters, a renormalization factor is proposed to estimate correctly the Lyapunov spectrum. Numerical simulation results in a double-scroll type chaotic oscillator and complex chaotic oscillators generating multidirectional multiscroll chaotic attractors on phase space confirm the usefulness of the reported algorithm.

Stability analysis of Markovian jumping stochastic Cohen—Grossberg neural networks with discrete and distributed time varying delays

International Nuclear Information System (INIS)

Ali, M. Syed

2014-01-01

In this paper, the global asymptotic stability problem of Markovian jumping stochastic Cohen—Grossberg neural networks with discrete and distributed time-varying delays (MJSCGNNs) is considered. A novel LMI-based stability criterion is obtained by constructing a new Lyapunov functional to guarantee the asymptotic stability of MJSCGNNs. Our results can be easily verified and they are also less restrictive than previously known criteria and can be applied to Cohen—Grossberg neural networks, recurrent neural networks, and cellular neural networks. Finally, the proposed stability conditions are demonstrated with numerical examples

The design of delay-dependent wide-area DOFC with prescribed degree of stability α for damping inter-area low-frequency oscillations in power system.

Science.gov (United States)

Sun, Miaoping; Nian, Xiaohong; Dai, Liqiong; Guo, Hua

2017-05-01

In this paper, the delay-dependent wide-area dynamic output feedback controller (DOFC) with prescribed degree of stability is proposed for interconnected power system to damp inter-area low-frequency oscillations. Here, the prescribed degree of stability α is used to maintain all the poles on the left of s=-α in the s-plane. Firstly, residue approach is adopted to select input-output control signals and the schur balanced truncation model reduction method is utilized to obtain the reduced power system model. Secondly, based on Lyapunov stability theory and transformation operation in complex plane, the sufficient condition of asymptotic stability for closed-loop power system with prescribed degree of stability α is derived. Then, a novel method based on linear matrix inequalities (LMIs) is presented to obtain the parameters of DOFC and calculate delay margin of the closed-loop system considering the prescribed degree of stability α. Finally, case studies are carried out on the two-area four-machine system, which is controlled by classical wide-area power system stabilizer (WAPSS) in reported reference and our proposed DOFC respectively. The effectiveness and advantages of the proposed method are verified by the simulation results under different operating conditions. Copyright © 2017 ISA. Published by Elsevier Ltd. All rights reserved.

Taxonomía de asteroides y cometas basada en los espectros de Lyapunov

Science.gov (United States)

Tancredi, G.; Motta, V.; Froeschlé, C.

Estudiaremos dos familias de objetos que sufren encuentros cercanos con planetas, a saber: la familia de cometas de Júpiter (JF) y los asteroides cercanos a la Tierra (NEAs). El movimiento de estos objetos es caótico en una escala de tiempo corta. Más aún, debido a los cambios erráticos en los elementos orbitales, la comparación de los valores actuales da poca información acerca de la posible vinculación dinámica entre los objetos de una misma familia. Calculamos una estimación finita de los Exponentes Característicos de Lyapunov (LCE), los llamamos Indicadores Característicos de Lyapunov (LCI) para ambas familias y analizamos las características del espacio de fase donde tiene lugar el movimiento de estos objetos. Integrando en un período suficientemente largo (e.g. 20000 años), encontramos que el LCI alcanza un valor cuasi-constante. La mayoría de los miembros de ambas familias muestran una concentración de los tiempos de Lyapunov (inverso del LCI) de alrededor de 50-100 años (Tancredi, 1995, Astron & Astrop., 299, 288). La concentración de los tiempos de Lyapunov es mayor para la familia de Júpiter que para los NEAs. Entre estos últimos, la menor dispersión se da para aquellos que cruzan la órbita de la Tierra. Se demostró que el espectro de los `indicadores locales' (Froeschlé et. al., 1990, Cel. Mec. 56, 307) o ``números de estiramiento'' (Voglis and Contopoulos, 1994, J. Phys. A 26, 4899) (relacionados con el LCI) son invariantes y nos dan una información más completa sobre el comportamiento caótico. Mediante la comparación de espectros discutimos la similitud entre los objetos de una misma familia y analizamos las diferentes posibles rutas al caos. Los espectros se clasifican mediante la comparación de los momentos de las distribuciones de los `números de estiramiento'. Aplicamos un método de agrupamiento jerárquico (Zappala et. al., 1990, Astron. J. 100, 2030) para identificar ``familias'' de espectros (grupos de espectros

Anti-windup adaptive PID control design for a class of uncertain chaotic systems with input saturation.

Science.gov (United States)

Tahoun, A H

2017-01-01

In this paper, the stabilization problem of actuators saturation in uncertain chaotic systems is investigated via an adaptive PID control method. The PID control parameters are auto-tuned adaptively via adaptive control laws. A multi-level augmented error is designed to account for the extra terms appearing due to the use of PID and saturation. The proposed control technique uses both the state-feedback and the output-feedback methodologies. Based on Lyapunov׳s stability theory, new anti-windup adaptive controllers are proposed. Demonstrative examples with MATLAB simulations are studied. The simulation results show the efficiency of the proposed adaptive PID controllers. Copyright © 2016 ISA. Published by Elsevier Ltd. All rights reserved.

STABLE ADAPTIVE CONTROL FOR A CLASS OF NONLINEAR SYSTEMS WITHOUT USE OF A SUPERVISORY TERM IN THE CONTROL LAW

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MOHAMED BAHITA

2012-02-01

Full Text Available In this paper, a direct adaptive control scheme for a class of nonlinear systems is proposed. The architecture employs a Gaussian radial basis function (RBF network to construct an adaptive controller. The parameters of the adaptive controller are adapted and changed according to a law derived using Lyapunov stability theory. The centres of the RBF network are adapted on line using the k-means algorithm. Asymptotic Lyapunov stability is established without the use of a supervisory (compensatory term in the control law and with the tracking errors converging to a neighbourhood of the origin. Finally, a simulation is provided to explore the feasibility of the proposed neuronal controller design method.

A Hyperchaotic Attractor with Multiple Positive Lyapunov Exponents

International Nuclear Information System (INIS)

Guo-Si, Hu

2009-01-01

There are many hyperchaotic systems, but few systems can generate hyperchaotic attractors with more than three PLEs (positive Lyapunov exponents). A new hyperchaotic system, constructed by adding an approximate time-delay state feedback to a five-dimensional hyperchaotic system, is presented. With the increasing number of phase-shift units used in this system, the number of PLEs also steadily increases. Hyperchaotic attractors with 25 PLEs can be generated by this system with 32 phase-shift units. The sum of the PLEs will reach the maximum value when 23 phase-shift units are used. A simple electronic circuit, consisting of 16 operational amplifiers and two analogy multipliers, is presented for confirming hyperchaos of order 5, i.e., with 5 PLEs

On exponential stability and periodic solutions of CNNs with delays

Science.gov (United States)

Cao, Jinde

2000-03-01

In this Letter, the author analyses further problems of global exponential stability and the existence of periodic solutions of cellular neural networks with delays (DCNNs). Some simple and new sufficient conditions are given ensuring global exponential stability and the existence of periodic solutions of DCNNs by applying some new analysis techniques and constructing suitable Lyapunov functionals. These conditions have important leading significance in the design and applications of globally stable DCNNs and periodic oscillatory DCNNs and are weaker than those in the earlier works [Phys. Rev. E 60 (1999) 3244], [J. Comput. Syst. Sci. 59 (1999)].

On the nonlinear stability of mKdV breathers

Science.gov (United States)

Alejo, Miguel A.; Muñoz, Claudio

2012-11-01

Breather modes of the mKdV equation on the real line are known to be elastic under collisions with other breathers and solitons. This fact indicates very strong stability properties of breathers. In this communication we describe a rigorous, mathematical proof of the stability of breathers under a class of small perturbations. Our proof involves the existence of a nonlinear equation satisfied by all breather profiles, and a new Lyapunov functional which controls the dynamics of small perturbations and instability modes. In order to construct such a functional, we work in a subspace of the energy one. However, our proof introduces new ideas in order to attack the corresponding stability problem in the energy space. Some remarks about the sine-Gordon case are also considered.

Global Asymptotic Stability of a Predator-Prey Model with Modified Leslie-Gower and Holling-Type II Schemes

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Shengbin Yu

2012-01-01

Full Text Available We study the predator-prey model proposed by Aziz-Alaoui and Okiye (Appl. Math. Lett. 16 (2003 1069–1075 First, the structure of equilibria and their linearized stability is investigated. Then, we provide two sufficient conditions on the global asymptotic stability of a positive equilibrium by employing the Fluctuation Lemma and Lyapunov direct method, respectively. The obtained results not only improve but also supplement existing ones.

