Bergstra, J.A.; Baeten, J.C.M.
1996-01-01
The axiom system ACP of [BeK84a] was extended with real time features in [BaB91]. Here we proceed to define a discrete time extension of ACP, along the lines of ATP [NiS94]. We present versions based on relative timing and on absolute timing. Both approaches are integrated using parametric timing. T
Time Discretization Techniques
Gottlieb, S.
2016-10-12
The time discretization of hyperbolic partial differential equations is typically the evolution of a system of ordinary differential equations obtained by spatial discretization of the original problem. Methods for this time evolution include multistep, multistage, or multiderivative methods, as well as a combination of these approaches. The time step constraint is mainly a result of the absolute stability requirement, as well as additional conditions that mimic physical properties of the solution, such as positivity or total variation stability. These conditions may be required for stability when the solution develops shocks or sharp gradients. This chapter contains a review of some of the methods historically used for the evolution of hyperbolic PDEs, as well as cutting edge methods that are now commonly used.
Principles of discrete time mechanics
Jaroszkiewicz, George
2014-01-01
Could time be discrete on some unimaginably small scale? Exploring the idea in depth, this unique introduction to discrete time mechanics systematically builds the theory up from scratch, beginning with the historical, physical and mathematical background to the chronon hypothesis. Covering classical and quantum discrete time mechanics, this book presents all the tools needed to formulate and develop applications of discrete time mechanics in a number of areas, including spreadsheet mechanics, classical and quantum register mechanics, and classical and quantum mechanics and field theories. A consistent emphasis on contextuality and the observer-system relationship is maintained throughout.
Alfa, Attahiru S
2016-01-01
This book introduces the theoretical fundamentals for modeling queues in discrete-time, and the basic procedures for developing queuing models in discrete-time. There is a focus on applications in modern telecommunication systems. It presents how most queueing models in discrete-time can be set up as discrete-time Markov chains. Techniques such as matrix-analytic methods (MAM) that can used to analyze the resulting Markov chains are included. This book covers single node systems, tandem system and queueing networks. It shows how queues with time-varying parameters can be analyzed, and illustrates numerical issues associated with computations for the discrete-time queueing systems. Optimal control of queues is also covered. Applied Discrete-Time Queues targets researchers, advanced-level students and analysts in the field of telecommunication networks. It is suitable as a reference book and can also be used as a secondary text book in computer engineering and computer science. Examples and exercises are includ...
Friis, Ib; Wind, Peter; Pedersen, Henrik Ærenlund
2008-01-01
Nekrolog over botanikeren Alfred Hansen, leder af Dansk Herbarium på Botanisk Museum, Københavns Universitet, med gennemgang af hans videnskabelige og formidlende publikationer og indsats som samler af videnskabeligt materiale.......Nekrolog over botanikeren Alfred Hansen, leder af Dansk Herbarium på Botanisk Museum, Københavns Universitet, med gennemgang af hans videnskabelige og formidlende publikationer og indsats som samler af videnskabeligt materiale....
Memorized discrete systems and time-delay
Luo, Albert C J
2017-01-01
This book examines discrete dynamical systems with memory—nonlinear systems that exist extensively in biological organisms and financial and economic organizations, and time-delay systems that can be discretized into the memorized, discrete dynamical systems. It book further discusses stability and bifurcations of time-delay dynamical systems that can be investigated through memorized dynamical systems as well as bifurcations of memorized nonlinear dynamical systems, discretization methods of time-delay systems, and periodic motions to chaos in nonlinear time-delay systems. The book helps readers find analytical solutions of MDS, change traditional perturbation analysis in time-delay systems, detect motion complexity and singularity in MDS; and determine stability, bifurcation, and chaos in any time-delay system.
Quantum Mechanics on discrete space and time
Lorente, M
2004-01-01
We propose the assumption of quantum mechanics on a discrete space and time, which implies the modification of mathematical expressions for some postulates of quantum mechanics. In particular we have a Hilbert space where the vectors are complex functions of discrete variable. As a concrete example we develop a discrete analog of the one-dimensional quantum harmonic oscillator, using the dependence of the Wigner functions in terms of Kravchuk polynomials. In this model the position operator has a discrete spectrum given by one index of the Wigner functions, in the same way that the energy eigenvalues are given by the other matricial index. Similar picture can be made for other models where the differential equation and their solutions correspond to the continuous limit of some difference operator and orthogonal polynomial of discrete variable.
Discrete-time nonlinear sliding mode controller
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: Discrete-time delay system, Sliding mode control, nonlinear sliding ... The concept of the sliding mode control in recent years has drawn the ...... His area of interest is dc-dc converters, electrical vehicle and distributed generation application.
... with facebook share with twitter share with linkedin Leprosy (Hansen's Disease) Leprosy (Hansen's Disease) is a chronic ... as Mycobacterium leprae . Why Is the Study of Leprosy (Hansen's Disease) a Priority for NIAID? At the ...
Discrete Time Crystals: Rigidity, Criticality, and Realizations
Yao, N. Y.; Potter, A. C.; Potirniche, I.-D.; Vishwanath, A.
2017-01-01
Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry. The period of the resulting discrete time crystal is quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization. Here, we consider a simple model for a one-dimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied. We numerically map out its phase diagram and compute the properties of the dynamical phase transition where the time crystal melts into a trivial Floquet insulator. Moreover, we demonstrate that the model can be realized with current experimental technologies and propose a blueprint based upon a one dimensional chain of trapped ions. Using experimental parameters (featuring long-range interactions), we identify the phase boundaries of the ion-time-crystal and propose a measurable signature of the symmetry breaking phase transition.
Discrete Time Crystals: Rigidity, Criticality, and Realizations.
Yao, N Y; Potter, A C; Potirniche, I-D; Vishwanath, A
2017-01-20
Despite being forbidden in equilibrium, spontaneous breaking of time translation symmetry can occur in periodically driven, Floquet systems with discrete time-translation symmetry. The period of the resulting discrete time crystal is quantized to an integer multiple of the drive period, arising from a combination of collective synchronization and many body localization. Here, we consider a simple model for a one-dimensional discrete time crystal which explicitly reveals the rigidity of the emergent oscillations as the drive is varied. We numerically map out its phase diagram and compute the properties of the dynamical phase transition where the time crystal melts into a trivial Floquet insulator. Moreover, we demonstrate that the model can be realized with current experimental technologies and propose a blueprint based upon a one dimensional chain of trapped ions. Using experimental parameters (featuring long-range interactions), we identify the phase boundaries of the ion-time-crystal and propose a measurable signature of the symmetry breaking phase transition.
Modeling discrete time-to-event data
Tutz, Gerhard
2016-01-01
This book focuses on statistical methods for the analysis of discrete failure times. Failure time analysis is one of the most important fields in statistical research, with applications affecting a wide range of disciplines, in particular, demography, econometrics, epidemiology and clinical research. Although there are a large variety of statistical methods for failure time analysis, many techniques are designed for failure times that are measured on a continuous scale. In empirical studies, however, failure times are often discrete, either because they have been measured in intervals (e.g., quarterly or yearly) or because they have been rounded or grouped. The book covers well-established methods like life-table analysis and discrete hazard regression models, but also introduces state-of-the art techniques for model evaluation, nonparametric estimation and variable selection. Throughout, the methods are illustrated by real life applications, and relationships to survival analysis in continuous time are expla...
Discrete time queues with phase dependent arrivals
Daigle, J. N.; Lee, Y.; Magalhaes, M. N.
1994-02-01
The queueing behavior of many communication systems is well modeled by a queueing system in which time is slotted, and the number of entities that arrive during a slot is dependent upon the state of a discrete time, discrete state Markov chain. Techniques for analyzing such systems have appeared in the literature from time to time, but distributions have been presented in only rare instances. In this paper, we present the probability generating function (PGF) for joint and marginal buffer occupancy distributions of statistical time division multiplexing systems in this class. We discuss inversion of the PGF using discrete Fourier transforms, and also discuss a simple technique for obtaining moments of the queue length distribution. Numerical results, including queue length distributions for some special cases, are presented.
Stability Criterion for Discrete-Time Systems
K. Ratchagit
2010-01-01
Full Text Available This paper is concerned with the problem of delay-dependent stability analysis for discrete-time systems with interval-like time-varying delays. The problem is solved by applying a novel Lyapunov functional, and an improved delay-dependent stability criterion is obtained in terms of a linear matrix inequality.
Observation of a Discrete Time Crystal
Zhang, J; Kyprianidis, A; Becker, P; Lee, A; Smith, J; Pagano, G; Potirniche, I -D; Potter, A C; Vishwanath, A; Yao, N Y; Monroe, C
2016-01-01
Spontaneous symmetry breaking is a fundamental concept in many areas of physics, ranging from cosmology and particle physics to condensed matter. A prime example is the breaking of spatial translation symmetry, which underlies the formation of crystals and the phase transition from liquid to solid. Analogous to crystals in space, the breaking of translation symmetry in time and the emergence of a "time crystal" was recently proposed, but later shown to be forbidden in thermal equilibrium. However, non-equilibrium Floquet systems subject to a periodic drive can exhibit persistent time-correlations at an emergent sub-harmonic frequency. This new phase of matter has been dubbed a "discrete time crystal" (DTC). Here, we present the first experimental observation of a discrete time crystal, in an interacting spin chain of trapped atomic ions. We apply a periodic Hamiltonian to the system under many-body localization (MBL) conditions, and observe a sub-harmonic temporal response that is robust to external perturbat...
Mixed continuous/discrete time modelling with exact time adjustments
Rovers, K.C.; Kuper, Jan; van de Burgwal, M.D.; Kokkeler, Andre B.J.; Smit, Gerardus Johannes Maria
2011-01-01
Many systems interact with their physical environment. Design of such systems need a modelling and simulation tool which can deal with both the continuous and discrete aspects. However, most current tools are not adequately able to do so, as they implement both continuous and discrete time signals
Early Universes with Effective Discrete Time
Baulieu, Laurent
2016-01-01
The mechanism for triggering the universe inflation could be that at very early periods the time variable was discrete instead of smooth. Alternatively, and perhaps equivalently, it could be the consequence that the metrics of the early universe was a strongly concentrated gravitational coherent state with very high frequency oscillations, allowing local pair creations by a generalisation to gravity of the Schwinger mechanism, perhaps by creation of black holes of masses superior to the Planck scale. The lattice spacing between two clicks in the discrete time picture corresponds to the inverse frequency of the gravitational coherent state in the other picture. In both cases, a much lower time than the Planck time might represent a new fundamental scale, giving new type of physics. To make possible a concrete estimation of the pair production probability, we propose that the oscillating coherent state metrics that defines this very early geometry minimises the Einstein gravity action coupled to interacting 1-,...
Compact phase space, cosmological constant, discrete time
Rovelli, Carlo
2015-01-01
We study the quantization of geometry in the presence of a cosmological constant, using a discretiza- tion with constant-curvature simplices. Phase space turns out to be compact and the Hilbert space finite dimensional for each link. Not only the intrinsic, but also the extrinsic geometry turns out to be discrete, pointing to discreetness of time, in addition to space. We work in 2+1 dimensions, but these results may be relevant also for the physical 3+1 case.
Controlling hopf bifurcations: Discrete-time systems
Guanrong Chen
2000-01-01
Full Text Available Bifurcation control has attracted increasing attention in recent years. A simple and unified state-feedback methodology is developed in this paper for Hopf bifurcation control for discrete-time systems. The control task can be either shifting an existing Hopf bifurcation or creating a new Hopf bifurcation. Some computer simulations are included to illustrate the methodology and to verify the theoretical results.
[Diagnosis of Hansen's disease].
Yotsu, Rie Roselyne; Suzuki, Koichi; Mori, Shuichi; Ishii, Norihisa
2011-02-01
The Leprosy Mailing List (LML) is an e-mailing list open to whoever interested in the field from all over the world. It acts as a forum for exchanging information related to Hansen's disease. It was established in February 2001 in Italy, and the present moderator of the LML is Dr. Salvatore Noto. He and his colleague have recently introduced an atlas for diagnosing Hansen's disease which they brought together information and photos collected through the LML. The atlas is divided into three sections, (1) Introduction, (2) Cardinal signs, and (3) Diagnosis and the clinical spectrum of leprosy, and they are all accompanied with relevant photos. This time, Dr. Noto kindly permitted us to translate the atlas into Japanese to be published in the Japanese Journal of Leprosy and posted in the Japanese Leprosy Association homepage. This article includes the translation and some of the most informative photos. For more information, please refer to the homepage where you will find all photos in the atlas.
Discrete-time modelling of musical instruments
Välimäki, Vesa; Pakarinen, Jyri; Erkut, Cumhur; Karjalainen, Matti
2006-01-01
This article describes physical modelling techniques that can be used for simulating musical instruments. The methods are closely related to digital signal processing. They discretize the system with respect to time, because the aim is to run the simulation using a computer. The physics-based modelling methods can be classified as mass-spring, modal, wave digital, finite difference, digital waveguide and source-filter models. We present the basic theory and a discussion on possible extensions for each modelling technique. For some methods, a simple model example is chosen from the existing literature demonstrating a typical use of the method. For instance, in the case of the digital waveguide modelling technique a vibrating string model is discussed, and in the case of the wave digital filter technique we present a classical piano hammer model. We tackle some nonlinear and time-varying models and include new results on the digital waveguide modelling of a nonlinear string. Current trends and future directions in physical modelling of musical instruments are discussed.
Discrete-time modelling of musical instruments
Vaelimaeki, Vesa; Pakarinen, Jyri; Erkut, Cumhur; Karjalainen, Matti [Laboratory of Acoustics and Audio Signal Processing, Helsinki University of Technology, PO Box 3000, FI-02015 TKK, Espoo (Finland)
2006-01-01
This article describes physical modelling techniques that can be used for simulating musical instruments. The methods are closely related to digital signal processing. They discretize the system with respect to time, because the aim is to run the simulation using a computer. The physics-based modelling methods can be classified as mass-spring, modal, wave digital, finite difference, digital waveguide and source-filter models. We present the basic theory and a discussion on possible extensions for each modelling technique. For some methods, a simple model example is chosen from the existing literature demonstrating a typical use of the method. For instance, in the case of the digital waveguide modelling technique a vibrating string model is discussed, and in the case of the wave digital filter technique we present a classical piano hammer model. We tackle some nonlinear and time-varying models and include new results on the digital waveguide modelling of a nonlinear string. Current trends and future directions in physical modelling of musical instruments are discussed.
DENG Shu-xian; DING Yu; GE Lei
2008-01-01
We usually describle a comparatively more complex control system, especially a multi-inputs and multioutputs system by time domation analytical procedure. While the system's controllability means whether the system is controllable according to certain requirements. It involves not only the system's outputs' controllability but also the controllability of the system's partial or total conditions. The movement is described by difference equation in the linear discrete-time system. Therefore, the problem of controllability of the linear discrete-time system has been converted into a problem of the controllability of discrete-time difference equation. The thesis makes out the determination method of the discrete-time system's controllability and puts forward the sufficient and necessary conditions to determine it's controllability by making a study on the controllability of the linear discrete-time equation.
APPROXIMATION LAWS OF DISCRETE-TIME VARIABLE STRUCTURE CONTROL SYSTEMS
无
2008-01-01
Two new approximation laws of sliding mode for discrete-time variable structure control systems are proposed in this paper. By applying the proposed approximation laws of sliding mode to discrete-time variable structure control systems,the stability of origin can be guaranteed,and the chattering along the switching surface caused by discrete-time variable structure control can be restrained effectively. In designing of these approximation laws,the problem that the system control input is restricted is also ...
Leibert, Todd W.
2012-01-01
Hansen (2012a) and the author are both concerned about trends in the counseling culture toward oversimplification. Their disagreement is, principally, about the locus of debate. The author responds to Hansen's counterarguments with the ultimate hope of transferring the focus from scientific ideology to economic realities pervading professional…
W-Stability of Multistable Nonlinear Discrete-Time Systems
Zhishuai Ding
2012-01-01
Full Text Available Motivated by the importance and application of discrete dynamical systems, this paper presents a new Lyapunov characterization which is an extension of conventional Lyapunov characterization for multistable discrete-time nonlinear systems. Based on a new type stability notion of W-stability introduced by D. Efimov, the estimates of solution and the Lyapunov stability theorem and converse theorem are proposed for multi-stable discrete-time nonlinear systems.
Discrete-Time Nonlinear Control of VSC-HVDC System
TianTian Qian
2015-01-01
Full Text Available Because VSC-HVDC is a kind of strong nonlinear, coupling, and multi-input multioutput (MIMO system, its control problem is always attracting much attention from scholars. And a lot of papers have done research on its control strategy in the continuous-time domain. But the control system is implemented through the computer discrete sampling in practical engineering. It is necessary to study the mathematical model and control algorithm in the discrete-time domain. The discrete mathematical model based on output feedback linearization and discrete sliding mode control algorithm is proposed in this paper. And to ensure the effectiveness of the control system in the quasi sliding mode state, the fast output sampling method is used in the output feedback. The results from simulation experiment in MATLAB/SIMULINK prove that the proposed discrete control algorithm can make the VSC-HVDC system have good static, dynamic, and robust characteristics in discrete-time domain.
Absolute Stability of Discrete-Time Systems with Delay
Medina Rigoberto
2008-01-01
Full Text Available We investigate the stability of nonlinear nonautonomous discrete-time systems with delaying arguments, whose linear part has slowly varying coefficients, and the nonlinear part has linear majorants. Based on the "freezing" technique to discrete-time systems, we derive explicit conditions for the absolute stability of the zero solution of such systems.
Local Parametric Analysis of Hedging in Discrete Time
Bossaerts, P.L.M.; Hillion, P.
1995-01-01
When continuous-time portfolio weights are applied to a discrete-time hedging problem, errors are likely to occur. This paper evaluates the overall importance of the discretization-induced tracking error. It does so by comparing the performance of Black-Scholes hedge ratios against those obtained
Discrete-time optimal control and games on large intervals
Zaslavski, Alexander J
2017-01-01
Devoted to the structure of approximate solutions of discrete-time optimal control problems and approximate solutions of dynamic discrete-time two-player zero-sum games, this book presents results on properties of approximate solutions in an interval that is independent lengthwise, for all sufficiently large intervals. Results concerning the so-called turnpike property of optimal control problems and zero-sum games in the regions close to the endpoints of the time intervals are the main focus of this book. The description of the structure of approximate solutions on sufficiently large intervals and its stability will interest graduate students and mathematicians in optimal control and game theory, engineering, and economics. This book begins with a brief overview and moves on to analyze the structure of approximate solutions of autonomous nonconcave discrete-time optimal control Lagrange problems.Next the structures of approximate solutions of autonomous discrete-time optimal control problems that are discret...
Solution of macromodels with Hansen-Sargent robust policies: Summary and some extensions
Giordani, Paolo; Söderlind, Paul
2002-01-01
We summarize some methods useful in formulating and solving Hansen-Sargent robust control problems, and suggest extensions to discretion and simple rules. Matlab, Octave, and Gauss software is provided. We illustrate these extensions with applications to the term structure of interest rates, the time inconsistency of optimal monetary policy, the effects of expectations on the variances of inflation and output, and on whether central banks should make their forecasts public.
Solution of Macromodels with Hansen-Sargent Robust Policies: Some Extensions
Giordani, Paolo; Söderlind, Paul
2004-01-01
We summarize some methods useful in formulating and solving Hansen-Sargent robust control problems, and suggest extensions to discretion and simple rules. Matlab, Octave, and Gauss software is provided. We illustrate these extensions with applications to the term structure of interest rates, the time inconsistency of optimal monetary policy, the effects of expectations on the variances of inflation and output, and on whether central banks should make their forecasts public.
2004-01-01
20. nov. 2004 Torontos surnud advokaadi, poliitiku ja aktiivse rahvusliku tegelase nekroloog. M. Hansen oli nii Eesti Liidu Kanadas, Toronto Eesti Seltsi kui ka Eesti Abistamiskomitee Kanadas asutajaks ning esimeseks esimeheks
Approximation law for discrete-time variable structure control systems
Yan ZHENG; Yuanwei JING
2006-01-01
Two approximation laws of sliding mode for discrete-time variable structure control systems are proposed to overcome the limitations of the exponential approximation law and the variable rate approximation law. By applying the proposed approximation laws of sliding mode to discrete-time variable structure control systems, the stability of origin can be guaranteed, and the chattering along the switching surface caused by discrete-time variable structure control can be restrained effectively. In designing of approximation laws, the problem that the system control input is restricted is also considered, which is very important in practical systems. Finally a simulation example shows the effectiveness of the two approximation laws proposed.
Discrete-time inverse optimal control for nonlinear systems
Sanchez, Edgar N
2013-01-01
Discrete-Time Inverse Optimal Control for Nonlinear Systems proposes a novel inverse optimal control scheme for stabilization and trajectory tracking of discrete-time nonlinear systems. This avoids the need to solve the associated Hamilton-Jacobi-Bellman equation and minimizes a cost functional, resulting in a more efficient controller. Design More Efficient Controllers for Stabilization and Trajectory Tracking of Discrete-Time Nonlinear Systems The book presents two approaches for controller synthesis: the first based on passivity theory and the second on a control Lyapunov function (CLF). Th
Losslessness of Nonlinear Stochastic Discrete-Time Systems
Xikui Liu
2015-01-01
Full Text Available This paper will study stochastic losslessness theory for nonlinear stochastic discrete-time systems, which are expressed by the Itô-type difference equations. A necessary and sufficient condition is developed for a nonlinear stochastic discrete-time system to be lossless. By the stochastic lossless theory, we show that a nonlinear stochastic discrete-time system can be lossless via state feedback if and only if it has relative degree 0,…,0 and lossless zero dynamics. The effectiveness of the proposed results is illustrated by a numerical example.