Fractional Differential Equations in Terms of Comparison Results and Lyapunov Stability with Initial Time Difference

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Coşkun Yakar

2010-01-01

Full Text Available The qualitative behavior of a perturbed fractional-order differential equation with Caputo's derivative that differs in initial position and initial time with respect to the unperturbed fractional-order differential equation with Caputo's derivative has been investigated. We compare the classical notion of stability to the notion of initial time difference stability for fractional-order differential equations in Caputo's sense. We present a comparison result which again gives the null solution a central role in the comparison fractional-order differential equation when establishing initial time difference stability of the perturbed fractional-order differential equation with respect to the unperturbed fractional-order differential equation.

Stability and square integrability of derivatives of solutions of nonlinear fourth order differential equations with delay.

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Korkmaz, Erdal

2017-01-01

In this paper, we give sufficient conditions for the boundedness, uniform asymptotic stability and square integrability of the solutions to a certain fourth order non-autonomous differential equations with delay by using Lyapunov's second method. The results obtained essentially improve, include and complement the results in the literature.

Integral φ0-Stability in terms of Two Measures for Impulsive Differential Equations with “Supremum”

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Peiguang Wang

2014-01-01

Full Text Available This paper establishes a criterion on integral φ0-stability in terms of two measures for impulsive differential equations with “supremum” by using the cone-valued piecewise continuous Lyapunov functions, Razumikhin method, and comparative method. Meantime, an example is given to illustrate our result.

Global exponential stability analysis on impulsive BAM neural networks with distributed delays

Science.gov (United States)

Li, Yao-Tang; Yang, Chang-Bo

2006-12-01

Using M-matrix and topological degree tool, sufficient conditions are obtained for the existence, uniqueness and global exponential stability of the equilibrium point of bidirectional associative memory (BAM) neural networks with distributed delays and subjected to impulsive state displacements at fixed instants of time by constructing a suitable Lyapunov functional. The results remove the usual assumptions that the boundedness, monotonicity, and differentiability of the activation functions. It is shown that in some cases, the stability criteria can be easily checked. Finally, an illustrative example is given to show the effectiveness of the presented criteria.

Global asymptotic stability of Cohen-Grossberg neural networks with constant and variable delays

International Nuclear Information System (INIS)

Wu Wei; Cui Baotong; Huang Min

2007-01-01

Global asymptotic stability of Cohen-Grossberg neural networks with constant and variable delays is studied. Some sufficient conditions for the neural networks are proposed to guarantee the global asymptotic convergence by using different Lyapunov functionals. Our criteria represent an extension of the existing results in literatures. A comparison between our results and the previous results admits that our results establish a new set of stability criteria for delayed Cohen-Grossberg neural networks. Those conditions are less restrictive than those given in the earlier reference

A Lyapunov based approach to energy maximization in renewable energy technologies

Science.gov (United States)

Iyasere, Erhun

system. The controller tracks a desired array voltage, designed online using an incremental conductance extremum-seeking algorithm, by varying the duty cycle of the switching converter. The stability of the control algorithm is demonstrated by means of Lyapunov analysis. Representative numerical results demonstrate that the grid power system can be controlled to track the maximum power point of the photovoltaic array panel in varying atmospheric conditions. Additionally, the performance of the proposed strategy is compared to the typical maximum power point tracking (MPPT) method of perturb and observe (P&O), where the converter dynamics are ignored, and is shown to yield better results.

Role of secondary instability theory and parabolized stability equations in transition modeling

Science.gov (United States)

El-Hady, Nabil M.; Dinavahi, Surya P.; Chang, Chau-Lyan; Zang, Thomas A.

1993-01-01

In modeling the laminar-turbulent transition region, the designer depends largely on benchmark data from experiments and/or direct numerical simulations that are usually extremely expensive. An understanding of the evolution of the Reynolds stresses, turbulent kinetic energy, and quantifies in the transport equations like the dissipation and production is essential in the modeling process. The secondary instability theory and the parabolized stability equations method are used to calculate these quantities, which are then compared with corresponding quantities calculated from available direct numerical simulation data for the incompressible boundary-layer flow of laminar-turbulent transition conditions. The potential of the secondary instability theory and the parabolized stability equations approach in predicting these quantities is discussed; results indicate that inexpensive data that are useful for transition modeling in the early stages of the transition region can be provided by these tools.

Delay-Dependent Stability Analysis of Uncertain Fuzzy Systems with State and Input Delays under Imperfect Premise Matching

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Zejian Zhang

2013-01-01

Full Text Available This paper discusses the stability and stabilization problem for uncertain T-S fuzzy systems with time-varying state and input delays. A new augmented Lyapunov function with an additional triple-integral term and different membership functions of the fuzzy models and fuzzy controllers are introduced to derive the stability criterion, which is less conservative than the existing results. Moreover, a new flexibility design method is also provided. Some numerical examples are given to demonstrate the effectiveness and less conservativeness of the proposed method.

Theory and theory-based models for the pedestal, edge stability and ELMs in tokamaks

International Nuclear Information System (INIS)

Guzdar, P.N.; Mahajan, S.M.; Yoshida, Z.; Dorland, W.; Rogers, B.N.; Bateman, G.; Kritz, A.H.; Pankin, A.; Voitsekhovitch, I.; Onjun, T.; Snyder, S.

2005-01-01

Theories for equilibrium and stability of H-modes, and models for use within integrated modeling codes with the objective of predicting the height, width and shape of the pedestal at the edge of H-mode plasmas in tokamaks, as well as the onset and frequency of Edge Localized Modes (ELMs), are developed. A theory model for relaxed plasma states with flow, which uses two-fluid Hall-MHD equations, predicts that the natural scale length of the pedestal is the ion skin depth and the pedestal width is larger than the ion poloidal gyro-radius, in agreement with experimental observations. Computations with the GS2 code are used to identify micro-instabilities, such as electron drift waves, that survive the strong flow shear, diamagnetic flows, and magnetic shear that are characteristic of the pedestal. Other instabilities on the pedestal and gyro-radius scale, such as the Kelvin-Helmholtz instability, are also investigated. Time-dependent integrated modeling simulations are used to follow the transition from L-mode to H-mode and the subsequent evolution of ELMs as the heating power is increased. The flow shear stabilization that produces the transport barrier at the edge of the plasma reduces different modes of anomalous transport and, consequently, different channels of transport at different rates. ELM crashes are triggered in the model by pressure-driven ballooning modes or by current-driven peeling modes. (author)

New results on global exponential stability of recurrent neural networks with time-varying delays

International Nuclear Information System (INIS)

Xu Shengyuan; Chu Yuming; Lu Junwei

2006-01-01

This Letter provides new sufficient conditions for the existence, uniqueness and global exponential stability of the equilibrium point of recurrent neural networks with time-varying delays by employing Lyapunov functions and using the Halanay inequality. The time-varying delays are not necessarily differentiable. Both Lipschitz continuous activation functions and monotone nondecreasing activation functions are considered. The derived stability criteria are expressed in terms of linear matrix inequalities (LMIs), which can be checked easily by resorting to recently developed algorithms solving LMIs. Furthermore, the proposed stability results are less conservative than some previous ones in the literature, which is demonstrated via some numerical examples

New results on global exponential stability of recurrent neural networks with time-varying delays

Energy Technology Data Exchange (ETDEWEB)

Xu Shengyuan [Department of Automation, Nanjing University of Science and Technology, Nanjing 210094 (China)]. E-mail: syxu02@yahoo.com.cn; Chu Yuming [Department of Mathematics, Huzhou Teacher' s College, Huzhou, Zhejiang 313000 (China); Lu Junwei [School of Electrical and Automation Engineering, Nanjing Normal University, 78 Bancang Street, Nanjing, 210042 (China)

2006-04-03

This Letter provides new sufficient conditions for the existence, uniqueness and global exponential stability of the equilibrium point of recurrent neural networks with time-varying delays by employing Lyapunov functions and using the Halanay inequality. The time-varying delays are not necessarily differentiable. Both Lipschitz continuous activation functions and monotone nondecreasing activation functions are considered. The derived stability criteria are expressed in terms of linear matrix inequalities (LMIs), which can be checked easily by resorting to recently developed algorithms solving LMIs. Furthermore, the proposed stability results are less conservative than some previous ones in the literature, which is demonstrated via some numerical examples.