Geometric Approach to Lie Symmetry of Discrete Time Toda Equation
JIA Xiao-Yu; WANG Na
2009-01-01
By using the extended Harrison and Estabrook geometric approach,we investigate the Lie symmetry of discrete time Toda equation from the geometric point of view.Its one-dimensional continuous symmetry group is presented.
Hybrid discretization method for time-delay nonlinear systems
Zhang, Zheng [Xi' an Jiaotong University, Xi' an (China); Zhang, Yuanliang; Kil Chong, To [Chonbuk National University, Jeonju (Korea, Republic of); Kostyukova, Olga [3Institute of Mathematics National Academy of Science of Belarus, Minsk (Belarus)
2010-03-15
A hybrid discretization scheme that combines the virtues of the Taylor series and Matrix exponential integration methods is proposed. In the algorithm, each sampling time interval is divided into two subintervals to be considered according to the time delay and sampling period. The algorithm is not too expensive computationally and lends itself to be easily inserted into large simulation packages. The mathematical structure of the new discretization scheme is explored and described in detail. The performance of the proposed discretization procedure is evaluated by employing case studies. Various input signals, sampling rates, and time-delay values are considered to test the proposed method. The results demonstrate that the proposed discretization scheme is better than previous Taylor series method for nonlinear time-delay systems, especially when a large sampling period is inevitable
On periodic orbits in discrete-time cascade systems
Huimin Li
2006-01-01
Full Text Available We present some results on existence, minimum period, number of periodic orbits, and stability of periodic orbits in discrete-time cascade systems. Some examples are presented to illustrate these results.
Absolute Stability of Discrete-Time Systems with Delay
Rigoberto Medina
2008-02-01
Full Text Available We investigate the stability of nonlinear nonautonomous discrete-time systems with delaying arguments, whose linear part has slowly varying coefficients, and the nonlinear part has linear majorants. Based on the Ã¢Â€ÂœfreezingÃ¢Â€Â technique to discrete-time systems, we derive explicit conditions for the absolute stability of the zero solution of such systems.
Approximate Controllability of Abstract Discrete-Time Systems
Cuevas Claudio
2010-01-01
Full Text Available Approximate controllability for semilinear abstract discrete-time systems is considered. Specifically, we consider the semilinear discrete-time system , , where are bounded linear operators acting on a Hilbert space , are -valued bounded linear operators defined on a Hilbert space , and is a nonlinear function. Assuming appropriate conditions, we will show that the approximate controllability of the associated linear system implies the approximate controllability of the semilinear system.
Discrete mechanics, “time machines” and hybrid systems
Elze Hans-Thomas
2013-09-01
Full Text Available Modifying the discrete mechanics proposed by T.D. Lee, we construct a class of discrete classical Hamiltonian systems, in which time is one of the dynamical variables. This includes a toy model of “time machines” which can travel forward and backward in time and which differ from models based on closed timelike curves (CTCs. In the continuum limit, we explore the interaction between such time reversing machines and quantum mechanical objects, employing a recent description of quantum-classical hybrids.
Engineering applications of discrete-time optimal control
Vidal, Rene Victor Valqui; Ravn, Hans V.
1990-01-01
of some well-known and new results in discrete time optimal control methods applicable to practical problem solving within engineering. Emphasis is placed on dynamic programming, the classical maximum principle and generalized versions of the maximum principle for optimal control of discrete time systems......Many problems of design and operation of engineering systems can be formulated as optimal control problems where time has been discretisized. This is also true even if 'time' is not involved in the formulation of the problem, but rather another one-dimensional parameter. This paper gives a review...
Engineering applications of discrete-time optimal control
Vidal, Rene Victor Valqui; Ravn, Hans V.
1990-01-01
Many problems of design and operation of engineering systems can be formulated as optimal control problems where time has been discretisized. This is also true even if 'time' is not involved in the formulation of the problem, but rather another one-dimensional parameter. This paper gives a review...... of some well-known and new results in discrete time optimal control methods applicable to practical problem solving within engineering. Emphasis is placed on dynamic programming, the classical maximum principle and generalized versions of the maximum principle for optimal control of discrete time systems...
Discrete time learning control in nonlinear systems
Longman, Richard W.; Chang, Chi-Kuang; Phan, Minh
1992-01-01
In this paper digital learning control methods are developed primarily for use in single-input, single-output nonlinear dynamic systems. Conditions for convergence of the basic form of learning control based on integral control concepts are given, and shown to be satisfied by a large class of nonlinear problems. It is shown that it is not the gross nonlinearities of the differential equations that matter in the convergence, but rather the much smaller nonlinearities that can manifest themselves during the short time interval of one sample time. New algorithms are developed that eliminate restrictions on the size of the learning gain, and on knowledge of the appropriate sign of the learning gain, for convergence to zero error in tracking a feasible desired output trajectory. It is shown that one of the new algorithms can give guaranteed convergence in the presence of actuator saturation constraints, and indicate when the requested trajectory is beyond the actuator capabilities.
Recurrence for discrete time unitary evolutions
Grünbaum, F A; Werner, A H; Werner, R F
2012-01-01
We consider quantum dynamical systems specified by a unitary operator U and an initial state vector \\phi. In each step the unitary is followed by a projective measurement checking whether the system has returned to the initial state. We call the system recurrent if this eventually happens with probability one. We show that recurrence is equivalent to the absence of an absolutely continuous part from the spectral measure of U with respect to \\phi. We also show that in the recurrent case the expected first return time is an integer or infinite, for which we give a topological interpretation. A key role in our theory is played by the first arrival amplitudes, which turn out to be the (complex conjugated) Taylor coefficients of the Schur function of the spectral measure. On the one hand, this provides a direct dynamical interpretation of these coefficients; on the other hand it links our definition of first return times to a large body of mathematical literature.
Time invariant scaling in discrete fragmentation models
Giraud, B G; Giraud, B G; Peschanski, R
1994-01-01
Linear rate equations are used to describe the cascading decay of an initial heavy cluster into fragments. We consider moments of arbitrary orders of the mass multiplicity spectrum and derive scaling properties pertaining to their time evolution. We suggest that the mass weighted multiplicity is a suitable observable for the discovery of scaling. Numerical tests validate such properties, even for moderate values of the initial mass (nuclei, percolation clusters, jets of particles etc.). Finite size effects can be simply parametrized.
Implementing Hansen's Proficiencies.
Carlson, J. Lon; Cohn, Raymond L.; Ramsey, David D.
2002-01-01
Describes an economics department framework that incorporates the William Lee Hansen curriculum proficiencies. Identifies tools students should be able to use to complete specific activities, significant prerequisite changes for upper division courses, and the development of a capstone project to employ student skills and knowledge. (JEH)
Suthakaran, V.
2012-01-01
Hansen (2012b) reiterates his view that the humanities should form the ideological foundation of the counseling profession by challenging the validity of the central premises for the author's argument that the humanities and science should have equal ideological standing. The author attempts to explain the reasons for their conflicting ideas on…
Andersen, Jan
Grønlandsforskeren Poul Hansen Egede er med sin eksemplariske indsamling, bearbejdning og formidling af viden om grønlandsk kultur og sprog en central skikkelse i Grønlands tidlige videnskabshistorie. Skildringen af Poul Egedes liv og værk bygger på hans egne optegnelser samt på hidtil upåagtede...
Kristensen, Birgit Juul
2011-01-01
Beskrivelse af gammel bogsamling fra Ladelund Landbrugsskole (nu Syddansk Universitetsbibliotek i Esbjerg), samlet af Statskonsulent K. Hansen (1858-1941). Derudover en fremstilling af hans liv og virke som statskonsulent i planteavl for Øerne, leder af Dansk Landbrugsmuseum, forfatter af...
Minimal Martingale Measures for Discrete-time Incomplete Financial Markets
Ping Li; Jian-ming Xia
2002-01-01
In this note, we give a characterization of the minimal martingale measure for a general discretetime incomplete financial market. Then we concretely work out the minimal martingale measure for a specific discrete-time market model in which the assets' returns in different times are independent.
Discrete Space-Time: History and Recent Developments
Crouse, David
2017-01-01
Discussed in this work is the long history and debate of whether space and time are discrete or continuous. Starting from Zeno of Elea and progressing to Heisenberg and others, the issues with discrete space are discussed, including: Lorentz contraction (time dilation) of the ostensibly smallest spatial (temporal) interval, maintaining isotropy, violations of causality, and conservation of energy and momentum. It is shown that there are solutions to all these issues, such that discrete space is a viable model, yet the solution require strict non-absolute space (i.e., Mach's principle) and a re-analysis of the concept of measurement and the foundations of special relativity. In developing these solutions, the long forgotten but important debate between Albert Einstein and Henri Bergson concerning time will be discussed. Also discussed is the resolution to the Weyl tile argument against discrete space; however, the solution involves a modified version of the typical distance formula. One example effect of discrete space is then discussed, namely how it necessarily imposes order upon Wheeler's quantum foam, changing the foam into a gravity crystal and yielding crystalline properties of bandgaps, Brilluoin zones and negative inertial mass for astronomical bodies.
Global Exponential Stability of Discrete-Time Neural Networks with Time-Varying Delays
S. Udpin
2013-01-01
Full Text Available This paper presents some global stability criteria of discrete-time neural networks with time-varying delays. Based on a discrete-type inequality, a new global stability condition for nonlinear difference equation is derived. We consider nonlinear discrete systems with time-varying delays and independence of delay time. Numerical examples are given to illustrate the effectiveness of our theoretical results.
Distinct timing mechanisms produce discrete and continuous movements.
Raoul Huys
2008-04-01
Full Text Available The differentiation of discrete and continuous movement is one of the pillars of motor behavior classification. Discrete movements have a definite beginning and end, whereas continuous movements do not have such discriminable end points. In the past decade there has been vigorous debate whether this classification implies different control processes. This debate up until the present has been empirically based. Here, we present an unambiguous non-empirical classification based on theorems in dynamical system theory that sets discrete and continuous movements apart. Through computational simulations of representative modes of each class and topological analysis of the flow in state space, we show that distinct control mechanisms underwrite discrete and fast rhythmic movements. In particular, we demonstrate that discrete movements require a time keeper while fast rhythmic movements do not. We validate our computational findings experimentally using a behavioral paradigm in which human participants performed finger flexion-extension movements at various movement paces and under different instructions. Our results demonstrate that the human motor system employs different timing control mechanisms (presumably via differential recruitment of neural subsystems to accomplish varying behavioral functions such as speed constraints.
Discrete-Time Controllability for Feedback Quantum Dynamics
Albertini, Francesca
2010-01-01
Controllability properties for discrete-time, Markovian quantum dynamics are investigated. We find that, while in general the controlled system is not finite-time controllable, feedback control allows for arbitrary asymptotic state-to-state transitions. Under further assumption on the form of the measurement, we show that finite-time controllability can be achieved in a time that scales linearly with the dimension of the system, and we provide an iterative procedure to design the unitary control actions.
A synopsis of the history of Hansen's disease.
Couto Dal Secco, Raissa Gonçalves; França, Katlein; Castillo, David; AlHarbi, Mana; Lotti, Torello; Fioranelli, Massimo; Roccia, Maria Grazia
2017-08-11
Leprosy is a contagious infectious disease caused by the bacillus Mycobacterium leprae. This microorganism was discovered by Dr. Gerhard Hansen, and the illness was then baptized as Hansen's disease. For a long time, Hansen's disease was thought to be hereditary-a curse or a punishment from God. The disease affects skin and nerves and can cause severe damage. Due to its destructive effects, leprosy has caused fear, segregation, and prejudice in all societies since Biblical times. Patients with Hansen's disease have not been treated humanely around the world throughout the ages. This article is a summary of curious and interesting facts about the history and cultural aspects of Hansen's disease, which has chastised humanity for centuries. These facts are about the discovery of the disease, its propagation, the evolution of treatments, and the prejudice of society towards patients.
Stability of Nonlinear Stochastic Discrete-Time Systems
2013-01-01
This paper studies the stability for nonlinear stochastic discrete-time systems. First of all, several definitions on stability are introduced, such as stability, asymptotical stability, and pth moment exponential stability. Moreover, using the method of the Lyapunov functionals, some efficient criteria for stochastic stability are obtained. Some examples are presented to illustrate the effectiveness of the proposed theoretical results.
Polynomial Transformations For Discrete-Time Linear Systems
Baram, Yoram
1991-01-01
Transformations based on polynomial matrices of finite degree developed for use in computing functions for compensation, inversion, and approximation of discrete-time, multivariable, linear systems. Method derived from z-transform transfer-function form of matrices. Applicable to cascade-compensation problems in design of control systems.
Asymptotical Behaviors of Nonautonomous Discrete Kolmogorov System with Time Lags
Shengqiang Liu
2010-01-01
Full Text Available We discuss a general n-species discrete Kolmogorov system with time lags. We build some new results about the sufficient conditions for permanence, extinction, and balancing survival. When applying these results to some Lotka-Volterra systems, we obtain the criteria on harmless delay for the permanence as well as profitless delay for balancing survival.
Asymptotical Behaviors of Nonautonomous Discrete Kolmogorov System with Time Lags
Liu Shengqiang
2010-01-01
Full Text Available We discuss a general -species discrete Kolmogorov system with time lags. We build some new results about the sufficient conditions for permanence, extinction, and balancing survival. When applying these results to some Lotka-Volterra systems, we obtain the criteria on harmless delay for the permanence as well as profitless delay for balancing survival.
STABILITY CRITERIA FOR STOCHASTIC DISCRETE-TIME FRACTIONAL ORDER SYSTEMS
Carmen BARBACIORU
2016-05-01
Full Text Available In this paper are discussed stability problems for a class of discrete-time fractional systems (DTFSs with independent random perturbations. Two notions of mean square stability (MSS and mean square asymptotic stability (MSAS are introduced for the DTFSs by using an approximating linear stochastic system. Necessary and sufficient conditions for MSS and MSA are then derived.
Generalized Synchronization of Time-Delayed Discrete Systems
JING Jian-Yi; MIN Le-Quan
2009-01-01
This paper establishes two theorems for two time-delayed (chaotic) discrete systems to achieve time-delayed generalized synchronization (TDGS). These two theorems uncover the general forms of two TDGS systems via a prescribed transformation. As examples, we convert the Lorenz three-dimensional chaotic map to an equal time-delayed system as the driving system, and construct the TDGS driven systems according to the Theorems 1 and 2. Numerical simulations demonstrate the effectiveness of the proposed theorems.
CYCLE TIMES ASSIGNMENT OF NONLINEAR DISCRETE EVENT DYNAMIC SYSTEMS
CHEN Wende
2000-01-01
In this paper, nonautonomous models of Discrete Event Dynamic Systems (DEDS) are established by min-max function, reachability and observability are defined,the problem on cycle times assignment of DEDS, which corresponds with the important problem on poles assignment of linear systems, is studied. By Gunawardena et al.'Duality Theorem following results are obtained: Cycle times of system can be assigned under state feedback(or output feedback) if and only if system is reachable (or reachable and obserbable).
Discrete-Time LPV Current Control of an Induction Motor
Bendtsen, Jan Dimon; Trangbæk, Klaus
2003-01-01
further complications. The synthesis method is applied to the model, yielding an LPV discrete-time controller. Finally, the efficiency of the control scheme is validated via simulations as well as on the actual induction motor, both in open-loop current control and when an outer speed control loop......In this paper we apply a new method for gain-scheduled output feedback control of nonlinear systems to current control of an induction motor. The method relies on recently developed controller synthesis results for linear parameter-varying (LPV) systems, where the controller synthesis is formulated...... as a set of linear matrix inequalities with full-block multipliers. A standard nonlinear model of the motor is constructed and written on LPV form. We then show that, although originally developed in continuous time, the controller synthesis results can be applied to a discrete-time model as well without...
Discrete-Time LPV Current Control of an Induction Motor
Bendtsen, Jan Dimon; Trangbæk, Klaus
2003-01-01
In this paper we apply a new method for gain-scheduled output feedback control of nonlinear systems to current control of an induction motor. The method relies on recently developed controller synthesis results for linear parameter-varying (LPV) systems, where the controller synthesis is formulated...... as a set of linear matrix inequalities with full-block multipliers. A standard nonlinear model of the motor is constructed and written on LPV form. We then show that, although originally developed in continuous time, the controller synthesis results can be applied to a discrete-time model as well without...... further complications. The synthesis method is applied to the model, yielding an LPV discrete-time controller. Finally, the efficiency of the control scheme is validated via simulations as well as on the actual induction motor, both in open-loop current control and when an outer speed control loop...
Discrete-Time LPV Current Control of an Induction Motor
Bendtsen, Jan Dimon; Trangbæk, Klaus
2001-01-01
In this paper we apply a new method for gain-scheduled output feedback control of nonlinear systems to current control of an induction motor. The method relies on recently developed controller synthesis results for linear parameter-varying (LPV) systems, where the controller synthesis is formulated...... as a set of linear matrix inequalities with full-block multipliers. A standard nonlinear model of the motor is then constructed and written on LPV form. We then show that, although originally developed in continuous time, the controller synthesis results can be applied to a discrete-time model as well...... without further complications. The synthesis method is applied to the model, yielding an LPV discrete-time controller. Finally, the efficiency of the control scheme is validated via simulations as well as experimentally on the actual induction motor, both in open-loop current control and when an outer...
Analyzing neuronal networks using discrete-time dynamics
Ahn, Sungwoo; Smith, Brian H.; Borisyuk, Alla; Terman, David
2010-05-01
We develop mathematical techniques for analyzing detailed Hodgkin-Huxley like models for excitatory-inhibitory neuronal networks. Our strategy for studying a given network is to first reduce it to a discrete-time dynamical system. The discrete model is considerably easier to analyze, both mathematically and computationally, and parameters in the discrete model correspond directly to parameters in the original system of differential equations. While these networks arise in many important applications, a primary focus of this paper is to better understand mechanisms that underlie temporally dynamic responses in early processing of olfactory sensory information. The models presented here exhibit several properties that have been described for olfactory codes in an insect’s Antennal Lobe. These include transient patterns of synchronization and decorrelation of sensory inputs. By reducing the model to a discrete system, we are able to systematically study how properties of the dynamics, including the complex structure of the transients and attractors, depend on factors related to connectivity and the intrinsic and synaptic properties of cells within the network.
Time-Discrete Higher-Order ALE Formulations: Stability
Bonito, Andrea
2013-01-01
Arbitrary Lagrangian Eulerian (ALE) formulations deal with PDEs on deformable domains upon extending the domain velocity from the boundary into the bulk with the purpose of keeping mesh regularity. This arbitrary extension has no effect on the stability of the PDE but may influence that of a discrete scheme. We examine this critical issue for higher-order time stepping without space discretization. We propose time-discrete discontinuous Galerkin (dG) numerical schemes of any order for a time-dependent advection-diffusion-model problem in moving domains, and study their stability properties. The analysis hinges on the validity of the Reynold\\'s identity for dG. Exploiting the variational structure and assuming exact integration, we prove that our conservative and nonconservative dG schemes are equivalent and unconditionally stable. The same results remain true for piecewise polynomial ALE maps of any degree and suitable quadrature that guarantees the validity of the Reynold\\'s identity. This approach generalizes the so-called geometric conservation law to higher-order methods. We also prove that simpler Runge-Kutta-Radau methods of any order are conditionally stable, that is, subject to a mild ALE constraint on the time steps. Numerical experiments corroborate and complement our theoretical results. © 2013 Society for Industrial and Applied Mathematics.
Discrete-time control system design with applications
Rabbath, C A
2014-01-01
This book presents practical techniques of discrete-time control system design. In general, the design techniques lead to low-order dynamic compensators that ensure satisfactory closed-loop performance for a wide range of sampling rates. The theory is given in the form of theorems, lemmas, and propositions. The design of the control systems is presented as step-by-step procedures and algorithms. The proposed feedback control schemes are applied to well-known dynamic system models. This book also discusses: Closed-loop performance of generic models of mobile robot and airborne pursuer dynamic systems under discrete-time feedback control with limited computing capabilities Concepts of discrete-time models and sampled-data models of continuous-time systems, for both single- and dual-rate operation Local versus global digital redesign Optimal, closed-loop digital redesign methods Plant input mapping design Generalized holds and samplers for use in feedback control loops, Numerical simulation of fixed-point arithm...
Robust stability of discrete-time nonlinear system with time-delay
LIU Xin-ge; WU Min
2005-01-01
The robustly asymptotical stability problem for discrete-time nonlinear systems with time-delay was investigated. Positive definite matrix are constructed through Lyapunov functional. With the identity transform, property of matrix inverse and S-procedure, a new sufficient condition independent of the size of time-delay for robust stability of discrete-time nonlinear systems with time-delay is established. With Schur complement, another equivalent sufficient condition for robust stability of discrete-time nonlinear systems with time-delay is given. Finally, a sufficient condition dependent on the size of time-delay for robust stability of discrete-time nonlinear systems with time-delay is obtained. A unified approach is used to cast the robust stability problem into a convex optimization involving linear matrix inequalities.