Analysis of Multiple Structural Changes in Financial Contagion Based on the Largest Lyapunov Exponents

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Rui Wang

2014-01-01

Full Text Available A modified multiple structural changes model is built to test structural breaks of the financial system based on calculating the largest Lyapunov exponents of the financial time series. Afterwards, the Lorenz system is used as a simulation example to inspect the new model. As the Lorenz system has strong nonlinearity, the verification results show that the new model has good capability in both finding the breakpoint and revealing the changes in nonlinear characteristics of the time series. The empirical study based on the model used daily data from the S&P 500 stock index during the global financial crisis from 2005 to 2012. The results provide four breakpoints of the period, which divide the contagion into four stages: stationary, local outbreak, global outbreak, and recovery period. An additional significant result is the obvious chaos characteristic difference in the largest Lyapunov exponents and the standard deviation at various stages, particularly at the local outbreak stage.

Asymptotic theory of neutral stability of the Couette flow of a vibrationally excited gas

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Grigor'ev, Yu. N.; Ershov, I. V.

2017-01-01

An asymptotic theory of the neutral stability curve for a supersonic plane Couette flow of a vibrationally excited gas is developed. The initial mathematical model consists of equations of two-temperature viscous gas dynamics, which are used to derive a spectral problem for a linear system of eighth-order ordinary differential equations within the framework of the classical linear stability theory. Unified transformations of the system for all shear flows are performed in accordance with the classical Lin scheme. The problem is reduced to an algebraic secular equation with separation into the "inviscid" and "viscous" parts, which is solved numerically. It is shown that the thus-calculated neutral stability curves agree well with the previously obtained results of the direct numerical solution of the original spectral problem. In particular, the critical Reynolds number increases with excitation enhancement, and the neutral stability curve is shifted toward the domain of higher wave numbers. This is also confirmed by means of solving an asymptotic equation for the critical Reynolds number at the Mach number M ≤ 4.

Finite-time Lyapunov dimension and hidden attractor of the Rabinovich system

OpenAIRE

Kuznetsov, N. V.; Leonov, G. A.; Mokaev, T. N.; Prasad, A.; Shrimali, M. D.

2015-01-01

The Rabinovich system, describing the process of interaction between waves in plasma, is considered. It is shown that the Rabinovich system can exhibit a hidden attractor in the case of multistability as well as a classical self-excited attractor. The hidden attractor in this system can be localized by analytical/numerical methods based on the continuation and perpetual points. The concept of finite-time Lyapunov dimension is developed for numerical study of the dimension of attractors. A con...

Synchronization and anti-synchronization coexist in Chen-Lee chaotic systems

International Nuclear Information System (INIS)

Chen, J.-H.; Chen, H.-K.; Lin, Y.-K.

2009-01-01

This study demonstrates that synchronization and anti-synchronization can coexist in Chen-Lee chaotic systems by direct linear coupling. Based on Lyapunov's direct method, a linear controller was designed to assure that two different types of synchronization can simultaneously be achieved. Further, the hybrid projective synchronization of Chen-Lee chaotic systems was studied using a nonlinear control scheme. The nonlinear controller was designed according to the Lyapunov stability theory to guarantee the hybrid projective synchronization, including synchronization, anti-synchronization, and projective synchronization. Finally, numerical examples are presented in order to illustrate the proposed synchronization approach.

Stabilization of wave equations with variable coefficient and delay in the dynamical boundary feedback

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Dandan Guo

2017-08-01

Full Text Available In this article we consider the boundary stabilization of a wave equation with variable coefficients. This equation has an acceleration term and a delayed velocity term on the boundary. Under suitable geometric conditions, we obtain the exponential decay for the solutions. Our proof relies on the geometric multiplier method and the Lyapunov approach.

The Fermi-Pasta-Ulam Problem and Its Underlying Integrable Dynamics: An Approach Through Lyapunov Exponents

Science.gov (United States)

Benettin, G.; Pasquali, S.; Ponno, A.

2018-05-01

FPU models, in dimension one, are perturbations either of the linear model or of the Toda model; perturbations of the linear model include the usual β -model, perturbations of Toda include the usual α +β model. In this paper we explore and compare two families, or hierarchies, of FPU models, closer and closer to either the linear or the Toda model, by computing numerically, for each model, the maximal Lyapunov exponent χ . More precisely, we consider statistically typical trajectories and study the asymptotics of χ for large N (the number of particles) and small ɛ (the specific energy E / N), and find, for all models, asymptotic power laws χ ˜eq Cɛ ^a, C and a depending on the model. The asymptotics turns out to be, in general, rather slow, and producing accurate results requires a great computational effort. We also revisit and extend the analytic computation of χ introduced by Casetti, Livi and Pettini, originally formulated for the β -model. With great evidence the theory extends successfully to all models of the linear hierarchy, but not to models close to Toda.

Finite Time Control for Fractional Order Nonlinear Hydroturbine Governing System via Frequency Distributed Model

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Bin Wang

2016-01-01

Full Text Available This paper studies the application of frequency distributed model for finite time control of a fractional order nonlinear hydroturbine governing system (HGS. Firstly, the mathematical model of HGS with external random disturbances is introduced. Secondly, a novel terminal sliding surface is proposed and its stability to origin is proved based on the frequency distributed model and Lyapunov stability theory. Furthermore, based on finite time stability and sliding mode control theory, a robust control law to ensure the occurrence of the sliding motion in a finite time is designed for stabilization of the fractional order HGS. Finally, simulation results show the effectiveness and robustness of the proposed scheme.

Mean Square Exponential Stability of Stochastic Switched System with Interval Time-Varying Delays

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Manlika Rajchakit

2012-01-01

Full Text Available This paper is concerned with mean square exponential stability of switched stochastic system with interval time-varying delays. The time delay is any continuous function belonging to a given interval, but not necessary to be differentiable. By constructing a suitable augmented Lyapunov-Krasovskii functional combined with Leibniz-Newton’s formula, a switching rule for the mean square exponential stability of switched stochastic system with interval time-varying delays and new delay-dependent sufficient conditions for the mean square exponential stability of the switched stochastic system are first established in terms of LMIs. Numerical example is given to show the effectiveness of the obtained result.

Global exponential stability of BAM neural networks with time-varying delays: The discrete-time case

Science.gov (United States)

Raja, R.; Marshal Anthoni, S.

2011-02-01

This paper deals with the problem of stability analysis for a class of discrete-time bidirectional associative memory (BAM) neural networks with time-varying delays. By employing the Lyapunov functional and linear matrix inequality (LMI) approach, a new sufficient conditions is proposed for the global exponential stability of discrete-time BAM neural networks. The proposed LMI based results can be easily checked by LMI control toolbox. Moreover, an example is also provided to demonstrate the effectiveness of the proposed method.

Constraints and stability in vector theories with spontaneous Lorentz violation

International Nuclear Information System (INIS)

Bluhm, Robert; Gagne, Nolan L.; Potting, Robertus; Vrublevskis, Arturs

2008-01-01

Vector theories with spontaneous Lorentz violation, known as bumblebee models, are examined in flat spacetime using a Hamiltonian constraint analysis. In some of these models, Nambu-Goldstone modes appear with properties similar to photons in electromagnetism. However, depending on the form of the theory, additional modes and constraints can appear that have no counterparts in electromagnetism. An examination of these constraints and additional degrees of freedom, including their nonlinear effects, is made for a variety of models with different kinetic and potential terms, and the results are compared with electromagnetism. The Hamiltonian constraint analysis also permits an investigation of the stability of these models. For certain bumblebee theories with a timelike vector, suitable restrictions of the initial-value solutions are identified that yield ghost-free models with a positive Hamiltonian. In each case, the restricted phase space is found to match that of electromagnetism in a nonlinear gauge

Robust Stabilization of Discrete-Time Systems with Time-Varying Delay: An LMI Approach

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Valter J. S. Leite

2008-01-01

Full Text Available Sufficient linear matrix inequality (LMI conditions to verify the robust stability and to design robust state feedback gains for the class of linear discrete-time systems with time-varying delay and polytopic uncertainties are presented. The conditions are obtained through parameter-dependent Lyapunov-Krasovskii functionals and use some extra variables, which yield less conservative LMI conditions. Both problems, robust stability analysis and robust synthesis, are formulated as convex problems where all system matrices can be affected by uncertainty. Some numerical examples are presented to illustrate the advantages of the proposed LMI conditions.

Global chaos synchronization of new chaotic systems via nonlinear control

International Nuclear Information System (INIS)

Chen, H.-K.

2005-01-01

Nonlinear control is an effective method for making two identical chaotic systems or two different chaotic systems be synchronized. However, this method assumes that the Lyapunov function of error dynamic (e) of synchronization is always formed as V (e) = 1/2e T e. In this paper, modification based on Lyapunov stability theory to design a controller is proposed in order to overcome this limitation. The method has been applied successfully to make two identical new systems and two different chaotic systems (new system and Lorenz system) globally asymptotically synchronized. Since the Lyapunov exponents are not required for the calculation, this method is effective and convenient to synchronize two identical systems and two different chaotic systems. Numerical simulations are also given to validate the proposed synchronization approach

Adaptive modified projective synchronization of a unified chaotic system with an uncertain parameter

International Nuclear Information System (INIS)

Park, Ju H.