Stability Analysis of Uncertain Discrete Time-Delay Control Systems
Long Xuming; Duan Ping
2006-01-01
Based on Lyapunov stability theory, a less conservative sufficient conditions for the stabilities of uncertain discrete delay-independent and delay-dependent control systems are obtained by using the linear matrix inequality (LMI) approach. Judgement of the stability of time-delay systems is transformed to judgement of the feasible solution of an LMI, and hence is solved by use of MATLAB. Numerical simulations verify the validity of the proposed method.
Algebraic convergence for discrete-time ergodic Markov chains
MAO; Yonghua(毛永华)
2003-01-01
This paper studies the e-ergodicity for discrete-time recurrent Markov chains. It proves that thee-order deviation matrix exists and is finite if and only if the chain is (e + 2)-ergodic, and then the algebraicdecay rates of the n-step transition probability to the stationary distribution are obtained. The criteria fore-ergodicity are given in terms of existence of solution to an equation. The main results are illustrated by some examples.
Identifying the topology of networks with discrete-time dynamics
Guo, Shu-Juan; Fu, Xin-Chu
2010-07-01
We suggest a method for identifying the topology of networks with discrete-time dynamics based on the dynamical evolution supported by the networks. The Frobenius matrix norm and Lasalle's invariance principle are used in this work. The network concerned can be directed or undirected, weighted or unweighted, and the local dynamics of each node can be nonidentical. The connections among the nodes can be all unknown or partially known. Finally, several examples are illustrated to verify the theoretical results.
Identifying the topology of networks with discrete-time dynamics
Guo Shujuan [School of Physics and Mathematics, Changzhou University, Changzhou 213164 (China); Fu Xinchu, E-mail: sjguo1@gmail.co, E-mail: enxcfu@gmail.co [Department of Mathematics, Shanghai University, Shanghai 200444 (China)
2010-07-23
We suggest a method for identifying the topology of networks with discrete-time dynamics based on the dynamical evolution supported by the networks. The Frobenius matrix norm and Lasalle's invariance principle are used in this work. The network concerned can be directed or undirected, weighted or unweighted, and the local dynamics of each node can be nonidentical. The connections among the nodes can be all unknown or partially known. Finally, several examples are illustrated to verify the theoretical results.
H∞ controller synthesis of piecewise discrete time linear systems
Gang FENG
2003-01-01
This paper presents an H∞ controller design method for piecewise discrete time linear systems based on a piecewise quadratic Lyapunov function. It is shown that the resulting closed loop system is globally stable with guaranteed H∞ perfomance and the controller can be obtained by solvng a set of bilinear matrix inequalities. It has been shown that piecewise quadratic Lyapnnov functions are less conservative than the global quadratic Lyapunov functions. A simulation example is also given to illustrate the advantage of the proposed approach.
Robust sliding mode control for uncertain discrete time systems
QU Shaocheng; WANG Yongji
2003-01-01
A novel variable structure control (VSC) strategy with a dynamic disturbance compensator based on the reaching law for a class of uncertain discrete systems is presented. The robust stability to disturbance and the system dynamics in the vicinity of the switching plane are studied. A measure of the uncertain parameters and external disturbance is obtained through delaying every sampling time. Theoretical analysis and experimental simulation results demonstrate that the dynamic performance and robustness of the closed-loop system are improved effectively.
A continuous-time/discrete-time mixed audio-band sigma delta ADC
Liu Yan; Hua Siliang; Wang Donghui; Hou Chaohuan
2011-01-01
This paper introduces a mixed continuous-time/discrete-time, single-loop, fourth-order, 4-bit audioband sigma delta ADC that combines the benefits of continuous-time and discrete-time circuits, while mitigating the challenges associated with continuous-time design. Measurement results show that the peak SNR of this ADC reaches 100 dB and the total power consumption is less than 30 mW.
On reevaluation rate in discrete time Hogg-Huberman model
Tanaka, Toshijiro; Shibata, Junko; Inoue, Masayoshi
2002-06-01
The discrete time Hogg-Huberman model is extended to a case with time-dependent reevaluation rate at which agents using one resource decide to evaluate their resource choice. In this paper the time dependence of the reevaluation rate is determined by states of the system. The dynamical behavior of the extended Hogg-Huberman model is discussed. It is found that the change of fraction of agents using resource 1 is suppressed to be smaller than that in the case of constant reevaluation rate.
Mixed Discretization of the Time Domain MFIE at Low Frequencies
Ulku, Huseyin Arda
2017-01-10
Solution of the magnetic field integral equation (MFIE), which is obtained by the classical marching on-in-time (MOT) scheme, becomes inaccurate when the time step is large, i.e., under low-frequency excitation. It is shown here that the inaccuracy stems from the classical MOT scheme’s failure to predict the correct scaling of the current’s Helmholtz components for large time steps. A recently proposed mixed discretization strategy is used to alleviate the inaccuracy problem by restoring the correct scaling of the current’s Helmholtz components under low-frequency excitation.
Output regulation problem for discrete-time linear time-delay systems by output feedback control
Yamin YAN; Jie HUANG
2016-01-01
In this paper, we study the output regulation problem of discrete linear time-delay systems by output feedback control. We have established some results parallel to those for the output regulation problem of continuous linear time-delay systems.
Distributed LQR control for discrete-time homogeneous systems
Wang, Wei; Zhang, Fangfang; Han, Chunyan
2016-11-01
This paper investigates the distributed linear quadratic regulation (LQR) controller design method for discrete-time homogeneous scalar systems. Based on the optimal centralised control theory, the existence condition for distributed optimal controller is firstly proposed. It shows that the globally optimal distributed controller is dependent on the structure of the penalty matrix. Such results can be used in consensus problems and used to find under which communication topology (may not be an all-to-all form) the optimal distributed controller exists. When the proposed condition cannot hold, a suboptimal design method with the aid of the decomposition of discrete algebraic Riccati equations and robustness of local controllers is proposed. The computation complexity and communication load for each subsystem are only dependent on the number of its neighbours.
The limitations of discrete-time approaches to continuous-time contagion dynamics
Fennell, Peter G; Gleeson, James P
2016-01-01
Continuous-time Markov process models of contagions are widely studied, not least because of their utility in predicting the evolution of real-world contagions and in formulating control measures. It is often the case, however, that discrete-time approaches are employed to analyze such models or to simulate them numerically. In such cases, time is discretized into uniform steps and transition rates between states are replaced by transition probabilities. In this paper, we illustrate potential limitations to this approach. We show how discretizing time leads to a restriction on the values of the model parameters that can accurately be studied. We examine numerical simulation schemes employed in the literature, showing how synchronous-type updating schemes can bias discrete-time formalisms when compared against continuous-time formalisms. Event-based simulations, such as the Gillespie algorithm, are proposed as optimal simulation schemes both in terms of replicating the continuous-time process and computational...
Satisfactory control of discrete-time linear periodic systems
Shiqian LIU; Jihong ZHU; JinChun HU
2007-01-01
In this paper satisfactory control for discrete-time linear periodic systems is studied.Based on a suitable time-invariant state sampled reformulation,periodic state feedback controller has been designed such that desired requirements of steady state covariance,H-infinity rejection bound and regional pole assignment for the periodic system are met simultaneously.By using satisfactory control theory,the problem of satisfactory periodic controller can be transformed into a linear programming problem subject to a set of linear matrix inequalities(LMIs).and a feasible designing approach is presented via LMI technique.Numeric example validates the obtained conclusion.
Space & time discontinuities in Liouville theory and its discrete analogue
Doikou, Anastasia
2016-01-01
We consider the deformed harmonic oscillator as a discrete version of the Liouville theory and study this model in the presence of local integrable defects. From this, the time evolution of the defect degrees of freedom are determined, found in the form of the local equations of motion. We also revisit the continuous Liouville theory, deriving its local integrals of motion and comparing these with previous results from the sine-Gordon point of view.Finally, the generic Backlund type relations are presented, corresponding to the implementation of time-like and space-like impurities in the continuum model.
Discrete-Time LPV Current Control of an Induction Motor
Bendtsen, Jan Dimon; Trangbæk, Klaus
2003-01-01
In this paper we apply a new method for gain-scheduled output feedback control of nonlinear systems to current control of an induction motor. The method relies on recently developed controller synthesis results for linear parameter-varying (LPV) systems, where the controller synthesis is formulated...... as a set of linear matrix inequalities with full-block multipliers. A standard nonlinear model of the motor is constructed and written on LPV form. We then show that, although originally developed in continuous time, the controller synthesis results can be applied to a discrete-time model as well without...
On Discrete Time Control of Continuous Time Systems
Poulsen, Niels Kjølstad
of Denmark. The focus in this paper is control of a continuous time system by means of a digital control. In this context the control signal can only change at sample instants and is constant between samples. The cost function do include the variations of output between samples....
Feedback control design for discrete-time piecewise affine systems
XU Jun; XIE Li-hua
2007-01-01
This paper investigates the design of state feedback and dynamic output feedback stabilizing controllers for discrete-time piecewise affine (PWA) systems. The main objective is to derive design methods that will incorporate the partition information of the PWA systems so as to reduce the design conservatism embedded in existing design methods. We first introduce a transformation that converts the feedback control design problem into a bilinear matrix inequality (BMI) problem. Then, two iterative algorithms are proposed to compute the feedback controllers characterized by the BMI. Several simulation examples are given to demonstrate the advantages of the proposed design.
Weak Approximation of SDEs by Discrete-Time Processes
Henryk Zähle
2008-01-01
Full Text Available We consider the martingale problem related to the solution of an SDE on the line. It is shown that the solution of this martingale problem can be approximated by solutions of the corresponding time-discrete martingale problems under some conditions. This criterion is especially expedient for establishing the convergence of population processes to SDEs. We also show that the criterion yields a weak Euler scheme approximation of SDEs under fairly weak assumptions on the driving force of the approximating processes.
Simulation of neutrino oscillations using discrete-time quantum walk
Mallick, Arindam; Chandrashekar, C M
2016-01-01
Neutrino oscillation is a well-known phenomenon observed in high energy physics. Here starting from a one-spatial dimensional discrete-time quantum walk we present a method to simulate neutrino oscillation. We present the set of walk parameters with which we can obtain the same oscillation probability profile obtained in both, long range and short range neutrino experiment. Our scheme to simulate three-generation neutrino oscillation from quantum walk evolution operators can be physically realized in any low energy experimental setup with access to control a single six-level system, a multiparticle three-qubits or a qubit-qutrit system.
Real-Time Exponential Curve Fits Using Discrete Calculus
Rowe, Geoffrey
2010-01-01
An improved solution for curve fitting data to an exponential equation (y = Ae(exp Bt) + C) has been developed. This improvement is in four areas -- speed, stability, determinant processing time, and the removal of limits. The solution presented avoids iterative techniques and their stability errors by using three mathematical ideas: discrete calculus, a special relationship (be tween exponential curves and the Mean Value Theorem for Derivatives), and a simple linear curve fit algorithm. This method can also be applied to fitting data to the general power law equation y = Ax(exp B) + C and the general geometric growth equation y = Ak(exp Bt) + C.
A parametric LTR solution for discrete-time systems
Niemann, Hans Henrik; Jannerup, Ole Erik
1989-01-01
and the full loop transfer function, is manipulated into a general form involving the target loop transfer matrix and the fundamental recovery matrix. A parametric LTR solution based on the recovery matrix is developed. It is shown that the LQR/LTR (linear quadratic Gaussian/loop transfer recovery) solution......A parametric LTR (loop transfer recovery) solution for discrete-time compensators incorporating filtering observers which achieve exact recovery is presented for both minimum- and non-minimum-phase systems. First the recovery error, which defines the difference between the target loop transfer...
Optimal Robust Fault Detection for Linear Discrete Time Systems
Nike Liu
2008-01-01
Full Text Available This paper considers robust fault-detection problems for linear discrete time systems. It is shown that the optimal robust detection filters for several well-recognized robust fault-detection problems, such as ℋ−/ℋ∞, ℋ2/ℋ∞, and ℋ∞/ℋ∞ problems, are the same and can be obtained by solving a standard algebraic Riccati equation. Optimal filters are also derived for many other optimization criteria and it is shown that some well-studied and seeming-sensible optimization criteria for fault-detection filter design could lead to (optimal but useless fault-detection filters.
New Results in Discrete-Time Loop Transfer Recovery
Niemann, Hans Henrik; Søgaard-Andersen, Per
1988-01-01
in terms of the system zeros and the corresponding zero-directions. Full-order as well as minimal-order observers are treated. Further it is shown how exact recovery is also applicable to non-minimum phase plants. In this case the achievable performance is parameterized explicitly.......For discrete-time compensators incorporating prediction observers asymptotic loop transfer recovery is not feasible. Instead loop transfer recovery objectives must be satisfied via exact recovery techniques. In this note the model-based compensators which achieves exact recovery are parametrized...
Control problems of discrete-time dynamical systems
Hasegawa, Yasumichi
2013-01-01
This monograph deals with control problems of discrete-time dynamical systems which include linear and nonlinear input/output relations. It will be of popular interest to researchers, engineers and graduate students who specialized in system theory. A new method which produces manipulated inputs is presented in the sense of state control and output control. This monograph provides new results and their extensions which can also be more applicable for nonlinear dynamical systems. To present the effectiveness of the method, many numerical examples of control problems are provided as well.
LARGE SIGNAL DISCRETE-TIME MODEL FOR PARALLELED BUCK CONVERTERS
无
2002-01-01
As a number of switch-combinations are involved in operation of multi-converter-system, conventional methods for obtaining discrete-time large signal model of these converter systems result in a very complex solution. A simple sampled-data technique for modeling distributed dc-dc PWM converters system (DCS) was proposed. The resulting model is nonlinear and can be linearized for analysis and design of DCS. These models are also suitable for fast simulation of these networks. As the input and output of dc-dc converters are slow varying, suitable model for DCS was obtained in terms of the finite order input/output approximation.
Signatures of discrete scale invariance in Dst time series
Balasis, Georgios; Papadimitriou, Constantinos; Daglis, Ioannis A.; Anastasiadis, Anastasios; Athanasopoulou, Labrini; Eftaxias, Konstantinos
2011-07-01
Self-similar systems are characterized by continuous scale invariance and, in response, the existence of power laws. However, a significant number of systems exhibits discrete scale invariance (DSI) which in turn leads to log-periodic corrections to scaling that decorate the pure power law. Here, we present the results of a search of log-periodic corrections to scaling in the squares of Dst index increments which are taken as proxies of the energy dissipation rate in the magnetosphere. We show that Dst time series exhibit DSI and discuss the consequence of this feature, as well as the possible implications of Dst DSI on space weather forecasting efforts.
ERROR ESTIMATES FOR THE TIME DISCRETIZATION FOR NONLINEAR MAXWELL'S EQUATIONS
Marián Slodi(c)ka; Ján Bu(s)a Jr.
2008-01-01
This paper is devoted to the study of a nonlinear evolution eddy current model of the type (б)tB(H) +▽×(▽×H) = 0 subject to homogeneous Dirichlet boundary conditions H×v = 0 and a given initial datum. Here, the magnetic properties of a soft ferromagnet are linked by a nonlinear material law described by B(H). We apply the backward Euler method for the time discretization and we derive the error estimates in suitable function spaces. The results depend on the nonlinearity of B(H).
Synchronization of Discrete-Time Chaotic Systems in Bandlimited Channels
Marcio Eisencraft
2009-01-01
Full Text Available Over the last couple of decades, many methods for synchronizing chaotic systems have been proposed with communications applications in view. Yet their performance has proved disappointing in face of the nonideal character of usual channels linking transmitter and receiver, that is, due to both noise and signal propagation distortion. Here we consider a discrete-time master-slave system that synchronizes despite channel bandwidth limitations and an allied communication system. Synchronization is achieved introducing a digital filter that limits the spectral content of the feedback loop responsible for producing the transmitted signal.
Hofstede, ter F.; Wedel, M.
1998-01-01
This study investigates the effects of time aggregation in discrete and continuous-time hazard models. A Monte Carlo study is conducted in which data are generated according to various continuous and discrete-time processes, and aggregated into daily, weekly and monthly intervals. These data are
COMPONENTWISE STABILITY OF DISCRETE-TIME INTERVAL BIDIRECTIONAL ASSOCIATIVE MEMORIES
Mihaela-Hanako MATCOVSCHI
2004-12-01
Full Text Available The componentwise stability is a special type of asymptotic stability, which incorporates the positive invariance of certain time-dependent rectangular sets with respect to the state space trajectories. The paper develops the analysis of componentwise stability for discrete-time Bidirectional Associative Memory (BAM neural networks with interval type parameters, providing criteria that allow monitoring the evolution of each state-space variable towards the equilibrium point. These criteria are formulated in terms of Schur stability of a test matrix adequately built from the intervals expressing the parameter uncertainties. Our approach represents a refinement of the classical results in stability theory, since the time-dependence of the considered invariant sets makes it possible to give a qualitative characterization of the dynamics at the level of the state vector components.
Continuous-time discrete-space models for animal movement
Hanks, Ephraim M.; Hooten, Mevin B.; Alldredge, Mat W.
2015-01-01
The processes influencing animal movement and resource selection are complex and varied. Past efforts to model behavioral changes over time used Bayesian statistical models with variable parameter space, such as reversible-jump Markov chain Monte Carlo approaches, which are computationally demanding and inaccessible to many practitioners. We present a continuous-time discrete-space (CTDS) model of animal movement that can be fit using standard generalized linear modeling (GLM) methods. This CTDS approach allows for the joint modeling of location-based as well as directional drivers of movement. Changing behavior over time is modeled using a varying-coefficient framework which maintains the computational simplicity of a GLM approach, and variable selection is accomplished using a group lasso penalty. We apply our approach to a study of two mountain lions (Puma concolor) in Colorado, USA.
Soundness of Timed-Arc Workflow Nets in Discrete and Continuous-Time Semantics
Mateo, Jose Antonio; Srba, Jiri; Sørensen, Mathias Grund
2015-01-01
Analysis of workflow processes with quantitative aspectslike timing is of interest in numerous time-critical applications. We suggest a workflow model based on timed-arc Petri nets and studythe foundational problems of soundness and strong (time-bounded) soundness.We first consider the discrete-t...
Hopf Bifurcation in a Cobweb Model with Discrete Time Delays
Luca Gori
2014-01-01
Full Text Available We develop a cobweb model with discrete time delays that characterise the length of production cycle. We assume a market comprised of homogeneous producers that operate as adapters by taking the (expected profit-maximising quantity as a target to adjust production and consumers with a marginal willingness to pay captured by an isoelastic demand. The dynamics of the economy is characterised by a one-dimensional delay differential equation. In this context, we show that (1 if the elasticity of market demand is sufficiently high, the steady-state equilibrium is locally asymptotically stable and (2 if the elasticity of market demand is sufficiently low, quasiperiodic oscillations emerge when the time lag (that represents the length of production cycle is high enough.
Discrete Time Markovian Agents Interacting Through a Potential
Budhiraja, Amarjit; Rubenthaler, Sylvain
2011-01-01
A discrete time stochastic model for a multiagent system given in terms of a large collection of interacting Markov chains is studied. The evolution of the interacting particles is described through a time inhomogeneous transition probability kernel that depends on the 'gradient' of the potential field. The particles, in turn, dynamically modify the potential field through their cumulative input. Interacting Markov processes of the above form have been suggested as models for active biological transport in response to external stimulus such as a chemical gradient. One of the basic mathematical challenges is to develop a general theory of stability for such interacting Markovian systems and for the corresponding nonlinear Markov processes that arise in the large agent limit. Such a theory would be key to a mathematical understanding of the interactive structure formation that results from the complex feedback between the agents and the potential field. It will also be a crucial ingredient in developing simulat...
On Extended Dissipativity of Discrete-Time Neural Networks With Time Delay.
Feng, Zhiguang; Zheng, Wei Xing
2015-12-01
In this brief, the problem of extended dissipativity analysis for discrete-time neural networks with time-varying delay is investigated. The definition of extended dissipativity of discrete-time neural networks is proposed, which unifies several performance measures, such as the H∞ performance, passivity, l2 - l∞ performance, and dissipativity. By introducing a triple-summable term in Lyapunov function, the reciprocally convex approach is utilized to bound the forward difference of the triple-summable term and then the extended dissipativity criterion for discrete-time neural networks with time-varying delay is established. The derived condition guarantees not only the extended dissipativity but also the stability of the neural networks. Two numerical examples are given to demonstrate the reduced conservatism and effectiveness of the obtained results.
Causal inference for continuous-time processes when covariates are observed only at discrete times
Zhang, Mingyuan; Small, Dylan S; 10.1214/10-AOS830
2011-01-01
Most of the work on the structural nested model and g-estimation for causal inference in longitudinal data assumes a discrete-time underlying data generating process. However, in some observational studies, it is more reasonable to assume that the data are generated from a continuous-time process and are only observable at discrete time points. When these circumstances arise, the sequential randomization assumption in the observed discrete-time data, which is essential in justifying discrete-time g-estimation, may not be reasonable. Under a deterministic model, we discuss other useful assumptions that guarantee the consistency of discrete-time g-estimation. In more general cases, when those assumptions are violated, we propose a controlling-the-future method that performs at least as well as g-estimation in most scenarios and which provides consistent estimation in some cases where g-estimation is severely inconsistent. We apply the methods discussed in this paper to simulated data, as well as to a data set c...
Discrete random walk models for space-time fractional diffusion
Gorenflo, Rudolf; Mainardi, Francesco; Moretti, Daniele; Pagnini, Gianni; Paradisi, Paolo
2002-11-01
A physical-mathematical approach to anomalous diffusion may be based on generalized diffusion equations (containing derivatives of fractional order in space or/and time) and related random walk models. By space-time fractional diffusion equation we mean an evolution equation obtained from the standard linear diffusion equation by replacing the second-order space derivative with a Riesz-Feller derivative of order {alpha} is part of (0,2] and skewness {theta} (module{theta}{<=}{l_brace}{alpha},2-{alpha}{r_brace}), and the first-order time derivative with a Caputo derivative of order {beta} is part of (0,1]. Such evolution equation implies for the flux a fractional Fick's law which accounts for spatial and temporal non-locality. The fundamental solution (for the Cauchy problem) of the fractional diffusion equation can be interpreted as a probability density evolving in time of a peculiar self-similar stochastic process that we view as a generalized diffusion process. By adopting appropriate finite-difference schemes of solution, we generate models of random walk discrete in space and time suitable for simulating random variables whose spatial probability density evolves in time according to this fractional diffusion equation.
Space-time discontinuous Galerkin discretization of rotating shallow water equations
Ambati, V.R.; Bokhove, Onno
2007-01-01
A space–time discontinuous Galerkin (DG) discretization is presented for the (rotating) shallow water equations over varying topography. We formulate the space–time DG finite element discretization in an efficient and conservative discretization. The HLLC flux is used as numerical flux through the
Space-time discontinuous Galerkin discretization of rotating shallow water equations on moving grids
Ambati, V.R.; Bokhove, Onno
2006-01-01
A space-time discontinuous Galerkin (DG) discretization is presented for the (rotating) shallow water equations over varying topography. We formulate the space-time DG finite element discretization in an efficient and conservative discretization. The HLLC flux is used as numerical flux through the
Formal methods for discrete-time dynamical systems
Belta, Calin; Aydin Gol, Ebru
2017-01-01
This book bridges fundamental gaps between control theory and formal methods. Although it focuses on discrete-time linear and piecewise affine systems, it also provides general frameworks for abstraction, analysis, and control of more general models. The book is self-contained, and while some mathematical knowledge is necessary, readers are not expected to have a background in formal methods or control theory. It rigorously defines concepts from formal methods, such as transition systems, temporal logics, model checking and synthesis. It then links these to the infinite state dynamical systems through abstractions that are intuitive and only require basic convex-analysis and control-theory terminology, which is provided in the appendix. Several examples and illustrations help readers understand and visualize the concepts introduced throughout the book.
Universal Denoising of Discrete-time Continuous-Amplitude Signals
Sivaramakrishnan, Kamakshi
2008-01-01
We consider the problem of reconstructing a discrete-time signal (sequence) with continuous-valued components corrupted by a known memoryless channel. When performance is measured using a per-symbol loss function satisfying mild regularity conditions, we develop a sequence of denoisers that, although independent of the distribution of the underlying `clean' sequence, is universally optimal in the limit of large sequence length. This sequence of denoisers is universal in the sense of performing as well as any sliding window denoising scheme which may be optimized for the underlying clean signal. Our results are initially developed in a ``semi-stochastic'' setting, where the noiseless signal is an unknown individual sequence, and the only source of randomness is due to the channel noise. It is subsequently shown that in the fully stochastic setting, where the noiseless sequence is a stationary stochastic process, our schemes universally attain optimum performance. The proposed schemes draw from nonparametric de...
Coordination Frictions and Job Heterogeneity: A Discrete Time Analysis
Kennes, John; Le Maire, Christian Daniel
This paper develops and extends a dynamic, discrete time, job to worker matching model in which jobs are heterogeneous in equilibrium. The key assumptions of this economic environment are (i) matching is directed and (ii) coordination frictions lead to heterogeneous local labor markets. We de- rive...... a number of new theoretical results, which are essential for the empirical application of this type of model to matched employer-employee microdata. First, we o¤er a robust equilibrium concept in which there is a continu- ous dispersion of job productivities and wages. Second, we show that our model can...... be readily solved with continuous exogenous worker heterogene- ity, where high type workers (high outside options and productivity) earn higher wages in high type jobs and are hired at least as frequently to the better job types as low type workers (low outside options and productivity). Third, we...
Parameter identification of linear discrete stochastic systems with time delays
Wong, E. C.
1980-01-01
An identification algorithm that uses the maximum likelihood technique to identify the unknown time delays, plant parameters, and noise covariances of linear discrete stochastic systems is presented. Cases of additive white noise and colored measurement noises are considered. The likelihood function is evaluated using either a minimum-variance (Kalman) filter or a minimal-order observer. The Kalman filter is used in the identification algorithm to provide minimum-variance estimates. The minimal-order observer is a lower-dimensional and computationally simpler filter, and is advantageous especially for systems with long delays. It provides a less optimal solution to the minimum-mean-square state estimation problem. The colored-noise observer algorithm has the disadvantage of having to compute an extra error covariance matrix of lower order.
Recurrence plots of discrete-time Gaussian stochastic processes
Ramdani, Sofiane; Bouchara, Frédéric; Lagarde, Julien; Lesne, Annick
2016-09-01
We investigate the statistical properties of recurrence plots (RPs) of data generated by discrete-time stationary Gaussian random processes. We analytically derive the theoretical values of the probabilities of occurrence of recurrence points and consecutive recurrence points forming diagonals in the RP, with an embedding dimension equal to 1. These results allow us to obtain theoretical values of three measures: (i) the recurrence rate (REC) (ii) the percent determinism (DET) and (iii) RP-based estimation of the ε-entropy κ(ε) in the sense of correlation entropy. We apply these results to two Gaussian processes, namely first order autoregressive processes and fractional Gaussian noise. For these processes, we simulate a number of realizations and compare the RP-based estimations of the three selected measures to their theoretical values. These comparisons provide useful information on the quality of the estimations, such as the minimum required data length and threshold radius used to construct the RP.
Stochasticity, decoherence and an arrow of time from the discretization of time?
M C Valsakumar
2005-04-01
Certain intriguing consequences of the discreteness of time on the time evolution of dynamical systems are discussed. In the discrete-time classical mechanics proposed here, there is an arrow of time that follows from the fact that the replacement of the time derivative by the backward difference operator alone can preserve the non-negativity of the phase space density. It is seen that, even for free particles, all the degrees of freedom are correlated in principle. The forward evolution of functions of phase space variables by a finite number of time steps, in this discrete-time mechanics, depends on the entire continuous-time history in the interval [0, ∞]. In this sense, discrete time evolution is non-local in time from a continuous-time point of view. A corresponding quantum mechanical treatment is possible via the density matrix approach. The interference between non-degenerate quantum mechanical states decays exponentially. This decoherence is present, in principle, for all systems; however, it is of practical importance only in macroscopic systems, or in processes involving large energy changes.
Evolución de la endemia de la lepra en Brasil Time trends of Hansen's disease in Brasil
Maria da Conceição Cavalcanti Magalhães
2005-12-01
Full Text Available La presente investigación se propone abordar la distribución territorial de la lepra en Brasil con el objetivo de identificar las regularidades de su diferenciación espacial y aportar conocimientos que permitan progresar en la comprensión de los procesos de su producción social. Fueron calculadas las tasas anuales de detección de casos, brutos y específicos, para las regiones y estados del país. La evolución espacio-temporal fue realizada mediante la construcción de series históricas. Se expone como substrato de los análisis una síntese sobre la distribución histórico-geográfica de la endemia en Brasil. La serie histórica del período 1960 - 2002, permite comparar las tasas de detección de las regiones, en la primera década, con las tasas más bajas, a excepción de la región Norte, que se destaca com la mayor detección. Todas las regiones elevan la detección a partir de la década del 70, siendo la Sul la de detección más baja. Las regiones Norte y Centro Oeste, mantienen las más altas detecciones de casos y los mayores incrementos, lo cual evidencia la desigual evolución regional de la endemia en el país. La permanencia histórica de elevada incidencia de la lepra en la región Norte, en el estado de Maranhão y Pernambuco en la región Nordeste, del estado de Paraná en la región Sul, así como relativamente bajas incidencias en el resto de esta última región, sugieren la existencia de contextos geográficos de diferente vulnerabilidad a la producción social de la lepra, y de nuevos componentes en la organización espacial en algunos territorios.The present investigation intends to study the territorial distribution of leprosy in Brazil in order to identify the regularities of its differentiation, and to contribute to the knowledge that allows progress in the understanding of the processes of its social production. Time trends of global and specific leprosy detection rates were calculated for regions and states
Reducing ambulance response times using discrete event simulation.
Wei Lam, Sean Shao; Zhang, Zhong Cheng; Oh, Hong Choon; Ng, Yih Ying; Wah, Win; Hock Ong, Marcus Eng
2014-01-01
The objectives of this study are to develop a discrete-event simulation (DES) model for the Singapore Emergency Medical Services (EMS), and to demonstrate the utility of this DES model for the evaluation of different policy alternatives to improve ambulance response times. A DES model was developed based on retrospective emergency call data over a continuous 6-month period in Singapore. The main outcome measure is the distribution of response times. The secondary outcome measure is ambulance utilization levels based on unit hour utilization (UHU) ratios. The DES model was used to evaluate different policy options in order to improve the response times, while maintaining reasonable fleet utilization. Three policy alternatives looking at the reallocation of ambulances, the addition of new ambulances, and alternative dispatch policies were evaluated. Modifications of dispatch policy combined with the reallocation of existing ambulances were able to achieve response time performance equivalent to that of adding 10 ambulances. The median (90th percentile) response time was 7.08 minutes (12.69 minutes). Overall, this combined strategy managed to narrow the gap between the ideal and existing response time distribution by 11-13%. Furthermore, the median UHU under this combined strategy was 0.324 with an interquartile range (IQR) of 0.047 versus a median utilization of 0.285 (IQR of 0.051) resulting from the introduction of additional ambulances. Response times were shown to be improved via a more effective reallocation of ambulances and dispatch policy. More importantly, the response time improvements were achieved without a reduction in the utilization levels and additional costs associated with the addition of ambulances. We demonstrated the effective use of DES as a versatile platform to model the dynamic system complexities of Singapore's national EMS systems for the evaluation of operational strategies to improve ambulance response times.
Constant pressure and temperature discrete-time Langevin molecular dynamics.
Grønbech-Jensen, Niels; Farago, Oded
2014-11-21
We present a new and improved method for simultaneous control of temperature and pressure in molecular dynamics simulations with periodic boundary conditions. The thermostat-barostat equations are built on our previously developed stochastic thermostat, which has been shown to provide correct statistical configurational sampling for any time step that yields stable trajectories. Here, we extend the method and develop a set of discrete-time equations of motion for both particle dynamics and system volume in order to seek pressure control that is insensitive to the choice of the numerical time step. The resulting method is simple, practical, and efficient. The method is demonstrated through direct numerical simulations of two characteristic model systems-a one-dimensional particle chain for which exact statistical results can be obtained and used as benchmarks, and a three-dimensional system of Lennard-Jones interacting particles simulated in both solid and liquid phases. The results, which are compared against the method of Kolb and Dünweg [J. Chem. Phys. 111, 4453 (1999)], show that the new method behaves according to the objective, namely that acquired statistical averages and fluctuations of configurational measures are accurate and robust against the chosen time step applied to the simulation.
Hopf Bifurcation Analysis for a Stochastic Discrete-Time Hyperchaotic System
Jie Ran
2015-01-01
Full Text Available The dynamics of a discrete-time hyperchaotic system and the amplitude control of Hopf bifurcation for a stochastic discrete-time hyperchaotic system are investigated in this paper. Numerical simulations are presented to exhibit the complex dynamical behaviors in the discrete-time hyperchaotic system. Furthermore, the stochastic discrete-time hyperchaotic system with random parameters is transformed into its equivalent deterministic system with the orthogonal polynomial theory of discrete random function. In addition, the dynamical features of the discrete-time hyperchaotic system with random disturbances are obtained through its equivalent deterministic system. By using the Hopf bifurcation conditions of the deterministic discrete-time system, the specific conditions for the existence of Hopf bifurcation in the equivalent deterministic system are derived. And the amplitude control with random intensity is discussed in detail. Finally, the feasibility of the control method is demonstrated by numerical simulations.
Discrete-Time Approximation for Nonlinear Continuous Systems with Time Delays
Bemri H’mida
2016-05-01
Full Text Available This paper is concerned with the discretization of nonlinear continuous time delay systems. Our approach is based on Taylor-Lie series. The main idea aims to minimize the effect of the delay and neglects the importance of nonlinear parameter by the linearization of the system study in an attempt to make its handling and easier programming as possible. We investigate a new method based on the development of new theoretical methods for the time discretization of nonlinear systems with time delay .The performance of these proposed discretization methods was validated by doing the numerical simulation using a nonlinear system with state delay. Some illustrative examples are given to show the effectiveness of the obtained results.
From Discrete-Time Models to Continuous-Time, Asynchronous Models of Financial Markets
K. Boer-Sorban (Katalin); U. Kaymak (Uzay); J. Spiering (Jaap)
2006-01-01
textabstractMost agent-based simulation models of financial markets are discrete-time in nature. In this paper, we investigate to what degree such models are extensible to continuous-time, asynchronous modelling of financial markets. We study the behaviour of a learning market maker in a market with
From Discrete-Time Models to Continuous-Time, Asynchronous Models of Financial Markets
K. Boer-Sorban (Katalin); U. Kaymak (Uzay); J. Spiering (Jaap)
2006-01-01
textabstractMost agent-based simulation models of financial markets are discrete-time in nature. In this paper, we investigate to what degree such models are extensible to continuous-time, asynchronous modelling of financial markets. We study the behaviour of a learning market maker in a market with
On Stochastic Finite-Time Control of Discrete-Time Fuzzy Systems with Packet Dropout
Yingqi Zhang
2012-01-01
Full Text Available This paper is concerned with the stochastic finite-time stability and stochastic finite-time boundedness problems for one family of fuzzy discrete-time systems over networks with packet dropout, parametric uncertainties, and time-varying norm-bounded disturbance. Firstly, we present the dynamic model description studied, in which the discrete-time fuzzy T-S systems with packet loss can be described by one class of fuzzy Markovian jump systems. Then, the concepts of stochastic finite-time stability and stochastic finite-time boundedness and problem formulation are given. Based on Lyapunov function approach, sufficient conditions on stochastic finite-time stability and stochastic finite-time boundedness are established for the resulting closed-loop fuzzy discrete-time system with Markovian jumps, and state-feedback controllers are designed to ensure stochastic finite-time stability and stochastic finite-time boundedness of the class of fuzzy systems. The stochastic finite-time stability and stochastic finite-time boundedness criteria can be tackled in the form of linear matrix inequalities with a fixed parameter. As an auxiliary result, we also give sufficient conditions on the stochastic stability of the class of fuzzy T-S systems with packet loss. Finally, two illustrative examples are presented to show the validity of the developed methodology.
Advanced discrete-time control designs and applications
Abidi, Khalid
2015-01-01
This book covers a wide spectrum of systems such as linear and nonlinear multivariable systems as well as control problems such as disturbance, uncertainty and time-delays. The purpose of this book is to provide researchers and practitioners a manual for the design and application of advanced discrete-time controllers. The book presents six different control approaches depending on the type of system and control problem. The first and second approaches are based on Sliding Mode control (SMC) theory and are intended for linear systems with exogenous disturbances. The third and fourth approaches are based on adaptive control theory and are aimed at linear/nonlinear systems with periodically varying parametric uncertainty or systems with input delay. The fifth approach is based on Iterative learning control (ILC) theory and is aimed at uncertain linear/nonlinear systems with repeatable tasks and the final approach is based on fuzzy logic control (FLC) and is intended for highly uncertain systems with heuristi...
Hansen's disease: a vanishing disease?
Sinésio Talhari
2012-12-01
Full Text Available The introduction, implementation, successes and failures of multidrug therapy (MDT in all Hansen's disease endemic countries are discussed in this paper. The high efficacy of leprosy treatment with MDT and the global reduction of prevalence led the World Health Organization, in 1991, to establish the goal of elimination of Hansen's disease (less than 1 patient per 10,000 inhabitants to be accomplished by the year 2000. Brazil, Nepal and East Timor are among the few countries that didn't reach the elimination goal by the year 2000 or even 2005. The implications of these aspects are highlighted in this paper. Current data from endemic and previously endemic countries that carry a regular leprosy control programme show that the important fall in prevalence was not followed by the reduction of the incidence. This means that transmission of Mycobacterium leprae is still an issue. It is reasonable to conclude that we are still far from the most important goal of Hansen's disease control: the interruption of transmission and reduction of incidence. It is necessary to emphasize to health managers the need of keeping Hansen's disease control activities to better develop control programmes in the future. The recent international proposal to interrupt the transmission of leprosy by the year 2020 seems to unrealistic and it is discussed in this paper. The possibility of epidemiological impact related to the human immunodeficiency virus/Hansen's disease coinfection is also considered.
Hansen's disease: a vanishing disease?
Talhari, Sinésio; Grossi, Maria Aparecida de Faria; Oliveira, Maria Leide W D R de; Gontijo, Bernardo; Talhari, Carolina; Penna, Gerson Oliveira
2012-12-01
The introduction, implementation, successes and failures of multidrug therapy (MDT) in all Hansen's disease endemic countries are discussed in this paper. The high efficacy of leprosy treatment with MDT and the global reduction of prevalence led the World Health Organization, in 1991, to establish the goal of elimination of Hansen's disease (less than 1 patient per 10,000 inhabitants) to be accomplished by the year 2000. Brazil, Nepal and East Timor are among the few countries that didn't reach the elimination goal by the year 2000 or even 2005. The implications of these aspects are highlighted in this paper. Current data from endemic and previously endemic countries that carry a regular leprosy control programme show that the important fall in prevalence was not followed by the reduction of the incidence. This means that transmission of Mycobacterium leprae is still an issue. It is reasonable to conclude that we are still far from the most important goal of Hansen's disease control: the interruption of transmission and reduction of incidence. It is necessary to emphasize to health managers the need of keeping Hansen's disease control activities to better develop control programmes in the future. The recent international proposal to interrupt the transmission of leprosy by the year 2020 seems to unrealistic and it is discussed in this paper. The possibility of epidemiological impact related to the human immunodeficiency virus/Hansen's disease coinfection is also considered.
Discrete-Time Sliding Mode Control for Uncertain Networked System Subject to Time Delay
Saulo C. Garcia
2015-01-01
Full Text Available We deal with uncertain systems with networked sliding mode control, subject to time delay. To minimize the degenerative effects of the time delay, a simpler format of state predictor is proposed in the control law. Some ultimate bounded stability analyses and stabilization conditions are provided for the uncertain time delay system with proposed discrete-time sliding mode control strategy. A numerical example is presented to corroborate the analyses.
Gilead, Leon; Wexler, Ruth
2016-10-01
Hansen's disease (HD) is an anthropophylic, infectious, chronic disease, caused by Mycobacterium leprae. The systemic disease, affecting both males and females at any age, involves mainly the skin and the peripheral nerves located in the limbs close to the skin. Traditionally the treatment of HD patients was entrusted to dermatologists. Current drug therapy given at an early stage can prevent many of the complications, and enables patients to go on with life. In 95% of the population there is an innate immunity, which following exposure, enables the development of an effective immune response preventing the development of overt clinical disease. So far, there is neither an effective vaccination nor a simple test which can predict susceptibility to the infection. A long history of ignorance and stigmatization may add a social dimension to the physical ailment and suffering of HD patients. Despite the elimination campaign declared by the WHO in the early 1990s, the disease continues to exist. New patients are diagnosed each year, though in lower numbers and HD patients can be found all over the world. The relatively low prevalence of HD in non-endemic countries and the misconception that it has been eradicated long ago, make the awareness to the disease extremely poor. HD is usually not included in the differential diagnosis even when clear symptoms are present. This results in a very late diagnosis of new HD patients, thus missing the window of opportunity for early treatment which could prevent complications and disability. The purpose of this update is to raise awareness to the existence of HD in Israel and its diagnosis, to present updated epidemiological data for Israel and a glimpse at the global situation.
Self-powered discrete time piezoelectric vibration damper
Konak, Michael J.; Powlesland, Ian G.; van der Velden, Stephen P.; Galea, Stephen C.
1997-11-01
Structural vibration suppression is of great interest to the aircraft industry as it can reduce the amplitude of excessive vibration in lightly damped panels caused by conditions in their operational environment. One technique of suppressing vibration is to use passive damping techniques such as constrained layered damping incorporating viscoelastic materials. However these techniques may not be acceptable because of weight concerns or extreme temperature variations. Over the past decade much work has been done by researchers on the use of piezoelectric ceramic devices, using passive and active techniques, for structural vibration suppression. The passive piezoelectric damping devices consist of a piezoelectric element and either a resistive or resonant shunt. The resonant circuit shunt, which is analogous to a mechanical vibration absorber, gives better vibration reduction compared to the resistor shunt. This device requires a large value of inductance in order to be tuned to a particular structural vibration mode. A large value inductor can be made by a using a gyrator type circuit however the circuit needs external power. A method of vibration control using a discrete time controller and piezoelectric devices is presented. That is, this paper describes the concept of a self-powered discrete time piezoelectric vibration damper which does not need tuning to the structural resonant frequency and is powered by piezoelectric elements, i.e. does not need an external power supply. This device is referred to as a strain amplitude minimization patch (STAMP) damper. A brief description of the theory used and of the scheme is presented. Also the operation of this device is compared with other 'passive' techniques, involving piezoelectric elements, such as the resistive passive damper and the parallel resonant passive damper cases. Experimental results presented, on a cantilevered beam, demonstrate the concept and show that the device, even in its current underdeveloped
Multiple Estimation Architecture in Discrete-Time Adaptive Mixing Control
Simone Baldi
2013-05-01
Full Text Available Adaptive mixing control (AMC is a recently developed control scheme for uncertain plants, where the control action coming from a bank of precomputed controller is mixed based on the parameter estimates generated by an on-line parameter estimator. Even if the stability of the control scheme, also in the presence of modeling errors and disturbances, has been shown analytically, its transient performance might be sensitive to the initial conditions of the parameter estimator. In particular, for some initial conditions, transient oscillations may not be acceptable in practical applications. In order to account for such a possible phenomenon and to improve the learning capability of the adaptive scheme, in this paper a new mixing architecture is developed, involving the use of parallel parameter estimators, or multi-estimators, each one working on a small subset of the uncertainty set. A supervisory logic, using performance signals based on the past and present estimation error, selects the parameter estimate to determine the mixing of the controllers. The stability and robustness properties of the resulting approach, referred to as multi-estimator adaptive mixing control (Multi-AMC, are analytically established. Besides, extensive simulations demonstrate that the scheme improves the transient performance of the original AMC with a single estimator. The control scheme and the analysis are carried out in a discrete-time framework, for easier implementation of the method in digital control.