2007-01-01

An adaptive modified projective synchronization (AMPS) is proposed to acquire a general kind of proportional relationship between the drive and response systems. Based on the Lyapunov stability theory, a nonlinear control scheme for the synchronization has been presented. The control performances are verified by numerical simulations

Pramana – Journal of Physics | Indian Academy of Sciences

Indian Academy of Sciences (India)

The study involving multiswitching of three drive systems and one response system is first of its kind. Various switched modified function projective antisynchronization schemes are obtained as special cases of MSCoAS, for a suitable choice of scaling factors. Using suitable controllers and Lyapunov stability theory, ...

Robust adaptive synchronization of general dynamical networks ...

Indian Academy of Sciences (India)

Home; Journals; Pramana – Journal of Physics; Volume 86; Issue 6. Robust ... A robust adaptive synchronization scheme for these general complex networks with multiple delays and uncertainties is established and raised by employing the robust adaptive control principle and the Lyapunov stability theory. We choose ...

Nonfragile Robust Model Predictive Control for Uncertain Constrained Systems with Time-Delay Compensation

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Wei Jiang

2016-01-01

Full Text Available This study investigates the problem of asymptotic stabilization for a class of discrete-time linear uncertain time-delayed systems with input constraints. Parametric uncertainty is assumed to be structured, and delay is assumed to be known. In Lyapunov stability theory framework, two synthesis schemes of designing nonfragile robust model predictive control (RMPC with time-delay compensation are put forward, where the additive and the multiplicative gain perturbations are, respectively, considered. First, by designing appropriate Lyapunov-Krasovskii (L-K functions, the robust performance index is defined as optimization problems that minimize upper bounds of infinite horizon cost function. Then, to guarantee closed-loop stability, the sufficient conditions for the existence of desired nonfragile RMPC are obtained in terms of linear matrix inequalities (LMIs. Finally, two numerical examples are provided to illustrate the effectiveness of the proposed approaches.

Existence and global exponential stability of periodic solution of memristor-based BAM neural networks with time-varying delays.

Science.gov (United States)

Li, Hongfei; Jiang, Haijun; Hu, Cheng

2016-03-01

In this paper, we investigate a class of memristor-based BAM neural networks with time-varying delays. Under the framework of Filippov solutions, boundedness and ultimate boundedness of solutions of memristor-based BAM neural networks are guaranteed by Chain rule and inequalities technique. Moreover, a new method involving Yoshizawa-like theorem is favorably employed to acquire the existence of periodic solution. By applying the theory of set-valued maps and functional differential inclusions, an available Lyapunov functional and some new testable algebraic criteria are derived for ensuring the uniqueness and global exponential stability of periodic solution of memristor-based BAM neural networks. The obtained results expand and complement some previous work on memristor-based BAM neural networks. Finally, a numerical example is provided to show the applicability and effectiveness of our theoretical results. Copyright © 2015 Elsevier Ltd. All rights reserved.

Stability and instability of axisymmetric droplets in thermocapillary-driven thin films

Science.gov (United States)

Nicolaou, Zachary G.

2018-03-01

The stability of compactly supported, axisymmetric droplet states is considered for driven thin viscous films evolving on two-dimensional surfaces. Stability is assessed using Lyapunov energy methods afforded by the Cahn-Hilliard variational form of the governing equation. For general driving forces, a criterion on the gradient of profiles at the boundary of their support (their contact slope) is shown to be a necessary condition for stability. Additional necessary and sufficient conditions for stability are established for a specific driving force corresponding to a thermocapillary-driven film. It is found that only droplets of sufficiently short height that satisfy the contact slope criterion are stable. This destabilization of droplets with increasing height is characterized as a saddle-node bifurcation between a branch of tall, unstable droplets and a branch of short, stable droplets.

Mean square stabilization and mean square exponential stabilization of stochastic BAM neural networks with Markovian jumping parameters

International Nuclear Information System (INIS)

Ye, Zhiyong; Zhang, He; Zhang, Hongyu; Zhang, Hua; Lu, Guichen

2015-01-01

Highlights: •This paper introduces a non-conservative Lyapunov functional. •The achieved results impose non-conservative and can be widely used. •The conditions are easily checked by the Matlab LMI Tool Box. The desired state feedback controller can be well represented by the conditions. -- Abstract: This paper addresses the mean square exponential stabilization problem of stochastic bidirectional associative memory (BAM) neural networks with Markovian jumping parameters and time-varying delays. By establishing a proper Lyapunov–Krasovskii functional and combining with LMIs technique, several sufficient conditions are derived for ensuring exponential stabilization in the mean square sense of such stochastic BAM neural networks. In addition, the achieved results are not difficult to verify for determining the mean square exponential stabilization of delayed BAM neural networks with Markovian jumping parameters and impose less restrictive and less conservative than the ones in previous papers. Finally, numerical results are given to show the effectiveness and applicability of the achieved results

Memory H ∞ performance control of a class T-S fuzzy system

Science.gov (United States)

Wang, Yanhua; He, Xiqin; Wu, Zhihua; Kang, Xiulan; Xiu, Wei

2018-03-01

For much nonlinear system in the control system, both the stability of the system and certain performance indicators are required. The characteristics of T-S model in fuzzy system make it possible to illustrate a great amount of nonlinear system efficiently. First and foremost, the T-S model with uncertainties and external disturbance is utilized to interpret nonlinear system so as to implement H∞ performance control by means of fuzzy control theory. Meantime, owing to the tremendous existence of time delay phenomenon in the controlled, feedback controller with memory fuzzy state is fabricated. On the basis of Lyapunov Stability Theory, the closed-loop system becomes stable by establishing Lyapunov function. Gain matrix of the memory state feedback controller is obtained by applying linear matrix inequality methodology. And simultaneously it makes the system meet the requirement of the H∞ performance indicator. Ultimately, the efficiency of the above-mentioned method is exemplified by the numerical computation.

Stability of Intelligent Transportation Network Dynamics: A Daily Path Flow Adjustment considering Travel Time Differentiation

Directory of Open Access Journals (Sweden)

Ming-Chorng Hwang

2015-01-01

Full Text Available A theoretic formulation on how traffic time information distributed by ITS operations influences the trajectory of network flows is presented in this paper. The interactions between users and ITS operator are decomposed into three parts: (i travel time induced path flow dynamics (PFDTT; (ii demand induced path flow dynamics (PFDD; and (iii predicted travel time dynamics for an origin-destination (OD pair (PTTDOD. PFDTT describes the collective results of user’s daily route selection by pairwise comparison of path travel time provided by ITS services. The other two components, PTTDOD and PFDD, are concentrated on the evolutions of system variables which are predicted and observed, respectively, by ITS operators to act as a benchmark in guiding the target system towards an expected status faster. In addition to the delivered modelings, the stability theorem of the equilibrium solution in the sense of Lyapunov stability is also provided. A Lyapunov function is developed and employed to the proof of stability theorem to show the asymptotic behavior of the aimed system. The information of network flow dynamics plays a key role in traffic control policy-making. The evaluation of ITS-based strategies will not be reasonable without a well-established modeling of network flow evolutions.

A new interpretation of zero Lyapunov exponents in BKL time for Mixmaster cosmology

International Nuclear Information System (INIS)

Wu Xin

2010-01-01

A global relationship between cosmological time and Belinskii-Khalatnikov-Lifshitz (BKL) time during the entire evolution of the Mixmaster Bianchi IX universe is used to explain why all the Lyapunov exponents are zero at the BKL time. The actual reason is that the domain of the cosmological time is finite as the BKL time runs from minus infinity to infinity.

Economic model predictive control theory, formulations and chemical process applications

CERN Document Server

Ellis, Matthew; Christofides, Panagiotis D

2017-01-01

This book presents general methods for the design of economic model predictive control (EMPC) systems for broad classes of nonlinear systems that address key theoretical and practical considerations including recursive feasibility, closed-loop stability, closed-loop performance, and computational efficiency. Specifically, the book proposes: Lyapunov-based EMPC methods for nonlinear systems; two-tier EMPC architectures that are highly computationally efficient; and EMPC schemes handling explicitly uncertainty, time-varying cost functions, time-delays and multiple-time-scale dynamics. The proposed methods employ a variety of tools ranging from nonlinear systems analysis, through Lyapunov-based control techniques to nonlinear dynamic optimization. The applicability and performance of the proposed methods are demonstrated through a number of chemical process examples. The book presents state-of-the-art methods for the design of economic model predictive control systems for chemical processes. In addition to being...