Various Synchronization Phenomena in Discrete-Time Coupled Chaotic Rotors
Morino, K.; Horita, T.; Miyazaki, S.
2010-06-01
Various synchronizations and related phenomena in discrete-time coupled chaotic rotors are studied. For unidirectional and bidirectional couplings, various dynamical forms of chaotic phase synchronization (CPS) and their relation to the Lyapunov spectra are shown. For a small positive maximum Lyapunov exponent of the coupled element in the case of the unidirectional coupling, the coupling strength at which CPS is achieved almost coincides with the coupling strength at which generalized synchronization (GS) is achieved. On the other hand, for a large positive maximum Lyapunov exponent, the coupling strength is much smaller on the CPS transition point than on the GS transition point. Statistical properties of the phase difference are analytically and numerically studied by large-deviation analysis. On the basis of the grand canonical formalism, the fluctuation spectrum is theoretically derived, which is compared with the numerical results. These agree with the theoretical es timation, and large deviations are detected out of the domain in which the central limit theorem cannot be applied.
Maintaining information online in discrete time; rethinking working memory processes.
Stephane, Massoud
2012-06-21
Linguistic operations occur with verbal information maintained online for a discrete time. It is posited that online maintenance of information is accomplished by verbal working memory (WM), a system that is: (a) independent from the linguistic operations carried out with the information (specialized), and (b) consists of a holding place where information is held in a phonological code (phonological loop) and a rehearsal mechanism that refreshes the phonological loop. This model does not account for the serial position effects associated with information maintenance and additional models are needed to explain the latter effects, which leaves us with a disjointed understanding of online maintenance of information. In this study, 36 middle-aged, healthy subjects (33 males and 3 females) were required to maintain linguistic information (letters) online. The letters called upon different cognitive operations (orthographic; orthographic and phonetic; or orthographic, phonetic and semantic). It was found that online maintenance capacity depends on the cognitive operations associated with the letters and on their serial position. Additionally, the cognitive operation effect on online maintenance was modulated by the serial position. These data favor a model for WM consisting of a simple holding place where verbal information maintenance depends on what the information is used for. We will discuss an integrated model for online information maintenance that accounts for the serial position effects. Published by Elsevier Ireland Ltd.
A new approach to consensus problems in discrete-time multiagent systems with time-delays
WANG Long; XIAO Feng
2007-01-01
In this paper, consensus problems in discrete-time multiagent systems with timeinvariant delays are considered. In order to characterize the structures of communication topologies, the concept of "pre-leader-follower" decomposition is introduced.Then, a necessary and sufficient condition for state consensus is established. By this method, consensus problems in networks with a single time-delay, as well as with multiple time-delays, are studied, and some necessary and sufficient conditions for solvability of consensus problems are obtained.
DISCRETE VARIABLE STRUCTURE CONTROL OF LINEAR TIME-INVARIANT SYSTEMS WITH TIME DELAY
蔡国平; 黄金枝
2002-01-01
A discrete variable structure control(DVSC) method for the linear time-invariant systems with time delay was presented. The continuous time-delay systems are first transformed into the standard discrete form which contains no time delay by augmenting the state variables. Then the switching surface is determined by using the ideal quasi-sliding mode. As it is difficult for the state trajectory to reach the switching surface exactly, the reaching condition in the form of approach law is used to design the controller. The deduced switching surface and controller contain not only the current step of state feedback but also some former steps of controls. Stability analysis with and without time-delay information is also investigated in this paper. Numerical simulation was carried out to demonstrate the effectiveness and feasibility of the presented control method.
Nonlinear Maps for Design of Discrete-Time Models of Neuronal Network Dynamics
2016-03-31
responsive tiring patterns . We propose to use modern DSP ideas to develop new efficient approaches to the design of such discrete-time models for...2016 Performance/Technic~ 03-01-2016- 03-31-2016 4. TITLE AND SUBTITLE Sa. CONTRACT NUMBER Nonlinear Maps for Design of Discrete-Time Models of...simulations is to design a neuronal model in the form of difference equations that generates neuronal states in discrete moments of time. In this
RECONFIGURABLE CONTROL SYSTEM WITH DISCRETE-TIME CONTROLLERS
A. G. Strizhnev
2015-01-01
Full Text Available The paper considers a synthesis problem for automatic control systems, which operate in various modes, for example, tracking step-wise effects and slowly changing input signals. Generally, one controller cannot ensure the required qualitative characteristics in all operational modes. One of the methods to solve this problem is to create a reconfigurable control system. The authors propose a reconfigurable control system with two discrete-time controllers. The first one is placed in series with the forward path and the second one is connected in parallel with the reverse path having additional gain and unity feedback. Such system structure is characterized by its simplicity and qualitative operational ability to track step-wise and sinusoidal inputs with different amplitudes.The paper presents a developed block diagram of the reconfigurable system and describes its operational principle. Three various plants have been chosen with the purpose to check the operation of the system. Digital controllers have been selected and their parameters have been determined in accordance with the requirements to qualitative operational characteristics of the system. Mathematical modeling has been executed in order to check the operation of the proposed system with various plants and digital controllers. The modeling confirms good –speed performance of the automatic control system while tracking stepwise signals, provision of minimum dynamic error for the given controllers and time delay while tracking harmonic signals with various amplitudes. The obtained results have been successfully tested and can be used for development of automatic control systems that contain other plants and digital controllers, if there are various and occasionally contradictory requirements to their operational quality.
Adaptive Control and Function Projective Synchronization in 2D Discrete-Time Chaotic Systems
LI Yin; CHEN Yong; LI Biao
2009-01-01
This study addresses the adaptive control and function projective synchronization problems between 2D Rulkov discrete-time system and Network discrete-time system.Based on backstepping design with three controllers, a systematic, concrete and automatic scheme is developed to investigate the function projective synchronization of discrete-time chaotic systems.In addition, the adaptive control function is applied to achieve the state synchronization of two discrete-time systems.Numerical results demonstrate the effectiveness of the proposed control scheme.
Stability Analysis of Uncertain Discrete-Time Piecewise Linear Systems with Time Delays
Ou Ou; Hong-Bin Zhang; Jue-Bang Yu
2009-01-01
This paper considers the stability analysis of uncertain discrete-time piecewise linear systems with time delays based on piecewise Lyapunov-Krasovskii functionals. It is shown that the stability can be established for the control systems if there is a piecewise Lyapunov-Krasovskii functional, and moreover, the functional can be obtained by solving a set of linear matrix inequalities (LMIs) that are numerically feasible. A numerical example is given to demonstrate the efficiency and advantage of the proposed method.
Minimal and non-minimal optimal fixed-order compensators for time-varying discrete-time systems
Willigenburg, van L.G.; Koning, de W.L.
2002-01-01
The finite horizon optimal fixed-order LQG compensation problem for time-varying discrete-time systems is considered. Using the minimality property of finite horizon time-varying compensators, established in this paper, strengthened discrete-time optimal projection equations and associated boundary
Localization Operators and an Uncertainty Principle for the Discrete Short Time Fourier Transform
Carmen Fernández
2014-01-01
Full Text Available Localization operators in the discrete setting are used to obtain information on a signal f from the knowledge on the support of its short time Fourier transform. In particular, the extremal functions of the uncertainty principle for the discrete short time Fourier transform are characterized and their connection with functions that generate a time-frequency basis is studied.
Timing skills and expertise: discrete and continuous timed movements among musicians and athletes
Braun Janzen, Thenille; Thompson, William Forde; Ammirante, Paolo; Ranvaud, Ronald
2014-01-01
Introduction: Movement-based expertise relies on precise timing of movements and the capacity to predict the timing of events. Music performance involves discrete rhythmic actions that adhere to regular cycles of timed events, whereas many sports involve continuous movements that are not timed in a cyclical manner. It has been proposed that the precision of discrete movements relies on event timing (clock mechanism), whereas continuous movements are controlled by emergent timing. We examined whether movement-based expertise influences the timing mode adopted to maintain precise rhythmic actions. Materials and Method: Timing precision was evaluated in musicians, athletes and control participants. Discrete and continuous movements were assessed using finger-tapping and circle-drawing tasks, respectively, based on the synchronization-continuation paradigm. In Experiment 1, no auditory feedback was provided in the continuation phase of the trials, whereas in Experiment 2 every action triggered a feedback tone. Results: Analysis of precision in the continuation phase indicated that athletes performed significantly better than musicians and controls in the circle-drawing task, whereas musicians were more precise than controls in the finger tapping task. Interestingly, musicians were also more precise than controls in the circle-drawing task. Results also showed that the timing mode adopted was dependent on expertise and the presence of auditory feedback. Discussion: Results showed that movement-based expertise is associated with enhanced timing, but these effects depend on the nature of the training. Expertise was found to influence the timing strategy adopted to maintain precise rhythmic movements, suggesting that event and emergent timing mechanisms are not strictly tied to specific tasks, but can both be adopted to achieve precise timing. PMID:25566154
Timing skills and expertise: discrete and continuous timed movements among musicians and athletes
Thenille eBraun Janzen
2014-12-01
Full Text Available Introduction: Movement-based expertise relies on precise timing of movements and the capacity to predict the timing of events. Music performance involves discrete rhythmic actions that adhere to regular cycles of timed events, whereas many sports involve continuous movements that are not timed in a cyclical manner. It has been proposed that the precision of discrete movements relies on event timing (clock mechanism, whereas continuous movements are controlled by emergent timing. We examined whether movement-based expertise influences the timing mode adopted to maintain precise rhythmic actions. Materials and Method: Timing precision was evaluated in musicians, athletes and control participants. Discrete and continuous movements were assessed using finger-tapping and circle-drawing tasks, respectively, based on the synchronization-continuation paradigm. In Experiment 1, no auditory feedback was provided in the continuation phase of the trials, whereas in Experiment 2 every action triggered a feedback tone. Results: Analysis of precision in the continuation phase indicated that athletes performed significantly better than musicians and controls in the circle-drawing task, whereas musicians were more precise than controls in the finger tapping task. Interestingly, musicians were also more precise than controls in the circle-drawing task. Results also showed that the timing mode adopted was dependent on expertise and the presence of auditory feedback. Discussion: Results showed that movement-based expertise is associated with enhanced timing, but these effects depend on the nature of the training. Expertise was found to influence the timing strategy adopted to maintain precise rhythmic movements, suggesting that event and emergent timing mechanisms are not strictly tied to specific tasks, but can both be adopted to achieve precise timing.
Periodic Solutions of a Discrete Time Predator-Prey System
Yong-li Song; Mao-an Han
2006-01-01
In this paper, we discuss a discrete predator-prey system with a non-monotonic functional response,which models the dynamics of the prey and the predator having non-overlapping generations. By using the coincidence degree theory, sufficient conditions are obtained for the existence of positive periodic solutions.
Sensor Fault Estimation Filter Design for Discrete-time Linear Time-varying Systems
WANG Zhen-Hua; RODRIGUES Mickael; THEILLIOL Didier; SHEN Yi
2014-01-01
This paper proposes a sensor fault diagnosis method for a class of discrete-time linear time-varying (LTV) systems. In this paper, the considered system is firstly formulated as a de-scriptor system representation by considering the sensor faults as auxiliary state variables. Based on the descriptor system model, a fault estimation filter which can simultaneously estimate the state and the sensor fault magnitudes is designed via a minimum-variance principle. Then, a fault diagnosis scheme is presented by using a bank of the proposed fault estimation filters. The novelty of this paper lies in developing a sensor fault diagnosis method for discrete LTV systems without any assumption on the dynamic of fault. Another advantage of the proposed method is its ability to detect, isolate and estimate sensor faults in the presence of process noise and measurement noise. Simulation results are given to illustrate the effectiveness of the proposed method.
On the mixed discretization of the time domain magnetic field integral equation
Ulku, Huseyin Arda
2012-09-01
Time domain magnetic field integral equation (MFIE) is discretized using divergence-conforming Rao-Wilton-Glisson (RWG) and curl-conforming Buffa-Christiansen (BC) functions as spatial basis and testing functions, respectively. The resulting mixed discretization scheme, unlike the classical scheme which uses RWG functions as both basis and testing functions, is proper: Testing functions belong to dual space of the basis functions. Numerical results demonstrate that the marching on-in-time (MOT) solution of the mixed discretized MFIE yields more accurate results than that of classically discretized MFIE. © 2012 IEEE.
Kawano, Yu; Ohtsuka, Toshiyuki
2011-01-01
In this paper, we consider local observability at an initial state for discrete-time autonomous polynomial systems. When testing for observability, for discrete-time nonlinear systems, a condition based on the inverse function theorem is commonly used. However, it is a sufficient condition. In this
Discrete-time delayed standard neural network model and its application
无
2006-01-01
A novel neural network model, termed the discrete-time delayed standard neural network model (DDSNNM), and similar to the nominal model in linear robust control theory, is suggested to facilitate the stability analysis of discrete-time recurrent neural networks (RNNs) and to ease the synthesis of controllers for discrete-time nonlinear systems. The model is composed of a discrete-time linear dynamic system and a bounded static delayed (or non-delayed) nonlinear operator. By combining various Lyapunov functionals with the S-procedure, sufficient conditions for the global asymptotic stability and global exponential stability of the DDSNNM are derived, which are formulated as linear or nonlinear matrix inequalities. Most discrete-time delayed or non-delayed RNNs, or discrete-time neural-network-based nonlinear control systems can be transformed into the DDSNNMs for stability analysis and controller synthesis in a unified way. Two application examples are given where the DDSNNMs are employed to analyze the stability of the discrete-time cellular neural networks (CNNs) and to synthesize the neuro-controllers for the discrete-time nonlinear systems, respectively. Through these examples, it is demonstrated that the DDSNNM not only makes the stability analysis of the RNNs much easier, but also provides a new approach to the synthesis of the controllers for the nonlinear systems.
Controllability of Linear Discrete-Time Systems with Both Delayed States and Delayed Inputs
Hong Shi
2013-01-01
Full Text Available The controllability issues for discrete-time linear systems with delay in state and control are addressed. By introducing a new concept, the controllability realization index (CRI, the characteristic of controllability is revealed. An easily testable necessary and sufficient condition for the controllability of discrete-time linear systems with state and control delay is established.
Neural-network-based approximate output regulation of discrete-time nonlinear systems.
Lan, Weiyao; Huang, Jie
2007-07-01
The existing approaches to the discrete-time nonlinear output regulation problem rely on the offline solution of a set of mixed nonlinear functional equations known as discrete regulator equations. For complex nonlinear systems, it is difficult to solve the discrete regulator equations even approximately. Moreover, for systems with uncertainty, these approaches cannot offer a reliable solution. By combining the approximation capability of the feedforward neural networks (NNs) with an online parameter optimization mechanism, we develop an approach to solving the discrete nonlinear output regulation problem without solving the discrete regulator equations explicitly. The approach of this paper can be viewed as a discrete counterpart of our previous paper on approximately solving the continuous-time nonlinear output regulation problem.
Pablo Soto-Quiros
2015-01-01
Full Text Available This paper presents a parallel implementation of a kind of discrete Fourier transform (DFT: the vector-valued DFT. The vector-valued DFT is a novel tool to analyze the spectra of vector-valued discrete-time signals. This parallel implementation is developed in terms of a mathematical framework with a set of block matrix operations. These block matrix operations contribute to analysis, design, and implementation of parallel algorithms in multicore processors. In this work, an implementation and experimental investigation of the mathematical framework are performed using MATLAB with the Parallel Computing Toolbox. We found that there is advantage to use multicore processors and a parallel computing environment to minimize the high execution time. Additionally, speedup increases when the number of logical processors and length of the signal increase.
Huang Zhenkun [Department of Mathematics, School of Sciences, Zhejiang University, Hangzhou, Zhejiang 310027 (China) and School of Sciences, Jimei University, Xiamen, Fujian 361021 (China)]. E-mail: huangdoc@tom.com; Wang Xinghua [Department of Mathematics, School of Sciences, Zhejiang University, Hangzhou, Zhejiang 310027 (China); Gao Feng [School of Sciences, Jimei University, Xiamen, Fujian 361021 (China)
2006-02-06
In this Letter, we discuss discrete-time analogue of a continuous-time cellular neural network. Sufficient conditions are obtained for the existence of a unique almost periodic sequence solution which is globally attractive. Our results demonstrate dynamics of the formulated discrete-time analogue as mathematical models for the continuous-time cellular neural network in almost periodic case. Finally, a computer simulation illustrates the suitability of our discrete-time analogue as numerical algorithms in simulating the continuous-time cellular neural network conveniently.
Data-based controllability analysis of discrete-time linear time-delay systems
Liu, Yang; Chen, Hong-Wei; Lu, Jian-Quan
2014-11-01
In this paper, a data-based method is used to analyse the controllability of discrete-time linear time-delay systems. By this method, one can directly construct a controllability matrix using the measured state data without identifying system parameters. Hence, one can save time in practice and avoid corresponding identification errors. Moreover, its calculation precision is higher than some other traditional approaches, which need to identify unknown parameters. Our methods are feasible to the study of characteristics of deterministic systems. A numerical example is given to show the advantage of our results.
Stochastic dynamics of time correlation in complex systems with discrete time
Yulmetyev; Hanggi; Gafarov
2000-11-01
In this paper we present the concept of description of random processes in complex systems with discrete time. It involves the description of kinetics of discrete processes by means of the chain of finite-difference non-Markov equations for time correlation functions (TCFs). We have introduced the dynamic (time dependent) information Shannon entropy S(i)(t) where i=0,1,2,3,ellipsis, as an information measure of stochastic dynamics of time correlation (i=0) and time memory (i=1,2,3,ellipsis). The set of functions S(i)(t) constitute the quantitative measure of time correlation disorder (i=0) and time memory disorder (i=1,2,3,ellipsis) in complex system. The theory developed started from the careful analysis of time correlation involving dynamics of vectors set of various chaotic states. We examine two stochastic processes involving the creation and annihilation of time correlation (or time memory) in details. We carry out the analysis of vectors' dynamics employing finite-difference equations for random variables and the evolution operator describing their natural motion. The existence of TCF results in the construction of the set of projection operators by the usage of scalar product operation. Harnessing the infinite set of orthogonal dynamic random variables on a basis of Gram-Shmidt orthogonalization procedure tends to creation of infinite chain of finite-difference non-Markov kinetic equations for discrete TCFs and memory functions (MFs). The solution of the equations above thereof brings to the recurrence relations between the TCF and MF of senior and junior orders. This offers new opportunities for detecting the frequency spectra of power of entropy function S(i)(t) for time correlation (i=0) and time memory (i=1,2,3,ellipsis). The results obtained offer considerable scope for attack on stochastic dynamics of discrete random processes in a complex systems. Application of this technique on the analysis of stochastic dynamics of RR intervals from human ECG
The H-theorem for the physico-chemical kinetic equations with explicit time discretization
Adzhiev, S. Z.; Melikhov, I. V.; Vedenyapin, V. V.
2017-09-01
There is demonstrated in the present paper, that the H-theorem in the case of explicit time discretization of the physico-chemical kinetic equations, generally speaking, is not valid. We prove the H-theorem, when the system of the physico-chemical kinetic equations with explicit time discretization has the form of non-linear analogue of the Markov process with doubly stochastic matrix, and for more general cases. In these cases the proof is reduced to the proof of the H-theorem for Markov chains. The simplest discrete velocity models of the Boltzmann equation with explicit time discretization -the Carleman and Broadwell models are discussed and the H-theorem for them in the case of discrete time is proved.
Improved robustness and performance of discrete time sliding mode control systems.
Chakrabarty, Sohom; Bartoszewicz, Andrzej
2016-11-01
This paper presents a theoretical analysis along with simulations to show that increased robustness can be achieved for discrete time sliding mode control systems by choosing the sliding variable, or the output, to be of relative degree two instead of relative degree one. In other words it successfully reduces the ultimate bound of the sliding variable compared to the ultimate bound for standard discrete time sliding mode control systems. It is also found out that for such a selection of relative degree two output of the discrete time system, the reduced order system during sliding becomes finite time stable in absence of disturbance. With disturbance, it becomes finite time ultimately bounded.