Lyapunov spectrum of the separated flow around the NACA 0012 airfoil and its dependence on numerical discretization

International Nuclear Information System (INIS)

Fernandez, P.; Wang, Q.

2017-01-01

We investigate the impact of numerical discretization on the Lyapunov spectrum of separated flow simulations. The two-dimensional chaotic flow around the NACA 0012 airfoil at a low Reynolds number and large angle of attack is considered to that end. Time, space and accuracy-order refinement studies are performed to examine each of these effects separately. Numerical results show that the time discretization has a small impact on the dynamics of the system, whereas the spatial discretization can dramatically change them. Also, the finite-time Lyapunov exponents associated to unstable modes are shown to be positively skewed, and quasi-homoclinic tangencies are observed in the attractor of the system. The implications of these results on flow physics and sensitivity analysis of chaotic flows are discussed.

Lyapunov spectrum of the separated flow around the NACA 0012 airfoil and its dependence on numerical discretization

Science.gov (United States)

Fernandez, P.; Wang, Q.

2017-12-01

We investigate the impact of numerical discretization on the Lyapunov spectrum of separated flow simulations. The two-dimensional chaotic flow around the NACA 0012 airfoil at a low Reynolds number and large angle of attack is considered to that end. Time, space and accuracy-order refinement studies are performed to examine each of these effects separately. Numerical results show that the time discretization has a small impact on the dynamics of the system, whereas the spatial discretization can dramatically change them. Also, the finite-time Lyapunov exponents associated to unstable modes are shown to be positively skewed, and quasi-homoclinic tangencies are observed in the attractor of the system. The implications of these results on flow physics and sensitivity analysis of chaotic flows are discussed.

Wake meandering under non-neutral atmospheric stability conditions – theory and facts

DEFF Research Database (Denmark)

Larsen, Gunner Chr.; Machefaux, Ewan; Chougule, Abhijit S.

2015-01-01

This paper deals with modelling of wake dynamics under influence of atmospheric stability conditions different from neutral. In particular, it is investigated how the basic split in turbulent scales, on which the Dynamic Wake Meandering model is based, can be utilized to include atmospheric...... stability effects in this model. This is done partly by analyzing a large number of turbulence spectra obtained from sonic measurements, partly by analyzing dedicated full-scale LiDAR measurements from which wake dynamics can be directly resolved. The theory behind generalizing the Dynamic Wake Meandering...

Aspects of Moduli Stabilization in Type IIB String Theory

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Shaaban Khalil

2016-01-01

Full Text Available We review moduli stabilization in type IIB string theory compactification with fluxes. We focus on KKLT and Large Volume Scenario (LVS. We show that the predicted soft SUSY breaking terms in KKLT model are not phenomenological viable. In LVS, the following result for scalar mass, gaugino mass, and trilinear term is obtained: m0=m1/2=-A0=m3/2, which may account for Higgs mass limit if m3/2~O(1.5 TeV. However, in this case, the relic abundance of the lightest neutralino cannot be consistent with the measured limits. We also study the cosmological consequences of moduli stabilization in both models. In particular, the associated inflation models such as racetrack inflation and Kähler inflation are analyzed. Finally, the problem of moduli destabilization and the effect of string moduli backreaction on the inflation models are discussed.

Stability analysis of hybrid-driven underwater glider

Science.gov (United States)

Niu, Wen-dong; Wang, Shu-xin; Wang, Yan-hui; Song, Yang; Zhu, Ya-qiang

2017-10-01

Hybrid-driven underwater glider is a new type of unmanned underwater vehicle, which combines the advantages of autonomous underwater vehicles and traditional underwater gliders. The autonomous underwater vehicles have good maneuverability and can travel with a high speed, while the traditional underwater gliders are highlighted by low power consumption, long voyage, long endurance and good stealth characteristics. The hybrid-driven underwater gliders can realize variable motion profiles by their own buoyancy-driven and propeller propulsion systems. Stability of the mechanical system determines the performance of the system. In this paper, the Petrel-II hybrid-driven underwater glider developed by Tianjin University is selected as the research object and the stability of hybrid-driven underwater glider unitedly controlled by buoyancy and propeller has been targeted and evidenced. The dimensionless equations of the hybrid-driven underwater glider are obtained when the propeller is working. Then, the steady speed and steady glide path angle under steady-state motion have also been achieved. The steady-state operating conditions can be calculated when the hybrid-driven underwater glider reaches the desired steady-state motion. And the steadystate operating conditions are relatively conservative at the lower bound of the velocity range compared with the range of the velocity derived from the method of the composite Lyapunov function. By calculating the hydrodynamic coefficients of the Petrel-II hybrid-driven underwater glider, the simulation analysis has been conducted. In addition, the results of the field trials conducted in the South China Sea and the Danjiangkou Reservoir of China have been presented to illustrate the validity of the analysis and simulation, and to show the feasibility of the method of the composite Lyapunov function which verifies the stability of the Petrel-II hybrid-driven underwater glider.

Dynamic stability analysis of fractional order leaky integrator echo state neural networks

Science.gov (United States)

Pahnehkolaei, Seyed Mehdi Abedi; Alfi, Alireza; Tenreiro Machado, J. A.

2017-06-01

The Leaky integrator echo state neural network (Leaky-ESN) is an improved model of the recurrent neural network (RNN) and adopts an interconnected recurrent grid of processing neurons. This paper presents a new proof for the convergence of a Lyapunov candidate function to zero when time tends to infinity by means of the Caputo fractional derivative with order lying in the range (0, 1). The stability of Fractional-Order Leaky-ESN (FO Leaky-ESN) is then analyzed, and the existence, uniqueness and stability of the equilibrium point are provided. A numerical example demonstrates the feasibility of the proposed method.

Stability in a diffusive food chain model with Michaelis-Menten functional response

DEFF Research Database (Denmark)

Lin, Zhigui; Pedersen, Michael

2004-01-01

This paper deals with the behavior of positive solutions to a reaction-diffusion system with homogeneous Neumann boundary conditions describing a three species food chain. A sufficient condition for the local asymptotical stability is given by linearization and also a sufficient condition...... for the global asymptotical stability is given by a Lyapunov function. Our result shows that the equilibrium solution is globally asymptotically stable if the net birth rate of the first species is big enough and the net death rate of the third species is neither too big nor too small. (C) 2004 Elsevier Ltd. All...

Chaos Q-S synchronization between Rossler system and the new unified chaotic system

International Nuclear Information System (INIS)

Yan Zhenya

2005-01-01

In this Letter, we investigate the Q-S synchronization between two different chaotic systems: the Rossler system and the new unified Lorenz-Chen-Lu system based on the backstepping design method and Lyapunov stability theory. Moreover numerical simulations are used to verify the effectiveness of the proposed controller

Uniform persistence and upper Lyapunov exponents for monotone skew-product semiflows

International Nuclear Information System (INIS)

Novo, Sylvia; Obaya, Rafael; Sanz, Ana M

2013-01-01

Several results of uniform persistence above and below a minimal set of an abstract monotone skew-product semiflow are obtained. When the minimal set has a continuous separation the results are given in terms of the principal spectrum. In the case that the semiflow is generated by the solutions of a family of non-autonomous differential equations of ordinary, delay or parabolic type, the former results are strongly improved. A method of calculus of the upper Lyapunov exponent of the minimal set is also determined. (paper)

Delay-dependent exponential stability for neural networks with discrete and distributed time-varying delays

International Nuclear Information System (INIS)

Zhu Xunlin; Wang Youyi

2009-01-01

This Letter studies the exponential stability for a class of neural networks (NNs) with both discrete and distributed time-varying delays. Under weaker assumptions on the activation functions, by defining a more general type of Lyapunov functionals and developing a new convex combination technique, new less conservative and less complex stability criteria are established to guarantee the global exponential stability of the discussed NNs. The obtained conditions are dependent on both discrete and distributed delays, are expressed in terms of linear matrix inequalities (LMIs), and contain fewer decision variables. Numerical examples are given to illustrate the effectiveness and the less conservatism of the proposed conditions.