A derivation of a microscopic entropy and time irreversibility from the discreteness of time
Riek, Roland
2014-01-01
All of the basic microsopic physical laws are time reversible. In contrast, the second law of thermodynamics, which is a macroscopic physical representation of the world, is able to describe irreversible processes in an isolated system through the change of entropy S larger than 0. It is the attempt of the present manuscript to bridge the microscopic physical world with its macrosocpic one with an alternative approach than the statistical mechanics theory of Gibbs and Boltzmann. It is proposed that time is discrete with constant step size. Its consequence is the presence of time irreversibility at the microscopic level if the present force is of complex nature (i.e. not const). In order to compare this discrete time irreversible mechamics (for simplicity a classical, single particle in a one dimensional space is selected) with its classical Newton analog, time reversibility is reintroduced by scaling the time steps for any given time step n by the variable sn leading to the Nose-Hoover Lagrangian. The corresp...
Real-Time Discrete SPAD Array Readout Architecture for Time of Flight PET
Tétrault, M -A; Boisvert, A; Thibaudeau, C; Dubois, F; Fontaine, R; Pratte, J -F
2014-01-01
Single photon avalanche diode (SPAD) arrays have proven themselves as serious candidates for time of flight positron emission tomography (PET). Discrete readout schemes mitigate the low-noise requirements of analog schemes and offer very fine control over threshold levels and timing pickup strategies. A high optical fill factor is paramount to timing performance in such detectors, and consequently space is limited for closely integrated electronics. Nonetheless, a production, daily used PET scanner must minimize bandwidth usage, data volume, data analysis time and power consumption and therefore requires a real-time readout and data processing architecture as close to the detector as possible. We propose a fully digital, embedded real-time readout architecture for SPAD-based detector. The readout circuit is located directly under the SPAD array instead of within or beside it to remove the fill factor versus circuit capabilities tradeoff. The overall real-time engine reduces transmitted data by a factor of 8 i...
Discrete time duration models with group-level heterogeneity
Frederiksen, Anders; Honoré, Bo; Hu, Loujia
2007-01-01
Dynamic discrete choice panel data models have received a great deal of attention. In those models, the dynamics is usually handled by including the lagged outcome as an explanatory variable. In this paper we consider an alternative model in which the dynamics is handled by using the duration...... in the current state as a covariate. We propose estimators that allow for group-specific effect in parametric and semiparametric versions of the model. The proposed method is illustrated by an empirical analysis of job durations allowing for firm-level effects....
Semi-Discretization for Time-Delay Systems
Insperger, Tamás
2011-01-01
This book presents the recently introduced and already widely referred semi-discretization method for the stability analysis of delayed dynamical systems. Delay differential equations often come up in different fields of engineering, like feedback control systems, machine tool vibrations, balancing/stabilization with reflex delay. The behavior of such systems is often counter-intuitive and closed form analytical formulas can rarely be given even for the linear stability conditions. If parametric excitation is coupled with the delay effect, then the governing equation is a delay differential eq
Chaos control in a discrete time system through asymmetric coupling
Rech, Paulo C. [Departamento de Fisica, Universidade do Estado de Santa Catarina, 89223-100 Joinville (Brazil)], E-mail: dfi2pcr@joinville.udesc.br
2008-06-09
We study a pair of asymmetrically coupled identical chaotic quadratic maps. We investigate, via numerical simulations, chaos suppression associated with the variation of both parameters, the coupling parameter and the parameter which measures the asymmetry. This is a new technique recently introduced for chaos suppression in continuous systems and, as far we know, not yet tested for discrete systems. Parameter-space regions where the chaotic dynamics is driven towards regular dynamics are shown. Lyapunov exponents and phase-space plots are also used to characterize the phenomenon observed as the parameters are changed.
Jørgensen, John Bagterp; Jørgensen, Sten Bay
2007-01-01
model is realized from a continuous-discrete-time linear stochastic system specified using transfer functions with time-delays. It is argued that the prediction-error criterion should be selected such that it is compatible with the objective function of the predictive controller in which the model......A Prediction-error-method tailored for model based predictive control is presented. The prediction-error method studied are based on predictions using the Kalman filter and Kalman predictors for a linear discrete-time stochastic state space model. The linear discrete-time stochastic state space...
A theory of Markovian time-inconsistent stochastic control in discrete time
Bjork, Tomas; Murgoci, Agatha
2014-01-01
We develop a theory for a general class of discrete-time stochastic control problems that, in various ways, are time-inconsistent in the sense that they do not admit a Bellman optimality principle. We attack these problems by viewing them within a game theoretic framework, and we look for subgame...... function. Most known examples of time-inconsistent stochastic control problems in the literature are easily seen to be special cases of the present theory. We also prove that for every time-inconsistent problem, there exists an associated time-consistent problem such that the optimal control...... and the optimal value function for the consistent problem coincide with the equilibrium control and value function, respectively for the time-inconsistent problem. To exemplify the theory, we study some concrete examples, such as hyperbolic discounting and mean–variance control....
Ocular manifestations of Hansen's disease.
Sekhar, G C; Vance, G; Otton, S; Kumar, S V; Stanley, J N; Rao, G N
1994-01-01
A detailed ophthalmic evaluation including slitlamp biomicroscopy, measurement of corneal sensitivity using Cochet and Bonnet aesthesiometer, Schirmer's test and Goldmann applanation tonometry was carried out in 89 patients of Hansen's disease attending the leprosy clinic with or without ocular symptoms and willing to undergo eye evaluation. Thirty-one patients had lepromatous leprosy (8 with erythema nodosum leprosum), 56 patients had borderline disease (13 with reversal reactions) and 2 had tuberculoid disease. In addition to the well documented changes of lagophthalmos (6.7%), uveitis (7.3%) and cataracts (19%), we noted prominent corneal nerves in 133 eyes (74.7%), beaded corneal nerves in 19 eyes (10.7%), corneal scarring in 10 eyes (5.6%), corneal hypoaesthesia in 51 eyes (28%) and dry eye in 18 eyes (13%). Beaded corneal nerves and/or stomal infiltrates occurred mainly in the lepromatous group (75%). Ocular hypotony (IOP less than 12 mm Hg) was not seen more frequently in Hansen's as compared to age and sex matched controls with refractive errors or cataracts (33.7%, vs. 37.8%, p = 0.33). Our study highlights the primary corneal involvement with corneal neuropathy as the predominant feature of Hansen's disease.
Computing the Discrete Fr\\'echet Distance in Subquadratic Time
Agarwal, Pankaj K; Kaplan, Haim; Sharir, Micha
2012-01-01
The Fr\\'echet distance is a similarity measure between two curves $A$ and $B$: Informally, it is the minimum length of a leash required to connect a dog, constrained to be on $A$, and its owner, constrained to be on $B$, as they walk without backtracking along their respective curves from one endpoint to the other. The advantage of this measure on other measures such as the Hausdorff distance is that it takes into account the ordering of the points along the curves. The discrete Fr\\'echet distance replaces the dog and its owner by a pair of frogs that can only reside on $n$ and $m$ specific pebbles on the curves $A$ and $B$, respectively. These frogs hop from a pebble to the next without backtracking. The discrete Fr\\'echet distance can be computed by a rather straightforward quadratic dynamic programming algorithm. However, despite a considerable amount of work on this problem and its variations, there is no subquadratic algorithm known, even for approximation versions of the problem. In this paper we presen...
Time-dependent switched discrete-time linear systems control and filtering
Zhang, Lixian; Shi, Peng; Lu, Qiugang
2016-01-01
This book focuses on the basic control and filtering synthesis problems for discrete-time switched linear systems under time-dependent switching signals. Chapter 1, as an introduction of the book, gives the backgrounds and motivations of switched systems, the definitions of the typical time-dependent switching signals, the differences and links to other types of systems with hybrid characteristics and a literature review mainly on the control and filtering for the underlying systems. By summarizing the multiple Lyapunov-like functions (MLFs) approach in which different requirements on comparisons of Lyapunov function values at switching instants, a series of methodologies are developed for the issues on stability and stabilization, and l2-gain performance or tube-based robustness for l∞ disturbance, respectively, in Chapters 2 and 3. Chapters 4 and 5 are devoted to the control and filtering problems for the time-dependent switched linear systems with either polytopic uncertainties or measurable time-varying...
Nguyen, Hoai-Nam
2014-01-01
A comprehensive development of interpolating control, this monograph demonstrates the reduced computational complexity of a ground-breaking technique compared with the established model predictive control. The text deals with the regulation problem for linear, time-invariant, discrete-time uncertain dynamical systems having polyhedral state and control constraints, with and without disturbances, and under state or output feedback. For output feedback a non-minimal state-space representation is used with old inputs and outputs as state variables. Constrained Control of Uncertain, Time-Varying, Discrete-time Systems details interpolating control in both its implicit and explicit forms. In the former at most two linear-programming or one quadratic-programming problem are solved on-line at each sampling instant to yield the value of the control variable. In the latter the control law is shown to be piecewise affine in the state, and so the state space is partitioned into polyhedral cells so that at each sampling ...
Universal fuzzy models and universal fuzzy controllers for discrete-time nonlinear systems.
Gao, Qing; Feng, Gang; Dong, Daoyi; Liu, Lu
2015-05-01
This paper investigates the problems of universal fuzzy model and universal fuzzy controller for discrete-time nonaffine nonlinear systems (NNSs). It is shown that a kind of generalized T-S fuzzy model is the universal fuzzy model for discrete-time NNSs satisfying a sufficient condition. The results on universal fuzzy controllers are presented for two classes of discrete-time stabilizable NNSs. Constructive procedures are provided to construct the model reference fuzzy controllers. The simulation example of an inverted pendulum is presented to illustrate the effectiveness and advantages of the proposed method. These results significantly extend the approach for potential applications in solving complex engineering problems.
Generalized computer-aided discrete time domain modeling and analysis of dc-dc converters
Lee, F. C.; Iwens, R. P.; Yu, Y.; Triner, J. E.
1977-01-01
A generalized discrete time domain modeling and analysis technique is presented for all types of switching regulators using any type of duty-cycle controller, and operating in both continuous and discontinuous inductor current. State space techniques are employed to derive an equivalent nonlinear discrete time model that describes the converter exactly. The system is linearized about its equilibrium state to obtain a linear discrete time model for small signal performance evaluations, such as stability, audiosusceptibility and transient response. The analysis makes extensive use of the digital computer as an analytical tool. It is universal, exact and easy to use.
Robust H∞ filtering for discrete-time impulsive systems with uncertainty
Sheng-tao PAN; Ji-tao SUN
2009-01-01
This paper investigates robust filter design for linear discrete-time impulsive systems with uncertainty under H∞ performance. First, an impulsive linear filter and a robust H∞ filtering problem are introduced for a discrete-time impulsive systems. Then,a sufficient condition of asymptotical stability and H∞ performance for the filtering error systems are provided by the discrete-time Lyapunov function method. The filter gains can be obtained by solving a set of linear matrix inequalities (LMIs). Finally, a numerical example is presented to show effectiveness of the obtained result.
Stability analysis of a general family of nonlinear positive discrete time-delay systems
Nam, P. T.; Phat, V. N.; Pathirana, P. N.; Trinh, H.
2016-07-01
In this paper, we propose a new approach to analyse the stability of a general family of nonlinear positive discrete time-delay systems. First, we introduce a new class of nonlinear positive discrete time-delay systems, which generalises some existing discrete time-delay systems. Second, through a new technique that relies on the comparison and mathematical induction method, we establish explicit criteria for stability and instability of the systems. Three numerical examples are given to illustrate the feasibility of the obtained results.
Dynamics of Uncertain Discrete-Time Neural Network with Delay and Impulses
Xuehui Mei
2015-01-01
Full Text Available The stability of discrete-time impulsive delay neural networks with and without uncertainty is investigated. First, by using Razumikhin-type theorem, a new less conservative condition for the exponential stability of discrete-time neural network with delay and impulse is proposed. Moreover, some new sufficient conditions are derived to guarantee the stability of uncertain discrete-time neural network with delay and impulse by using Lyapunov function and linear matrix inequality (LMI. Finally, several examples with numerical simulation are presented to demonstrate the effectiveness of the obtained results.
Delay-dependent stability analysis for discrete-time systems with time varying state delay
Stojanović Sreten B.
2011-01-01
Full Text Available The stability of discrete systems with time-varying delay is considered. Some sufficient delaydependent stability conditions are derived using an appropriate model transformation of the original system. The criteria are presented in the form of LMI, which are dependent on the minimum and maximum delay bounds. It is shown that the stability criteria are approximately the same conservative as the existing ones, but have much simpler mathematical form. The numerical example is presented to illustrate the applicability of the developed results.
Simple stability conditions of linear discrete time systems with multiple delay
Stojanović Sreten B.
2010-01-01
Full Text Available In this paper we have established a new Lyapunov-Krasovskii method for linear discrete time systems with multiple time delay. Based on this method, two sufficient conditions for delay-independent asymptotic stability of the linear discrete time systems with multiple delays are derived in the shape of Lyapunov inequality. Numerical examples are presented to demonstrate the applicability of the present approach.
A Derivation of a Microscopic Entropy and Time Irreversibility From the Discreteness of Time
Roland Riek
2014-06-01
Full Text Available The basic microsopic physical laws are time reversible. In contrast, the second law of thermodynamics, which is a macroscopic physical representation of the world, is able to describe irreversible processes in an isolated system through the change of entropy ΔS > 0. It is the attempt of the present manuscript to bridge the microscopic physical world with its macrosocpic one with an alternative approach than the statistical mechanics theory of Gibbs and Boltzmann. It is proposed that time is discrete with constant step size. Its consequence is the presence of time irreversibility at the microscopic level if the present force is of complex nature (F(r ≠ const. In order to compare this discrete time irreversible mechamics (for simplicity a “classical”, single particle in a one dimensional space is selected with its classical Newton analog, time reversibility is reintroduced by scaling the time steps for any given time step n by the variable sn leading to the Nosé-Hoover Lagrangian. The corresponding Nos´e-Hoover Hamiltonian comprises a term Ndf kB T ln sn (kB the Boltzmann constant, T the temperature, and Ndf the number of degrees of freedom which is defined as the microscopic entropy Sn at time point n multiplied by T. Upon ensemble averaging this microscopic entropy Sn in equilibrium for a system which does not have fast changing forces approximates its macroscopic counterpart known from thermodynamics. The presented derivation with the resulting analogy between the ensemble averaged microscopic entropy and its thermodynamic analog suggests that the original description of the entropy by Boltzmann and Gibbs is just an ensemble averaging of the time scaling variable sn which is in equilibrium close to 1, but that the entropy
Joint modeling of longitudinal data and discrete-time survival outcome.
Qiu, Feiyou; Stein, Catherine M; Elston, Robert C
2016-08-01
A predictive joint shared parameter model is proposed for discrete time-to-event and longitudinal data. A discrete survival model with frailty and a generalized linear mixed model for the longitudinal data are joined to predict the probability of events. This joint model focuses on predicting discrete time-to-event outcome, taking advantage of repeated measurements. We show that the probability of an event in a time window can be more precisely predicted by incorporating the longitudinal measurements. The model was investigated by comparison with a two-step model and a discrete-time survival model. Results from both a study on the occurrence of tuberculosis and simulated data show that the joint model is superior to the other models in discrimination ability, especially as the latent variables related to both survival times and the longitudinal measurements depart from 0.
Song, Haiyu; Yu, Li; Zhang, Dan; Zhang, Wen-An
2012-12-01
This paper is concerned with the finite-time quantized H∞ control problem for a class of discrete-time switched time-delay systems with time-varying exogenous disturbances. By using the sector bound approach and the average dwell time method, sufficient conditions are derived for the switched system to be finite-time bounded and ensure a prescribed H∞ disturbance attenuation level, and a mode-dependent quantized state feedback controller is designed by solving an optimization problem. Two illustrative examples are provided to demonstrate the effectiveness of the proposed theoretical results.
Parameter estimation for the subcritical Heston model based on discrete time observations
2014-01-01
We study asymptotic properties of some (essentially conditional least squares) parameter estimators for the subcritical Heston model based on discrete time observations derived from conditional least squares estimators of some modified parameters.
Dong, Lu; Zhong, Xiangnan; Sun, Changyin; He, Haibo
2016-04-08
This paper presents the design of a novel adaptive event-triggered control method based on the heuristic dynamic programming (HDP) technique for nonlinear discrete-time systems with unknown system dynamics. In the proposed method, the control law is only updated when the event-triggered condition is violated. Compared with the periodic updates in the traditional adaptive dynamic programming (ADP) control, the proposed method can reduce the computation and transmission cost. An actor-critic framework is used to learn the optimal event-triggered control law and the value function. Furthermore, a model network is designed to estimate the system state vector. The main contribution of this paper is to design a new trigger threshold for discrete-time systems. A detailed Lyapunov stability analysis shows that our proposed event-triggered controller can asymptotically stabilize the discrete-time systems. Finally, we test our method on two different discrete-time systems, and the simulation results are included.
Synchronization of High-order Discrete-time Linear Complex Networks with Time-varying Delays
HaiLong Li; JianXiang Xi; YaoQing Cao; DuoSheng Wu
2014-01-01
Synchronization of high-order discrete-time complex networks with undirected topologies is studied and the impacts of time delays are investigated. Firstly, by the state decomposition, synchronization problems are transformed into asymptotic stability ones of multiple lower dimensional time-delayed subsystems. Then, linear matrix inequality ( LMI) criteria for synchronization are given, which can guarantee the scalability of complex networks since they only include three LMI constraints independent of the number of agents. Moreover, an explicit expression of the synchronization function is presented, which can describe the synchronization behavior of all agents in complex networks. Finally, a numerical example is given to demonstrate the theoretical results, where it is shown that if the gain matrices of synchronization protocols satisfy LMI criteria for synchronization, synchronization can be achieved.
Stability Analysis and H∞ Model Reduction for Switched Discrete-Time Time-Delay Systems
Zheng-Fan Liu
2014-01-01
Full Text Available This paper is concerned with the problem of exponential stability and H∞ model reduction of a class of switched discrete-time systems with state time-varying delay. Some subsystems can be unstable. Based on the average dwell time technique and Lyapunov-Krasovskii functional (LKF approach, sufficient conditions for exponential stability with H∞ performance of such systems are derived in terms of linear matrix inequalities (LMIs. For the high-order systems, sufficient conditions for the existence of reduced-order model are derived in terms of LMIs. Moreover, the error system is guaranteed to be exponentially stable and an H∞ error performance is guaranteed. Numerical examples are also given to demonstrate the effectiveness and reduced conservatism of the obtained results.
A discrete-time queueing system with changes in the vacation times
Atencia Ivan
2016-06-01
Full Text Available This paper considers a discrete-time queueing system in which an arriving customer can decide to follow a last come first served (LCFS service discipline or to become a negative customer that eliminates the one at service, if any. After service completion, the server can opt for a vacation time or it can remain on duty. Changes in the vacation times as well as their associated distribution are thoroughly studied. An extensive analysis of the system is carried out and, using a probability generating function approach, steady-state performance measures such as the first moments of the busy period of the queue content and of customers delay are obtained. Finally, some numerical examples to show the influence of the parameters on several performance characteristics are given.
Analysis of Nonlinear Discrete Time Active Control System with Boring Chatter
Shujing Wu
2014-03-01
Full Text Available In this work we study the design and analysis for nonlinear discrete time active control system with boring charter. It is shown that most analysis result for continuous time nonlinear system can be extended to the discrete time case. In previous studies, a method of nonlinear Model Following Control System (MFCS was proposed by Okubo (1985. In this study, the method of nonlinear MFCS will be extended to nonlinear discrete time system with boring charter. Nonlinear systems which are dealt in this study have the property of norm constraints ║ƒ (v (k║&le&alpha+&betaβ║v (k║&gamma, where &alpha&ge0, &beta&ge0, 0&le&gamma&le1. When 0&le&gamma&le1. It is easy to extend the method to discrete time systems. But in the case &gamma = 1 discrete time systems, the proof becomes difficult. In this case, a new criterion is proposed to ensure that internal states are stable. We expect that this method will provide a useful tool in areas related to stability analysis and design for nonlinear discrete time systems as well.
Viability decision of linear discrete-time stochastic systems with probability criterion
Wansheng TANG; Jun ZHENG; Jianxiong ZHANG
2009-01-01
In this paper,the optimal viability decision problem of linear discrete-time stochastic systems with probability criterion is investigated.Under the condition of sequence-reachable discrete-time dynamic systems,the existence theorem of optimal viability strategy is given and the solving procedure of the optimal strategy is provided based on dynamic programming.A numerical example shows the effectiveness of the proposed methods.
A polynomial criterion for adaptive stabilizability of discrete-time nonlinear systems
Li, Chanying; Xie, Liang-Liang; Guo, Lei
2006-01-01
In this paper, we will investigate the maximum capability of adaptive feedback in stabilizing a basic class of discrete-time nonlinear systems with both multiple unknown parameters and bounded noises. We will present a complete proof of the polynomial criterion for feedback capability as stated in "Robust stability of discrete-time adaptive nonlinear control" (C. Li, L.-L. Xie. and L. Guo, IFAC World Congress, Prague, July 3-8, 2005), by providing both the necessity and sufficiency analyze...
An Audio Data Encryption with Single and Double Dimension Discrete-Time Chaotic Systems
AKGÜL, Akif; KAÇAR, Sezgin; Pehlivan, İhsan
2015-01-01
— In this article, a study on increasing security of audio data encryption with single and double dimension discrete-time chaotic systems was carried out and application and security analyses were executed. Audio data samples of both mono and stereo types were encrypted. In the application here, single and double dimension discrete-time chaotic systems were used. In order to enhance security during encryption, a different method was applied by also using a non-linear function. In the chaos ba...
BI-DIRECTIONAL COHEN-GROSSBERG NEURAL NETWORK WITH DISCRETE TIME
无
2009-01-01
Discrete-time version of the bi-directional Cohen-Grossberg neural network is stud-ied in this paper. Some sufficient conditions are obtained to ensure the global exponen-tial stability of such networks with discrete time based on Lyapunov method. These results do not require the symmetry of the connection matrix and the monotonicity, boundedness and differentiability of the activation function.
BI-DIRECTIONAL COHEN-GROSSBERG NEURAL NETWORK WITH DISCRETE TIME
Du Dejun; Chen Anping
2009-01-01
Discrete-time version of the bi-directional Cohen-Grossberg neural network is stu-died in this paper. Some sufficient conditions are obtained to ensure the global ex-ponential stability of such" networks with discrete time based on Lyapunov method. These results do not require the symmetry of the connection matrix and the monoto-nicity, boundedness and differentiability of the activation function.
A discrete-time Lagrangian network for solving constrained quadratic programs.
Tang, W S; Wang, J
2000-08-01
A discrete-time recurrent neural network which is called the discrete-time Lagrangian network is proposed in this letter for solving convex quadratic programs. It is developed based on the classical Lagrange optimization method and solves quadratic programs without using any penalty parameter. The condition for the neural network to globally converge to the optimal solution of the quadratic program is given. Simulation results are presented to illustrate its performance.
Function Projective Synchronization in Discrete-Time Chaotic System with Uncertain Parameters
CHEN Yong; LI Xin
2009-01-01
The function projective synchronization of discrete-time chaotic systems is presented. Based on backstep-ping design with three controllers, a systematic, concrete and automatic scheme is developed to investigate function projective synchronization (FPS) of discrete-time chaotic systems with uncertain parameters. With the aid of symbolic-numeric computation, we use the proposed scheme to illustrate FPS between two identical 3D Henon-like maps with uncertain parameters. Numeric simulations are used to verify the effectiveness of our scheme.
Fei Chen
2013-01-01
Full Text Available This paper deals with the finite-time stabilization problem for discrete-time Markov jump nonlinear systems with time delays and norm-bounded exogenous disturbance. The nonlinearities in different jump modes are parameterized by neural networks. Subsequently, a linear difference inclusion state space representation for a class of neural networks is established. Based on this, sufficient conditions are derived in terms of linear matrix inequalities to guarantee stochastic finite-time boundedness and stochastic finite-time stabilization of the closed-loop system. A numerical example is illustrated to verify the efficiency of the proposed technique.
Wang, Tong; Ding, Yongsheng; Zhang, Lei; Hao, Kuangrong
2016-08-01
This paper considered the synchronisation of continuous complex dynamical networks with discrete-time communications and delayed nodes. The nodes in the dynamical networks act in the continuous manner, while the communications between nodes are discrete-time; that is, they communicate with others only at discrete time instants. The communication intervals in communication period can be uncertain and variable. By using a piecewise Lyapunov-Krasovskii function to govern the characteristics of the discrete communication instants, we investigate the adaptive feedback synchronisation and a criterion is derived to guarantee the existence of the desired controllers. The globally exponential synchronisation can be achieved by the controllers under the updating laws. Finally, two numerical examples including globally coupled network and nearest-neighbour coupled networks are presented to demonstrate the validity and effectiveness of the proposed control scheme.
Attractors of relaxation discrete-time systems with chaotic dynamics on a fast time scale
Maslennikov, Oleg V.; Nekorkin, Vladimir I. [Institute of Applied Physics of RAS, Nizhny Novgorod (Russian Federation)
2016-07-15
In this work, a new type of relaxation systems is considered. Their prominent feature is that they comprise two distinct epochs, one is slow regular motion and another is fast chaotic motion. Unlike traditionally studied slow-fast systems that have smooth manifolds of slow motions in the phase space and fast trajectories between them, in this new type one observes, apart the same geometric objects, areas of transient chaos. Alternating periods of slow regular motions and fast chaotic ones as well as transitions between them result in a specific chaotic attractor with chaos on a fast time scale. We formulate basic properties of such attractors in the framework of discrete-time systems and consider several examples. Finally, we provide an important application of such systems, the neuronal electrical activity in the form of chaotic spike-burst oscillations.
Attractors of relaxation discrete-time systems with chaotic dynamics on a fast time scale.
Maslennikov, Oleg V; Nekorkin, Vladimir I
2016-07-01
In this work, a new type of relaxation systems is considered. Their prominent feature is that they comprise two distinct epochs, one is slow regular motion and another is fast chaotic motion. Unlike traditionally studied slow-fast systems that have smooth manifolds of slow motions in the phase space and fast trajectories between them, in this new type one observes, apart the same geometric objects, areas of transient chaos. Alternating periods of slow regular motions and fast chaotic ones as well as transitions between them result in a specific chaotic attractor with chaos on a fast time scale. We formulate basic properties of such attractors in the framework of discrete-time systems and consider several examples. Finally, we provide an important application of such systems, the neuronal electrical activity in the form of chaotic spike-burst oscillations.
On the controllability and observability of discrete-time linear time-delay systems
Liu, Yuan-Ming; Fong, I.-Kong
2012-04-01
This article studies the controllability and observability of discrete-time linear time-delay systems, so that the two properties can play a more fundamental role in system analysis before controller and observer design is engaged. Complete definitions of controllability and observability, which imply the stabilisability and detectability, respectively, and determine the feasibility of eigenvalue assignment, are proposed for systems with delays in both state variables and input/output signals. Necessary and sufficient criteria are developed to check the controllability and observability efficiently. The proofs are based on the equivalent expanded system, but the criteria only involve the delays and matrices of the same dimension as the original system. Finally, the duality between the suggested controllability and observability is presented.
Klebsiella ozaenae Septicemia Associated with Hansen's Disease
Murray, Katherine A.; Clements, Bruce H.; Keas, Stephen E.
1981-01-01
Two cases of Klebsiella ozaenae septicemia from the National Hansen's Disease Center, Carville, La., are discussed: one fatal and one nonfatal. Although both patients had nasal complications of Hansen's disease (leprosy), the organism was grown initially from spinal fluid, blood, and wound cultures. This report confirms the potential pathogenicity of the K. ozaenae species and its widening disease spectrum. PMID:7037843
STATISTICAL MECHANICS IN A DISCRETE SPACE-TIME. THERMODYNAMICS AND TIME-IRREVERSIBILITY
J.P.Badiali
2003-01-01
Full Text Available The introduction of a discrete space-time represents an attempt to describe the physics at the Planck's scale. We show that this concept can be also very useful in describing thermodynamics in a pre-relativistic world. From this concept a new approach of statistical mechanics based on a dynamic viewpoint and an entropy representation is presented. The entropy is connected with the counting of the paths in space-time. It contains a time interval that represents the time that we have to wait in order to relax the quantum fluctuations and to reach the thermal regime. It is shown that this time is β hbar. The mathematical expressions we derive for thermal quantities like the entropy and the free energy are identical to those obtained by the traditional path-integral formalism starting from the canonical form of the thermal density matrix. However, the introduction of a quantized space-time shows that thermodynamics is consistent with an equation of motion that is time-irreversible at a microscopic level. As a consequence, the problem of irreversibility is revisited and the derivation of a H-theorem becomes possible in the future.
Leader-follower Formation for Nonholonomic Mobile Robots: Discrete-time Approach
Raul Dali Cruz-Morales
2016-03-01
Full Text Available This paper presents a novel solution for the classical leader-follower formation problem considering the case of nonholonomic mobile robots. A formation control strategy is proposed in a discrete-time context by considering the exact discrete-time discretization of the non-linear continuous-time kinematic model of the vehicle. The geometric formation of the robots allows us to derive an alternative model that describes the time evolution of the relative distance and angle between the robots. These variables are obtained in real-time by a vision-based localization system on board, in which the follower robot is equipped with a Kinect device, together with a recognition board mounted on the leader robot. The boundedness of the relative position error is formally proven by considering a feedback law that is delayed by one sampling period of time. Numerical simulations and real-time experiments are presented to verify the performance of the control strategy.
STABILITY OF DISCRETE-TIME COHEN-GROSSBERG BAM NEURAL NETWORKS WITH DELAYS
无
2008-01-01
In this paper, we study the existence and stability of an equilibrium of discrete-time Cohen-Grossberg BAM Neural Networks with delays. We obtain several sufficient conditions ensuring the existence and stability of an equilibrium of such systems, using discrete Halanay-type inequality and vector Lyapunov methods. In addition, we show that the proposed sufficient condition is independent of the delay parameter. An example is given to demonstrate the effectiveness of the results obtained.
TAO Liang; LUO Bin
2005-01-01
An efficient algorithm for the representation and approximation of linear time-varying systems is presented via the fast real-valued discrete Gabor transform. Compared with the existing algorithm based on the traditional complex-valued discrete Gabor transform, the proposed algorithm runs faster, can more easily be implemented in software or hardware, and leads to a more compact representation. Simulation results are given for demonstration.
Introduction to fractional linear systems. Part 2: discrete-time case
Ortigueira, M.D.
2000-01-01
IEE Proceedings - Vision, Image, and Signal Processing, Vol. 147, nº 1 In the paper, the class of discrete linear systems is enlarged with the inclusion of discrete-time fractional linear systems. These are systems described by fractional difference equations and fractional frequency responses. It is shown how io compute the impulse response and transfer function. Fractal signals are introduced as output of special linear systems: fractional differaccumulators, systems that can be co...
Pilot-Wave Quantum Theory in Discrete Space and Time and the Principle of Least Action
Gluza, Janusz; Kosek, Jerzy
2016-11-01
The idea of obtaining a pilot-wave quantum theory on a lattice with discrete time is presented. The motion of quantum particles is described by a |Ψ |^2-distributed Markov chain. Stochastic matrices of the process are found by the discrete version of the least-action principle. Probability currents are the consequence of Hamilton's principle and the stochasticity of the Markov process is minimized. As an example, stochastic motion of single particles in a double-slit experiment is examined.
Subspace-based identification of discrete time-delay system
Qiang LIU; Jia-chen MA
2016-01-01
We investigate the identification problems of a class of linear stochastic time-delay systems with unknown delayed states in this study. A time-delay system is expressed as a delay differential equation with a single delay in the state vector. We first derive an equivalent linear time-invariant (LTI) system for the time-delay system using a state augmentation technique. Then a conventional subspace identification method is used to estimate augmented system matrices and Kalman state sequences up to a similarity transformation. To obtain a state-space model for the time-delay system, an alternate convex search (ACS) algorithm is presented to find a similarity transformation that takes the identified augmented system back to a form so that the time-delay system can be recovered. Finally, we reconstruct the Kalman state sequences based on the similarity transformation. The time-delay system matrices under the same state-space basis can be recovered from the Kalman state sequences and input-output data by solving two least squares problems. Numerical examples are to show the effectiveness of the proposed method.
H∞ State Feedback Delay-dependent Control for Discrete Systems with Multi-time-delay
Bai-Da Qu
2005-01-01
In this paper,H∞ state feedback control with delay information for discrete systems with multi-time-delay is discussed. Making use of linear matrix inequality (LMI) approach, a time-delay-dependent criterion for a discrete system with multi-time-delay to satisfy H∞ performance indices is induced, and then a strategy for H∞ state feedback control with delay values for plant with multi-time-delay is obtained. By solving corresponding LMI, a delay-dependent state feedback controller satisfying H∞ performance indices is designed. Finally, a simulation example demonstrates the validity of the proposed approach.
Discreteness of time in the evolution of the universe
Faizal, Mir; Ali, Ahmed Farag; Das, Saurya
2017-04-01
In this paper, we will first derive the Wheeler-DeWitt equation for the generalized geometry which occurs in M-theory. Then we will observe that M2-branes act as probes for this generalized geometry, and as M2-branes have an extended structure, their extended structure will limits the resolution to which this generalized geometry can be defined. We will demonstrate that this will deform the Wheeler-DeWitt equation for the generalized geometry. We analyze such a deformed Wheeler-DeWitt equation in the minisuperspace approximation, and observe that this deformation can be used as a solution to the problem of time. This is because this deformation gives rise to time crystals in our universe due to the spontaneous breaking of time reparametrization invariance.
When to be discrete: the importance of time formulation in understanding animal movement.
McClintock, Brett T; Johnson, Devin S; Hooten, Mevin B; Ver Hoef, Jay M; Morales, Juan M
2014-01-01
Animal movement is essential to our understanding of population dynamics, animal behavior, and the impacts of global change. Coupled with high-resolution biotelemetry data, exciting new inferences about animal movement have been facilitated by various specifications of contemporary models. These approaches differ, but most share common themes. One key distinction is whether the underlying movement process is conceptualized in discrete or continuous time. This is perhaps the greatest source of confusion among practitioners, both in terms of implementation and biological interpretation. In general, animal movement occurs in continuous time but we observe it at fixed discrete-time intervals. Thus, continuous time is conceptually and theoretically appealing, but in practice it is perhaps more intuitive to interpret movement in discrete intervals. With an emphasis on state-space models, we explore the differences and similarities between continuous and discrete versions of mechanistic movement models, establish some common terminology, and indicate under which circumstances one form might be preferred over another. Counter to the overly simplistic view that discrete- and continuous-time conceptualizations are merely different means to the same end, we present novel mathematical results revealing hitherto unappreciated consequences of model formulation on inferences about animal movement. Notably, the speed and direction of movement are intrinsically linked in current continuous-time random walk formulations, and this can have important implications when interpreting animal behavior. We illustrate these concepts in the context of state-space models with multiple movement behavior states using northern fur seal (Callorhinus ursinus) biotelemetry data.
Ratio limits and limiting conditional distributions for discrete-time birth-death processes
Doorn, van Erik A.; Schrijner, Pauline
1995-01-01
We consider discrete-time birth-death processes with an absorbing state and study the conditional state distribution at time n given that absorption has not occurred by that time but will occur eventually. In particular, we establish conditions for the convergence of these distributions to a proper
Sampled-data and discrete-time H2 optimal control
Trentelman, Harry L.; Stoorvogel, Anton A.
1993-01-01
This paper deals with the sampled-data H2 optimal control problem. Given a linear time-invariant continuous-time system, the problem of minimizing the H2 performance over all sampled-data controllers with a fixed sampling period can be reduced to a pure discrete-time H2 optimal control problem. This
Sampled-Data and Discrete-Time H2 Optimal Control
Trentelman, H.L.; Stoorvogel, A.A.
1995-01-01
This paper deals with the sampled-data H2 optimal control problem. Given a linear time-invariant continuous-time system, the problem of minimizing the H2 performance over all sampled-data controllers with a fixed sampling period can be reduced to a pure discrete-time H2 optimal control problem. This
A mean-variance frontier in discrete and continuous time
Bekker, Paul A.
2004-01-01
The paper presents a mean-variance frontier based on dynamic frictionless investment strategies in continuous time. The result applies to a finite number of risky assets whose price process is given by multivariate geometric Brownian motion with deterministically varying coefficients. The derivation
On the ?2-stability of time-varying linear and nonlinear discrete-time MIMO systems
Y.V.VENKATESH
2014-01-01
New conditions are derived for the 2-stability of time-varying linear and nonlinear discrete-time multiple-input multiple-output (MIMO) systems, having a linear time time-invariant block with the transfer function Γ(z), in negative feedback with a matrix of periodic/aperiodic gains A(k),k =0,1,2,. . . and a vector of certain classes of non-monotone/monotone nonlinearitiesϕ( · ), without restrictions on their slopes and also not requiring path-independence of their line integrals. The stability conditions, which are derived in the frequency domain, have the following features: i) They involve the positive definiteness of the real part (as evaluated on |z| = 1) of the product of Γ(z) and a matrix multiplier function of z. ii) For periodic A(k), one class of multiplier functions can be chosen so as to impose no constraint on the rate of variations A(k), but for aperiodic A(k), which allows a more general multiplier function, constraints are imposed on certain global averages of the generalized eigenvalues of (A(k+1),A(k)),k=1,2,. . . . iii) They are distinct from and less restrictive than recent results in the literature.
Stability analysis of extended discrete-time BAM neural networks based on LMI approach
无
2005-01-01
We propose a new approach for analyzing the global asymptotic stability of the extended discrete-time bidirectional associative memory (BAM) neural networks. By using the Euler rule, we discretize the continuous-time BAM neural networks as the extended discrete-time BAM neural networks with non-threshold activation functions. Here we present some conditions under which the neural networks have unique equilibrium points. To judge the global asymptotic stability of the equilibrium points, we introduce a new neural network model - standard neural network model (SNNM).For the SNNMs, we derive the sufficient conditions for the global asymptotic stability of the equilibrium points, which are formulated as some linear matrix inequalities (LMIs). We transform the discrete-time BAM into the SNNM and apply the general result about the SNNM to the determination of global asymptotic stability of the discrete-time BAM. The approach proposed extends the known stability results, has lower conservativeness, can be verified easily, and can also be applied to other forms of recurrent neural networks.
Psychosocial aspects of Hansen's disease (leprosy).
Singh, Gurvinder Pal
2012-09-01
In general, the prevalence of psychiatric disorders among people with Hansen's disease has greatly increased to date. However, inadequate psychiatric care of people with Hansen's disease is an area of increasing concern. Many studies have been conducted in India and abroad to find out the prevalence of comorbid psychiatric disorders in patients suffering from Hansen's disease. Although efforts have been made by the government and international organizations to solve the medical problems among this group of patients, this disease still carries a number of psychosocial issues. The social stigma connected to these patients makes this disease completely different from others. Even nowadays people affected by Hansen's disease have to leave their village and are socially isolated. Depression is the most common psychiatric disorder found in these patients. Early detection and treatment of psychiatric disorders among Hansen's disease patients is a powerful psychotherapeutic measure. Integrated healthcare strategy will be beneficial to these patients. A comprehensive MEDLINE search and review of relevant literature was carried out and the data extracted and studied with particular reference to psychosocial issues in Hansen's disease. The focus of this research work is related to psychiatric and social aspects vis-à-vis stigma in these patients with Hansen's disease.
Wei, Qinglai; Liu, Derong; Lin, Qiao
2016-08-03
In this paper, a novel local value iteration adaptive dynamic programming (ADP) algorithm is developed to solve infinite horizon optimal control problems for discrete-time nonlinear systems. The focuses of this paper are to study admissibility properties and the termination criteria of discrete-time local value iteration ADP algorithms. In the discrete-time local value iteration ADP algorithm, the iterative value functions and the iterative control laws are both updated in a given subset of the state space in each iteration, instead of the whole state space. For the first time, admissibility properties of iterative control laws are analyzed for the local value iteration ADP algorithm. New termination criteria are established, which terminate the iterative local ADP algorithm with an admissible approximate optimal control law. Finally, simulation results are given to illustrate the performance of the developed algorithm.
Control of discrete time systems based on recurrent Super-Twisting-like algorithm.
Salgado, I; Kamal, S; Bandyopadhyay, B; Chairez, I; Fridman, L
2016-09-01
Most of the research in sliding mode theory has been carried out to in continuous time to solve the estimation and control problems. However, in discrete time, the results in high order sliding modes have been less developed. In this paper, a discrete time super-twisting-like algorithm (DSTA) was proposed to solve the problems of control and state estimation. The stability proof was developed in terms of the discrete time Lyapunov approach and the linear matrix inequalities theory. The system trajectories were ultimately bounded inside a small region dependent on the sampling period. Simulation results tested the DSTA. The DSTA was applied as a controller for a Furuta pendulum and for a DC motor supplied by a DSTA signal differentiator.
Sequential Monte Carlo methods for nonlinear discrete-time filtering
Bruno, Marcelo GS
2013-01-01
In these notes, we introduce particle filtering as a recursive importance sampling method that approximates the minimum-mean-square-error (MMSE) estimate of a sequence of hidden state vectors in scenarios where the joint probability distribution of the states and the observations is non-Gaussian and, therefore, closed-form analytical expressions for the MMSE estimate are generally unavailable.We begin the notes with a review of Bayesian approaches to static (i.e., time-invariant) parameter estimation. In the sequel, we describe the solution to the problem of sequential state estimation in line
Reaching a consensus: a discrete nonlinear time-varying case
Saburov, M.; Saburov, K.
2016-07-01
In this paper, we have considered a nonlinear protocol for a structured time-varying and synchronous multi-agent system. By means of cubic triple stochastic matrices, we present an opinion sharing dynamics of the multi-agent system as a trajectory of a non-homogeneous system of cubic triple stochastic matrices. We show that the multi-agent system eventually reaches to a consensus if either of the following two conditions is satisfied: (1) every member of the group people has a positive subjective distribution on the given task after some revision steps or (2) all entries of some cubic triple stochastic matrix are positive.
Particle Swarm Based Approach of a Real-Time Discrete Neural Identifier for Linear Induction Motors
Alma Y. Alanis
2013-01-01
Full Text Available This paper focusses on a discrete-time neural identifier applied to a linear induction motor (LIM model, whose model is assumed to be unknown. This neural identifier is robust in presence of external and internal uncertainties. The proposed scheme is based on a discrete-time recurrent high-order neural network (RHONN trained with a novel algorithm based on extended Kalman filter (EKF and particle swarm optimization (PSO, using an online series-parallel con figuration. Real-time results are included in order to illustrate the applicability of the proposed scheme.