Boundedness and stability for recurrent neural networks with variable coefficients and time-varying delays

International Nuclear Information System (INIS)

Liang Jinling; Cao Jinde

2003-01-01

In this Letter, the problems of boundedness and stability for a general class of non-autonomous recurrent neural networks with variable coefficients and time-varying delays are analyzed via employing Young inequality technique and Lyapunov method. Some simple sufficient conditions are given for boundedness and stability of the solutions for the recurrent neural networks. These results generalize and improve the previous works, and they are easy to check and apply in practice. Two illustrative examples and their numerical simulations are also given to demonstrate the effectiveness of the proposed results

Delay-dependent asymptotic stability of a two-neuron system with different time delays

International Nuclear Information System (INIS)

Tu Fenghua; Liao Xiaofeng; Zhang Wei

2006-01-01

In this paper, we consider a two-neuron system with time-delayed connections between neurons. Based on the construction of Lyapunov functionals, we obtain sufficient criteria to ensure local and global asymptotic stability of the equilibrium of the neural network. The obtained conditions are shown to be less conservative and restrictive than those reported in the literature. Some examples are included to illustrate our results

Effect of parameter calculation in direct estimation of the Lyapunov exponent in short time series

Directory of Open Access Journals (Sweden)

A. M. López Jiménez

2002-01-01

Full Text Available The literature about non-linear dynamics offers a few recommendations, which sometimes are divergent, about the criteria to be used in order to select the optimal calculus parameters in the estimation of Lyapunov exponents by direct methods. These few recommendations are circumscribed to the analysis of chaotic systems. We have found no recommendation for the estimation of λ starting from the time series of classic systems. The reason for this is the interest in distinguishing variability due to a chaotic behavior of determinist dynamic systems of variability caused by white noise or linear stochastic processes, and less in the identification of non-linear terms from the analysis of time series. In this study we have centered in the dependence of the Lyapunov exponent, obtained by means of direct estimation, of the initial distance and the time evolution. We have used generated series of chaotic systems and generated series of classic systems with varying complexity. To generate the series we have used the logistic map.

A theory of life satisfaction dynamics : Stability, change and volatility in 25-year life trajectories in Germany

NARCIS (Netherlands)

Headey, Bruce; Muffels, R.J.A.

2018-01-01

An adequate theory of life satisfaction (LS) needs to take account of both factors that tend to stabilise LS and those that change it. The most widely accepted theory in the recent past—set-point theory—focussed solely on stability (Brickman and Campbell, in:Appley (ed) Adaptation level theory,

Theory of asymptotic matching for resistive magnetohydrodynamic stability in a negative magnetic shear configuration

International Nuclear Information System (INIS)

Tokuda, Shinji; Watanabe, Tomoko.

1996-11-01

A theory and a numerical method are presented for the asymptotic matching analysis of resistive magnetohydrodynamic stability in a negative magnetic shear configuration with two rational surfaces. The theory formulates the problem of solving both the Newcomb equations in the ideal MHD region and the inner-layer equations around rational surfaces as boundary value/eigenvalue problems to which the finite element method and the finite difference method can be applied. Hence, the problem of stability analysis is solved by a numerically stable method. The present numerical method has been applied to model equations having analytic solutions in a negative magnetic shear configuration. Comparison of the numerical solutions with the analytical ones verifies the validity of the numerical method proposed. (author)

Method for stability analysis based on the Floquet theory and Vidyn calculations

Energy Technology Data Exchange (ETDEWEB)

Ganander, Hans

2005-03-01

This report presents the activity 3.7 of the STEM-project Aerobig and deals with aeroelastic stability of the complete wind turbine structure at operation. As a consequence of the increase of sizes of wind turbines dynamic couplings are being more important for loads and dynamic properties. The steady ambition to increase the cost competitiveness of wind turbine energy by using optimisation methods lowers design margins, which in turn makes questions about stability of the turbines more important. The main objective of the project is to develop a general stability analysis tool, based on the VIDYN methodology regarding the turbine dynamic equations and the Floquet theory for the stability analysis. The reason for selecting the Floquet theory is that it is independent of number of blades, thus can be used for 2 as well as 3 bladed turbines. Although the latter ones are dominating on the market, the former has large potential when talking about offshore large turbines. The fact that cyclic and individual blade pitch controls are being developed as a mean for reduction of fatigue also speaks for general methods as Floquet. The first step of a general system for stability analysis has been developed, the code VIDSTAB. Together with other methods, as the snap shot method, the Coleman transformation and the use of Fourier series, eigenfrequences and modes can be analysed. It is general with no restrictions on the number of blades nor the symmetry of the rotor. The derivatives of the aerodynamic forces are calculated numerically in this first version. Later versions would include state space formulations of these forces. This would also be the case for the controllers of turbine rotation speed, yaw direction and pitch angle.

Phase space reconstruction and estimation of the largest Lyapunov exponent for gait kinematic data

Energy Technology Data Exchange (ETDEWEB)

Josiński, Henryk [Silesian University of Technology, Akademicka 16, 44-100 Gliwice (Poland); Świtoński, Adam [Polish-Japanese Institute of Information Technology, Aleja Legionów 2, 41-902 Bytom (Poland); Silesian University of Technology, Akademicka 16, 44-100 Gliwice (Poland); Michalczuk, Agnieszka; Wojciechowski, Konrad [Polish-Japanese Institute of Information Technology, Aleja Legionów 2, 41-902 Bytom (Poland)

2015-03-10

The authors describe an example of application of nonlinear time series analysis directed at identifying the presence of deterministic chaos in human motion data by means of the largest Lyapunov exponent. The method was previously verified on the basis of a time series constructed from the numerical solutions of both the Lorenz and the Rössler nonlinear dynamical systems.

Existence and Globally Asymptotic Stability of Equilibrium Solution for Fractional-Order Hybrid BAM Neural Networks with Distributed Delays and Impulses

Directory of Open Access Journals (Sweden)

Hai Zhang

2017-01-01

Full Text Available This paper investigates the existence and globally asymptotic stability of equilibrium solution for Riemann-Liouville fractional-order hybrid BAM neural networks with distributed delays and impulses. The factors of such network systems including the distributed delays, impulsive effects, and two different fractional-order derivatives between the U-layer and V-layer are taken into account synchronously. Based on the contraction mapping principle, the sufficient conditions are derived to ensure the existence and uniqueness of the equilibrium solution for such network systems. By constructing a novel Lyapunov functional composed of fractional integral and definite integral terms, the globally asymptotic stability criteria of the equilibrium solution are obtained, which are dependent on the order of fractional derivative and network parameters. The advantage of our constructed method is that one may directly calculate integer-order derivative of the Lyapunov functional. A numerical example is also presented to show the validity and feasibility of the theoretical results.

A novel stabilization condition for T-S polynomial fuzzy system with time-delay:A sum-of-squares approach

OpenAIRE

Tsai, Shun Hung; Chen, Yu-An; Chen, Yu-Wen; Lo, Ji-Chang; Lam, Hak-Keung

2017-01-01

A novel stabilization problem for T-S polynomial fuzzy system with time-delay is investigated in this paper. Firstly, a polynomial fuzzy controller for T-S polynomial fuzzy system with time-delay is proposed. In addition, based on polynomial Lyapunov-Krasovskii function and the developed polynomial slack variable matrices, a novel stabilization condition for T-S polynomial fuzzy system with time-delay is presented in terms of sum-of-square (SOS) form. Lastly, nonlinear system with time-delay ...

Information-entropic method for studying the stability bound of nonrelativistic polytropic stars within modified gravity theories

Science.gov (United States)

Wibisono, C.; Sulaksono, A.

We study the stability of nonrelativistic polytropic stars within two modified gravity theories, i.e. beyond Horndeski gravity and Eddington-inspired Born-Infeld theories, using the configuration entropy method. We use the spatially localized bounded function of energy density as solutions from stellar effective equations to construct the corresponding configuration entropy. We use the same argument as the one used by Gleiser and coworkers [M. Gleiser and D. Sowinski, Phys. Lett. B 727 (2013) 272; M. Gleiser and N. Jiang, Phys. Rev. D 92 (2015) 044046] that the stars are stable if there is a peak in configuration entropy as a function of adiabatic index curve. Specifically, the boundary between stable and unstable regions which corresponds to Chandrasekhar stability bound is indicated from the existence of the maximum peak while the most stable polytropic stars are indicated by the minimum peak in the corresponding curve. We have found that the values of critical adiabatic indexes of Chandrasekhar stability bound and the most stable polytropic stars predicted by the nonrelativistic limits of beyond Horndeski gravity and Eddington-inspired Born-Infeld theories are different to those predicted by general relativity where the corresponding differences depend on the free parameters of both theories.

[Analysis of the heart sound with arrhythmia based on nonlinear chaos theory].

Science.gov (United States)

Ding, Xiaorong; Guo, Xingming; Zhong, Lisha; Xiao, Shouzhong

2012-10-01

In this paper, a new method based on the nonlinear chaos theory was proposed to study the arrhythmia with the combination of the correlation dimension and largest Lyapunov exponent, through computing and analyzing these two parameters of 30 cases normal heart sound and 30 cases with arrhythmia. The results showed that the two parameters of the heart sounds with arrhythmia were higher than those with the normal, and there was significant difference between these two kinds of heart sounds. That is probably due to the irregularity of the arrhythmia which causes the decrease of predictability, and it's more complex than the normal heart sound. Therefore, the correlation dimension and the largest Lyapunov exponent can be used to analyze the arrhythmia and for its feature extraction.

Pramana – Journal of Physics | Indian Academy of Sciences

Indian Academy of Sciences (India)

In this work, a novel combination synchronization scheme in which synchronization of a new combination hyperchaotic drive system formed by combining state variables of ... By Lyapunov stability theory, the adaptive control law and the parameter update law are derived to make the state of two systems as modified function ...

Two (multi point nonlinear Lyapunov systems associated with an n th order nonlinear system of differential equations – existence and uniqueness

Directory of Open Access Journals (Sweden)

Murty K. N.

2000-01-01

Full Text Available This paper presents a criterion for the existence and uniqueness of solutions to two and multipoint boundary value problems associated with an n th order nonlinear Lyapunov system. A variation of parameters formula is developed and used as a tool to obtain existence and uniqueness. We discuss solution of the second order problem by the ADI method and develop a fixed point method to find the general solution of the n th order Lyapunov system. The results of Barnett (SIAM J. Appl. Anal. 24(1, 1973 are a particular case.

Stability analysis of embedded nonlinear predictor neural generalized predictive controller

Directory of Open Access Journals (Sweden)

Hesham F. Abdel Ghaffar

2014-03-01

Full Text Available Nonlinear Predictor-Neural Generalized Predictive Controller (NGPC is one of the most advanced control techniques that are used with severe nonlinear processes. In this paper, a hybrid solution from NGPC and Internal Model Principle (IMP is implemented to stabilize nonlinear, non-minimum phase, variable dead time processes under high disturbance values over wide range of operation. Also, the superiority of NGPC over linear predictive controllers, like GPC, is proved for severe nonlinear processes over wide range of operation. The necessary conditions required to stabilize NGPC is derived using Lyapunov stability analysis for nonlinear processes. The NGPC stability conditions and improvement in disturbance suppression are verified by both simulation using Duffing’s nonlinear equation and real-time using continuous stirred tank reactor. Up to our knowledge, the paper offers the first hardware embedded Neural GPC which has been utilized to verify NGPC–IMP improvement in realtime.

A new chaotic attractor with two quadratic nonlinearities, its synchronization and circuit implementation

Science.gov (United States)

Vaidyanathan, S.; Sambas, A.; Sukono; Mamat, M.; Gundara, G.; Mada Sanjaya, W. S.; Subiyanto

2018-03-01

A 3-D new chaotic attractor with two quadratic nonlinearities is proposed in this paper. The dynamical properties of the new chaotic system are described in terms of phase portraits, equilibrium points, Lyapunov exponents, Kaplan-Yorke dimension, dissipativity, etc. We show that the new chaotic system has three unstable equilibrium points. The new chaotic attractor is dissipative in nature. As an engineering application, adaptive synchronization of identical new chaotic attractors is designed via nonlinear control and Lyapunov stability theory. Furthermore, an electronic circuit realization of the new chaotic attractor is presented in detail to confirm the feasibility of the theoretical chaotic attractor model.

Hyperchaos Numerical Simulation and Control in a 4D Hyperchaotic System

Directory of Open Access Journals (Sweden)

Junhai Ma

2013-01-01

Full Text Available A hyperchaotic system is introduced, and the complex dynamical behaviors of such system are investigated by means of numerical simulations. The bifurcation diagrams, Lyapunov exponents, hyperchaotic attractors, the power spectrums, and time charts are mapped out through the theory analysis and dynamic simulations. The chaotic and hyper-chaotic attractors exist and alter over a wide range of parameters according to the variety of Lyapunov exponents and bifurcation diagrams. Furthermore, linear feedback controllers are designed for stabilizing the hyperchaos to the unstable equilibrium points; thus, we achieve the goal of a second control which is more useful in application.

A family of nonlinear PID-like regulators for a class of torque-driven robot manipulators equipped with torque-constrained actuators

Directory of Open Access Journals (Sweden)

Adriana Salinas

2016-02-01

Full Text Available This article addresses the joint position control of torque-driven robot manipulators under actuators subject to torque saturation. Robots having viscous friction, but without gravity vector, are considered. By assuming a static model for the torque actuator (specifically, a model of nonlinear and non-differentiable hard saturation function, a family of nonlinear proportional–integral–derivative-like controllers is proposed. Lyapunov stability theory is used to establish conditions for local asymptotic stability of the closed-loop system. A notable feature of the proposed controller is that stability conditions do not depend on the saturation levels of the actuators. In addition, an experimental study complements the proposed theory.

Global stability and quadratic Hamiltonian structure in Lotka-Volterra and quasi-polynomial systems

Energy Technology Data Exchange (ETDEWEB)

Szederkenyi, Gabor; Hangos, Katalin M

2004-04-26

We show that the global stability of quasi-polynomial (QP) and Lotka-Volterra (LV) systems with the well-known logarithmic Lyapunov function is equivalent to the existence of a local generalized dissipative Hamiltonian description of the LV system with a diagonal quadratic form as a Hamiltonian function. The Hamiltonian function can be calculated and the quadratic dissipativity neighborhood of the origin can be estimated by solving linear matrix inequalities.

Global stability and quadratic Hamiltonian structure in Lotka-Volterra and quasi-polynomial systems

Science.gov (United States)

Szederkényi, Gábor; Hangos, Katalin M.

2004-04-01

We show that the global stability of quasi-polynomial (QP) and Lotka-Volterra (LV) systems with the well-known logarithmic Lyapunov function is equivalent to the existence of a local generalized dissipative Hamiltonian description of the LV system with a diagonal quadratic form as a Hamiltonian function. The Hamiltonian function can be calculated and the quadratic dissipativity neighborhood of the origin can be estimated by solving linear matrix inequalities.

Global stability and quadratic Hamiltonian structure in Lotka-Volterra and quasi-polynomial systems

International Nuclear Information System (INIS)

Szederkenyi, Gabor; Hangos, Katalin M.

2004-01-01

We show that the global stability of quasi-polynomial (QP) and Lotka-Volterra (LV) systems with the well-known logarithmic Lyapunov function is equivalent to the existence of a local generalized dissipative Hamiltonian description of the LV system with a diagonal quadratic form as a Hamiltonian function. The Hamiltonian function can be calculated and the quadratic dissipativity neighborhood of the origin can be estimated by solving linear matrix inequalities

Stochastic stability of four-wheel-steering system

International Nuclear Information System (INIS)

Huang Dongwei; Wang Hongli; Zhu Zhiwen; Feng Zhang

2007-01-01

A four-wheel-steering system subjected to white noise excitations was reduced to a two-degree-of-freedom quasi-non-integrable-Hamiltonian system. Subsequently we obtained an one-dimensional Ito stochastic differential equation for the averaged Hamiltonian of the system by using the stochastic averaging method for quasi-non-integrable-Hamiltonian systems. Thus, the stochastic stability of four-wheel-steering system was analyzed by analyzing the sample behaviors of the averaged Hamiltonian at the boundary H = 0 and calculating its Lyapunov exponent. An example given at the end demonstrated that the conclusion obtained is of considerable significance

On the stability of shear-Alfven vortices

International Nuclear Information System (INIS)

Jovanovic, D.; Horton, W.

1993-08-01

Linear stability of shear-Alfven vortices is studied analytically using the Lyapunov method. Instability is demonstrated for vortices belonging to the drift mode, which is a generalization of the standard Hasegawa-Mima vortex to the case of large parallel phase velocities. In the case of the convective-cell mode, short perpendicular-wavelength perturbations are stable for a broad class of vortices. Eventually, instability of convective-cell vortices may occur on the perpendicular scale comparable with the vortex size, but it is followed by a simultaneous excitation of coherent structures with better localization than the original vortex

Linear and nonlinear stability analysis, associated to experimental fast reactors. Part 2

International Nuclear Information System (INIS)

Amorim, E.S. do; Moura Neto, C. de; Rosa, M.A.P.

1980-07-01

The nonlinear effects in fast reactors kinetics and their stability are studied. The Lyapunov criteria and the Lurie-Letov functions for nonlinear systems were established and simulated. Small oscillations were studied by a Fourier analysis to clarify particular aspects of feedback and load functions in fast reactor at zero power, or/and in normal power level. The results were in agreement with the experimental data existing in the literature. (E.G.) [pt

Implementation on Electronic Circuits and RTR Pragmatical Adaptive Synchronization: Time-Reversed Uncertain Dynamical Systems' Analysis and Applications

Directory of Open Access Journals (Sweden)

Shih-Yu Li

2013-01-01

Full Text Available We expose the chaotic attractors of time-reversed nonlinear system, further implement its behavior on electronic circuit, and apply the pragmatical asymptotically stability theory to strictly prove that the adaptive synchronization of given master and slave systems with uncertain parameters can be achieved. In this paper, the variety chaotic motions of time-reversed Lorentz system are investigated through Lyapunov exponents, phase portraits, and bifurcation diagrams. For further applying the complex signal in secure communication and file encryption, we construct the circuit to show the similar chaotic signal of time-reversed Lorentz system. In addition, pragmatical asymptotically stability theorem and an assumption of equal probability for ergodic initial conditions (Ge et al., 1999, Ge and Yu, 2000, and Matsushima, 1972 are proposed to strictly prove that adaptive control can be accomplished successfully. The current scheme of adaptive control—by traditional Lyapunov stability theorem and Barbalat lemma, which are used to prove the error vector—approaches zero, as time approaches infinity. However, the core question—why the estimated or given parameters also approach to the uncertain parameters—remains without answer. By the new stability theory, those estimated parameters can be proved approaching the uncertain values strictly, and the simulation results are shown in this paper.

Stability result of the Timoshenko system with delay and boundary feedback

KAUST Repository

Said-Houari, Belkacem; Soufyane, Abdelaziz

2012-01-01

Our interest in this paper is to analyse the asymptotic behaviour of a Timoshenko beam system together with two boundary controls, with delay terms in the first and second equation. Assuming the weights of the delay are small enough, we show that the system is well-posed using the semigroup theory. Furthermore, we introduce a Lyapunov functional that gives the exponential decay of the total energy. © 2012 The author.

Stability result of the Timoshenko system with delay and boundary feedback

KAUST Repository

Said-Houari, Belkacem

2012-01-06

Our interest in this paper is to analyse the asymptotic behaviour of a Timoshenko beam system together with two boundary controls, with delay terms in the first and second equation. Assuming the weights of the delay are small enough, we show that the system is well-posed using the semigroup theory. Furthermore, we introduce a Lyapunov functional that gives the exponential decay of the total energy. © 2012 The author.

Adaptive synchronization of Rossler system with uncertain parameters

International Nuclear Information System (INIS)

Park, Ju H.

2005-01-01

This article addresses control for the chaos synchronization of Rossler systems with three uncertain parameters. Based on the Lyapunov stability theory, an adaptive control law is derived to make the states of two identical Rossler systems asymptotically synchronized. A numerical simulations is presented to show the effectiveness of the proposed chaos synchronization scheme

Nonlinear feedback synchronisation control between fractional-order and integer-order chaotic systems

International Nuclear Information System (INIS)

Jia Li-Xin; Dai Hao; Hui Meng

2010-01-01

This paper focuses on the synchronisation between fractional-order and integer-order chaotic systems. Based on Lyapunov stability theory and numerical differentiation, a nonlinear feedback controller is obtained to achieve the synchronisation between fractional-order and integer-order chaotic systems. Numerical simulation results are presented to illustrate the effectiveness of this method

Improved Robust Stability Criterion of Networked Control Systems with Transmission Delays and Packet Loss

Directory of Open Access Journals (Sweden)

Shenping Xiao

2014-01-01

Full Text Available The problem of stability analysis for a class of networked control systems (NCSs with network-induced delay and packet dropout is investigated in this paper. Based on the working mechanism of zero-order holder, the closed-loop NCS is modeled as a continuous-time linear system with input delay. By introducing a novel Lyapunov-Krasovskii functional which splits both the lower and upper bounds of the delay into two subintervals, respectively, and utilizes reciprocally convex combination technique, a new stability criterion is derived in terms of linear matrix inequalities. Compared with previous results in the literature, the obtained stability criterion is less conservative. Numerical examples demonstrate the validity and feasibility of the proposed method.

Evaluating Noise Sensitivity on the Time Series Determination of Lyapunov Exponents Applied to the Nonlinear Pendulum

Directory of Open Access Journals (Sweden)

L.F.P. Franca

2003-01-01

Full Text Available This contribution presents an investigation on noise sensitivity of some of the most disseminated techniques employed to estimate Lyapunov exponents from time series. Since noise contamination is unavoidable in cases of data acquisition, it is important to recognize techniques that could be employed for a correct identification of chaos. State space reconstruction and the determination of Lyapunov exponents are carried out to investigate the response of a nonlinear pendulum. Signals are generated by numerical integration of the mathematical model, selecting a single variable of the system as a time series. In order to simulate experimental data sets, a random noise is introduced in the signal. Basically, the analyses of periodic and chaotic motions are carried out. Results obtained from mathematical model are compared with the one obtained from time series analysis, evaluating noise sensitivity. This procedure allows the identification of the best techniques to be employed in the analysis of experimental data.

Boundedness and global robust stability analysis of delayed complex-valued neural networks with interval parameter uncertainties.

Science.gov (United States)

Song, Qiankun; Yu, Qinqin; Zhao, Zhenjiang; Liu, Yurong; Alsaadi, Fuad E

2018-07-01

In this paper, the boundedness and robust stability for a class of delayed complex-valued neural networks with interval parameter uncertainties are investigated. By using Homomorphic mapping theorem, Lyapunov method and inequality techniques, sufficient condition to guarantee the boundedness of networks and the existence, uniqueness and global robust stability of equilibrium point is derived for the considered uncertain neural networks. The obtained robust stability criterion is expressed in complex-valued LMI, which can be calculated numerically using YALMIP with solver of SDPT3 in MATLAB. An example with simulations is supplied to show the applicability and advantages of the acquired result. Copyright © 2018 Elsevier Ltd. All rights reserved.

The use of Lyapunov differential inequalities for estimating the transients of mechanical systems

Science.gov (United States)

Alyshev, A. S.; Dudarenko, N. A.; Melnikov, V. G.; Melnikov, G. I.

2018-05-01

In this paper we consider an autonomous mechanical system in a finite neighborhood of the zero of the phase space of states. The system is given as a matrix differential equation in the Cauchy form with the right-hand side of the polynomial structure. We propose a method for constructing a sequence of linear inhomogeneous differential inequalities for Lyapunov functions. As a result, we obtain estimates of transient processes in the form of functional inequalities.

Construction of the Courant-Snyder invariants for the non-linear equations of motion and criterion for the long-term stability of the beam in a storage ring

International Nuclear Information System (INIS)

Garczynski, V.

1993-01-01

The Courant-Snyder invariants become Lyapunov functions when the β-functions admit non-zero lower, and finite upper bounds. The long-term stability of motion then follows. This alternative criterion for the long-term stability of motion can be generalized to the nonlinear case. A single particle subjected to an arbitrary static magnetic field is considered in some detail, as an example

Global exponential stability of fuzzy cellular neural networks with delays and reaction-diffusion terms

International Nuclear Information System (INIS)

Wang Jian; Lu Junguo

2008-01-01

In this paper, we study the global exponential stability of fuzzy cellular neural networks with delays and reaction-diffusion terms. By constructing a suitable Lyapunov functional and utilizing some inequality techniques, we obtain a sufficient condition for the uniqueness and global exponential stability of the equilibrium solution for a class of fuzzy cellular neural networks with delays and reaction-diffusion terms. The result imposes constraint conditions on the network parameters independently of the delay parameter. The result is also easy to check and plays an important role in the design and application of globally exponentially stable fuzzy neural circuits

Simultaneous control and piezoelectric insert optimization for manipulators with flexible link

OpenAIRE

Bottega, Valdecir; Pergher, Rejane; Fonseca, Jun S. O.

2009-01-01

This work proposes a tracking control model for a flexible link robotic manipulator using simultaneously motor torques and piezoelectric actuators. The dynamic model of manipulator is obtained in a closed form through the Lagrangian approach. The control uses the motor torques for the tracking control of the joints and also to reduce the low frequency vibration induced in the manipulator links. The stability of this control is guaranteed by the Lyapunov stability theory. Piezoelectric actuato...

Partial Finite-Time Synchronization of Switched Stochastic Chua's Circuits via Sliding-Mode Control

Directory of Open Access Journals (Sweden)

Zhang-Lin Wan

2011-01-01

Full Text Available This paper considers the problem of partial finite-time synchronization between switched stochastic Chua's circuits accompanied by a time-driven switching law. Based on the Ito formula and Lyapunov stability theory, a sliding-mode controller is developed to guarantee the synchronization of switched stochastic master-slave Chua's circuits and for the mean of error states to obtain the partial finite-time stability. Numerical simulations demonstrate the effectiveness of the proposed methods.

Adaptive controller design for modified projective synchronization of Genesio-Tesi chaotic system with uncertain parameters