Discrete Time Optimal Adaptive Control for Linear Stochastic Systems
JIANG Rui; LUO Guiming
2007-01-01
The least-squares(LS)algorithm has been used for system modeling for a long time. Without any excitation conditions, only the convergence rate of the common LS algorithm can be obtained. This paper analyzed the weighted least-squares(WLS)algorithm and described the good properties of the WLS algorithm. The WLS algorithm was then used for daptive control of linear stochastic systems to show that the linear closed-loop system was globally stable and that the system identification was consistent. Compared to the past optimal adaptive controller,this controller does not impose restricted conditions on the coefficients of the system, such as knowing the first coefficient before the controller. Without any persistent excitation conditions, the analysis shows that, with the regulation of the adaptive control, the closed-loop system was globally stable and the adaptive controller converged to the one-step-ahead optimal controller in some sense.
Periodontal findings in patients with Hansen's disease.
Ranganathan, Aravindhan Thiruputkuzhi; Khalid, Waleed; Saraswathy, Ponnandai Krishnamurthy; Chandran, Chitraa Rama; Mahalingam, Lakshmiganthan
2014-09-01
To find out whether there are any relationship between leprosy and periodontitis as evidenced by clinical parameters. Fifteen diagnosed patients with Hansen's disease were selected and compared against 50 healthy individuals. Clinical parameters like probing pocket depth and clinical attachment level were evaluated for both the groups and the results were subjected to statistical analysis. Mean probing depth and attachment loss is seen more in patients with Hansen's disease than the healthy controls which are statistically significant. Patients with Hansen's disease tend to have more periodontal destruction than the healthy controls. Copyright © 2014 Hainan Medical College. Published by Elsevier B.V. All rights reserved.
Boundedness regions of discrete-time dynamic systems
Siljak, D.; Thaler, G. J.; Weissenberger, S.
1972-01-01
Techniques for obtaining quantitative information about boundedness properties are developed and applied to the sampled-data control of satellite attitude with quantization. Relevant stability concepts are introduced as a series of definitions, and interrelationships between various definitions are discussed. The boundedness regions are estimated by means of quadratic Liapunov functions, and a sufficient condition for the existence of a boundedness region is given for a certain class of systems. A quadratic Liapunov function is applied to the Lur'e-Postinkov class of systems, where the linear part of the system is not asymptotically stable and the quantizer represents the nonlinear characteristic. A numerical calculation of the region of boundedness estimates is performed for satellite attitude control and is compared with simulation results. It is tentatively concluded that the Liapunov results may be good and that simulation results may be difficult to interpret and time-consuming to generate. The Lur'e-based technique yields estimates of regions of absolute boundedness, but at the cost of greater analytical complexity.
Linear discrete-time Pareto-Nash-Stackelberg control problem and principles for its solving
Valeriu Ungureanu
2013-04-01
Full Text Available A direct-straightforward method for solving linear discrete-time optimal control problem is applied to solve control problem of a linear discrete-time system as a mixture of multi-criteria Stackelberg and Nash games. For simplicity, the exposure starts with the simplest case of linear discrete-time optimal control problem and, by sequential considering of more general cases, investigation finalizes with the highlighted Pareto-Nash-Stackelberg and set valued control problems. Different principles of solving are compared and their equivalence is proved. Mathematics Subject Classification 2010: 49K21, 49N05, 93C05, 93C55, 90C05, 90C29, 91A10, 91A20, 91A44, 91A50.
Li, Shaobao; Feng, Gang; Luo, Xiaoyuan; Guan, Xinping
2015-12-01
This paper investigates the output consensus problem of heterogeneous discrete-time multiagent systems with individual agents subject to structural uncertainties and different disturbances. A novel distributed control law based on internal reference models is first presented for output consensus of heterogeneous discrete-time multiagent systems without structural uncertainties, where internal reference models embedded in controllers are designed with the objective of reducing communication costs. Then based on the distributed internal reference models and the well-known internal model principle, a distributed control law is further presented for output consensus of heterogeneous discrete-time multiagent systems with structural uncertainties. It is shown in both cases that the consensus trajectory of the internal reference models determines the output trajectories of agents. Finally, numerical simulation results are provided to illustrate the effectiveness of the proposed control schemes.
Estimating Periodic Software Rejuvenation Schedules under Discrete-Time Operation Circumstance
Iwamoto, Kazuki; Dohi, Tadashi; Kaio, Naoto
Software rejuvenation is a preventive and proactive solution that is particularly useful for counteracting the phenomenon of software aging. In this article, we consider periodic software rejuvenation models based on the expected cost per unit time in the steady state under discrete-time operation circumstance. By applying the discrete renewal reward processes, we describe the stochastic behavior of a telecommunication billing application with a degradation mode, and determine the optimal periodic software rejuvenation schedule minimizing the expected cost. Similar to the earlier work by the same authors, we develop a statistically non-parametric algorithm to estimate the optimal software rejuvenation schedule, by applying the discrete total time on test concept. Numerical examples are presented to estimate the optimal software rejuvenation schedules from the simulation data. We discuss the asymptotic behavior of estimators developed in this paper.
Chellaboina Vijaysekhar
2005-01-01
Full Text Available We develop thermodynamic models for discrete-time large-scale dynamical systems. Specifically, using compartmental dynamical system theory, we develop energy flow models possessing energy conservation, energy equipartition, temperature equipartition, and entropy nonconservation principles for discrete-time, large-scale dynamical systems. Furthermore, we introduce a new and dual notion to entropy; namely, ectropy, as a measure of the tendency of a dynamical system to do useful work and grow more organized, and show that conservation of energy in an isolated thermodynamic system necessarily leads to nonconservation of ectropy and entropy. In addition, using the system ectropy as a Lyapunov function candidate, we show that our discrete-time, large-scale thermodynamic energy flow model has convergent trajectories to Lyapunov stable equilibria determined by the system initial subsystem energies.
U-D factorisation of the strengthened discrete-time optimal projection equations
Van Willigenburg, L. Gerard; De Koning, Willem L.
2016-04-01
Algorithms for optimal reduced-order dynamic output feedback control of linear discrete-time systems with white stochastic parameters are U-D factored in this paper. U-D factorisation enhances computational accuracy, stability and possibly efficiency. Since U-D factorisation of algorithms for optimal full-order output feedback controller design was recently published by us, this paper focusses on the U-D factorisation of the optimal oblique projection matrix that becomes part of the solution as a result of order-reduction. The equations producing the solution are known as the optimal projection equations which for discrete-time systems have been strengthened in the past. The U-D factored strengthened discrete-time optimal projection equations are presented in this paper by means of a transformation that has to be applied recursively until convergence. The U-D factored and conventional algorithms are compared through a series of examples.
Permitted and forbidden sets in discrete-time linear threshold recurrent neural networks.
Yi, Zhang; Zhang, Lei; Yu, Jiali; Tan, Kok Kiong
2009-06-01
The concepts of permitted and forbidden sets enable a new perspective of the memory in neural networks. Such concepts exhibit interesting dynamics in recurrent neural networks. This paper studies the basic theories of permitted and forbidden sets of the linear threshold discrete-time recurrent neural networks. The linear threshold transfer function has been regarded as an adequate transfer function for recurrent neural networks. Networks with this transfer function form a class of hybrid analog and digital networks which are especially useful for perceptual computations. Networks in discrete time can directly provide algorithms for efficient implementation in digital hardware. The main contribution of this paper is to establish foundations of permitted and forbidden sets. Necessary and sufficient conditions for the linear threshold discrete-time recurrent neural networks are obtained for complete convergence, existence of permitted and forbidden sets, as well as conditionally multiattractivity, respectively. Simulation studies explore some possible interesting practical applications.
Stabilization of nonlinear sandwich systems via state feedback-Discrete-time systems
Wang, Xu; Stoorvogel, Anton A.; Saberi, Ali; Grip, H°avard Fjær; Sannuti, Peddapullaiah
2011-01-01
A recent paper (IEEE Trans. Aut. Contr. 2010; 55(9):2156–2160) considered stabilization of a class of continuous-time nonlinear sandwich systems via state feedback. This paper is a discrete-time counterpart of it. The class of nonlinear sandwich systems consists of saturation elements sandwiched bet
More relaxed condition for dynamics of discrete time delayed Hopfield neural networks
Zhang Qiang
2008-01-01
The dynamics of discrete time delayed Hopfield neural networks is investigated.By using a difference inequality combining with the linear matrix inequality,a sufficient condition ensuring global exponential stability of the unique equilibrium point of the networks is found.The result obtained holds not only for constant delay but also for time-varying delays.
Densmore, Jeffery D [Los Alamos National Laboratory; Warsa, James S [Los Alamos National Laboratory; Lowrie, Robert B [Los Alamos National Laboratory; Morel, Jim E [TEXAS A& M UNIV
2008-01-01
The Fokker-Planck equation is a widely used approximation for modeling the Compton scattering of photons in high energy density applications. In this paper, we perform a stability analysis of three implicit time discretizations for the Compton-Scattering Fokker-Planck equation. Specifically, we examine (i) a Semi-Implicit (SI) scheme that employs backward-Euler differencing but evaluates temperature-dependent coefficients at their beginning-of-time-step values, (ii) a Fully Implicit (FI) discretization that instead evaluates temperature-dependent coefficients at their end-of-time-step values, and (iii) a Linearized Implicit (LI) scheme, which is developed by linearizing the temperature dependence of the FI discretization within each time step. Our stability analysis shows that the FI and LI schemes are unconditionally stable and cannot generate oscillatory solutions regardless of time-step size, whereas the SI discretization can suffer from instabilities and nonphysical oscillations for sufficiently large time steps. With the results of this analysis, we present time-step limits for the SI scheme that prevent undesirable behavior. We test the validity of our stability analysis and time-step limits with a set of numerical examples.
Single-experiment observability decomposition of discrete-time analytic systems
Kawano, Yu; Kotta, Ülle
2016-01-01
This paper addresses the single-experiment observability decomposition of discrete-time analytic systems. Unlike the continuous-time case, there exist systems which cannot be decomposed into observable and unobservable subsystems due to the fact that the observable space is not integrable. In this p
Local discrete cosine transformation domain Volterra prediction of chaotic time series
张家树; 李恒超; 肖先赐
2005-01-01
In this paper a local discrete cosine transformation (DCT) domain Volterra prediction method is proposed to predict chaotic time series, where the DCT is used to lessen the complexity of solving the coefficient matrix. Numerical simulation results show that the proposed prediction method can effectively predict chaotic time series and improve the prediction accuracy compared with the traditional local linear prediction methods.
The uniform measure for discrete-time quantum walks in one dimension
Konno, Norio
2013-01-01
We obtain the uniform measure as a stationary measure of the one-dimensional discrete-time quantum walks by solving the corresponding eigenvalue problem. As an application, the uniform probability measure on a finite interval at a time can be given.
A Model of Discrete-Continuum Time for a Simple Physical System
Karimov A. R.
2008-04-01
Full Text Available Proceeding from the assumption that the time flow of an individual object is a real physical value, in the framework of a physical kinetics approach we propose an analogy between time and temperature. The use of such an analogy makes it possible to work out a discrete-continuum model of time for a simple physical system. The possible physical properties of time for the single object and time for the whole system are discussed.
Ecological monitoring in a discrete-time prey-predator model.
Gámez, M; López, I; Rodríguez, C; Varga, Z; Garay, J
2017-09-21
The paper is aimed at the methodological development of ecological monitoring in discrete-time dynamic models. In earlier papers, in the framework of continuous-time models, we have shown how a systems-theoretical methodology can be applied to the monitoring of the state process of a system of interacting populations, also estimating certain abiotic environmental changes such as pollution, climatic or seasonal changes. In practice, however, there may be good reasons to use discrete-time models. (For instance, there may be discrete cycles in the development of the populations, or observations can be made only at discrete time steps.) Therefore the present paper is devoted to the development of the monitoring methodology in the framework of discrete-time models of population ecology. By monitoring we mean that, observing only certain component(s) of the system, we reconstruct the whole state process. This may be necessary, e.g., when in a complex ecosystem the observation of the densities of certain species is impossible, or too expensive. For the first presentation of the offered methodology, we have chosen a discrete-time version of the classical Lotka-Volterra prey-predator model. This is a minimal but not trivial system where the methodology can still be presented. We also show how this methodology can be applied to estimate the effect of an abiotic environmental change, using a component of the population system as an environmental indicator. Although this approach is illustrated in a simplest possible case, it can be easily extended to larger ecosystems with several interacting populations and different types of abiotic environmental effects. Copyright © 2017 Elsevier Ltd. All rights reserved.
Variable structure control with sliding mode prediction for discrete-time nonlinear systems
Lingfei XIAO; Hongye SU; Xiaoyu ZHANG; Jian CHU
2006-01-01
A new variable structure control algorithm based on sliding mode prediction for a class of discrete-time nonlinear systems is presented. By employing a special model to predict future sliding mode value, and combining feedback correction and receding horizon optimization methods which are extensively applied on predictive control strategy, a discrete-time variable structure control law is constructed. The closed-loop systems are proved to have robustness to uncertainties with unspecified boundaries. Numerical simulation and pendulum experiment results illustrate that the closed-loop systems possess desired performance, such as strong robustness, fast convergence and chattering elimination.
A Novel Analytic Technique for the Service Station Reliability in a Discrete-Time Repairable Queue
Renbin Liu
2013-01-01
Full Text Available This paper presents a decomposition technique for the service station reliability in a discrete-time repairable GeomX/G/1 queueing system, in which the server takes exhaustive service and multiple adaptive delayed vacation discipline. Using such a novel analytic technique, some important reliability indices and reliability relation equations of the service station are derived. Furthermore, the structures of the service station indices are also found. Finally, special cases and numerical examples validate the derived results and show that our analytic technique is applicable to reliability analysis of some complex discrete-time repairable bulk arrival queueing systems.
阮炯; 王军平; 郭德典
2004-01-01
In this paper, we first introduce the model of discrete-time neural networks with generalized input-output function and present a proof of the existence of a fixed point by Schauder fixed-point principle. Secondly, we study the uniformly asymptotical stability of equilibrium in non-autonomous discrete-time neural networks and give some sufficient conditions that guarantee the stability of it by using the converse theorem of Lyapunov function. Finally, several examples and numerical simulations are given to illustrate and reinforce our theories.
A discrete-time model for binary detection with rectangular hysteresis operators
Korman, Can E.
2006-02-01
The operation of a nonlinear binary detector with hysteresis is investigated. Prior models developed for continuous time inputs are extended for the computationally more efficient discrete-time inputs. The input to the rectangular hysteresis detector is modeled to be a binary signal in the presence of additive independent identically distributed noise. The rectangular hysteresis loop models one of a number of rate independent repeaters in an optical communication link. The link is terminated by a binary discriminator that is tuned to a particular bit duration. The study shows that key calculations to compute the bit error probability can be performed by employing the formalism of discrete Markov chains.
Hansen Solubility Parameters for Octahedral Oligomeric Silsesquioxanes
2012-08-28
and thermal and electrical insulation enhancers. The inorganic core is both mechanically robust, resistant to oxidation, and thermally stable, and...Choi, P.; Kavassalis, T. A.; Rudin, A. Estimation of Hansen Solubility Parameters for (Hydroxyethyl)- Cellulose and (Hydroxypropyl) Cellulose through
[Epidemiology of Hansen's disease in Israel].
Seidenbaum, M; Slater, P E; Ever-Hadani, P; Costin, C; Leviatan, A
1993-08-01
There are currently 200 patients with Hansen's disease in Israel who are being followed by the Hansen's Disease Government Hospital and the Ministry of Health (prevalence 4.4/100,000). Most of them immigrated from countries where the disease is endemic. Dermatological findings dominated the initial clinical picture, although 5% of patients are asymptomatic contacts of known cases. Age at onset of disease was less than 20 years in 1/4 of the cases. The incidence in Israel is falling: 0.4/100,000 in 1985-89 compared to 3.6/100,000 in 1950-54. Neurologic and dermatologic findings in an immigrant of any age originating from countries where Hansen's disease is endemic, should prompt appropriate diagnostic evaluation, even years after immigration to Israel. Contacts of known cases of Hansen's disease should be aggressively screened, even if asymptomatic.
Organogel formation rationalized by Hansen solubility parameters.
Raynal, Matthieu; Bouteiller, Laurent
2011-08-07
Some organic compounds gelate particular solvents by forming a network of anisotropic fibres. We show that Hansen solubility parameters can be used to predict the range of solvents that are likely to be gelled by any given gelator.
Ailing Qi; Xuewei Ju; Qing Zhang; Zengqiang Chen
2016-01-01
This paper is concerned with the structural controllability analysis for discrete-time linear control systems with time-delay. By adding virtual delay nodes, the linear systems with time-delay are transformed into corresponding linear systems without time-delay, and the structural controllability of them is equivalent. That is to say, the time-delay does not affect or change the controllability of the systems. Several examples are also presented to illustrate the theoretical results.
Effect of Velocity and Time-Step on the Continuity of a Discrete Moving Sound Image
Yoshikazu Seki
2014-01-01
Full Text Available As a basic study into 3-D audio display systems, this paper reports the conditions of moving sound image velocity and time-step where a discrete moving sound image is perceived as continuous motion. In this study, the discrete moving sound image was presented through headphones and ran along the ear-axis. The experiments tested the continuity of a discrete moving sound image using various conditions of velocity (0.25, 0.5, 0.75, 1, 2, 3, and 4 m/s and time-step (0, 0.02, 0.04, 0.06, 0.08, 0.10, 0.12, and 0.14 s. As a result, the following were required in order to present the discrete moving sound image as continuous movement. (1 The 3-D audio display system was required to complete the sound image presentation process, including head tracking and HRTF simulation, in a time shorter than 0.02 s, in order to present sound image movement at all velocities. (2 A processing time longer than 0.1 s was not acceptable. (3 If the 3-D audio display system only presented very slow movement (less than about 0.5 m/s, processing times ranging from 0.04 s to 0.06 s were still acceptable.
Synthesis of nonlinear discrete control systems via time-delay affine Takagi-Sugeno fuzzy models.
Chang, Wen-Jer; Chang, Wei
2005-04-01
The affine Takagi-Sugeno (TS) fuzzy model played a more important role in nonlinear control because it can be used to approximate the nonlinear systems more than the homogeneous TS fuzzy models. Besides, it is known that the time delays exist in physical systems and the previous works did not consider the time delay effects in the analysis of affine TS fuzzy models. Hence a parallel distributed compensation based fuzzy controller design issue for discrete time-delay affine TS fuzzy models is considered in this paper. The time-delay effect is considered in the discrete affine TS fuzzy models and the stabilization issue is developed for the nonlinear time-delay systems. Finally, a numerical simulation for a time-delayed nonlinear truck-trailer system is given to show the applications of the present approach.
Carpentier, Pierre; Cohen, Guy; De Lara, Michel
2015-01-01
The focus of the present volume is stochastic optimization of dynamical systems in discrete time where - by concentrating on the role of information regarding optimization problems - it discusses the related discretization issues. There is a growing need to tackle uncertainty in applications of optimization. For example the massive introduction of renewable energies in power systems challenges traditional ways to manage them. This book lays out basic and advanced tools to handle and numerically solve such problems and thereby is building a bridge between Stochastic Programming and Stochastic Control. It is intended for graduates readers and scholars in optimization or stochastic control, as well as engineers with a background in applied mathematics.
EXISTENCE OF PERIODIC SOLUTIONS FOR A DISCRETE-TIME MODEL OF TWO-CELL CNNS
无
2006-01-01
We investigate a class of discrete-time model of two-cell cellular neural networks with symmetric template. By using the Lyapunov direct method, La-Salle's invariance principle, we discuss the existence and the stability of periodic solutions. The model considered has attractive 2-periodic and unstable 2-periodic solutions.
A Note on the Mean-Variance Criteria for Discrete Time Financial Markets
Xin-hua Liu
2005-01-01
It was shown in Xia[3] that for incomplete markets with continuous assets' price processes and for complete markets the mean-variance portfolio selection can be viewed as expected utility maximization with non-negative marginal utility. In this paper we show that for discrete time incomplete markets this result is not true.
Oostveen, J
1996-01-01
In this paper we present results about the algebraic Riccati equation (ARE) and a weaker version of the ARE, the algebraic Riccati system (ARS), for infinite-dimensional, discrete-time systems. We introduce an operator pencil, associated with these equations, the so-called extended symplectic Pencil
ON THE ANISOTROPIC NORM OF DISCRETE TIME STOCHASTIC SYSTEMS WITH STATE DEPENDENT NOISE
Isaac Yaesh
2013-01-01
Full Text Available The purpose of this paper is to determine conditions for the bound-edness of the anisotropic norm of discrete-time linear stochastic sys-tems with state dependent noise. It is proved that these conditions canbe expressed in terms of the feasibility of a specific system of matrixinequalities.
Discrete-Time Mixing Receiver Architecture for RF-Sampling Software-Defined Radio
Ru, Z.; Klumperink, Eric A.M.; Nauta, Bram
2010-01-01
Abstract—A discrete-time (DT) mixing architecture for RF-sampling receivers is presented. This architecture makes RF sampling more suitable for software-defined radio (SDR) as it achieves wideband quadrature demodulation and wideband harmonic rejection. The paper consists of two parts. In the first
Linear quadratic Gaussian balancing for discrete-time infinite-dimensional linear systems
Opmeer, MR; Curtain, RF
2004-01-01
In this paper, we study the existence of linear quadratic Gaussian (LQG)-balanced realizations for discrete-time infinite-dimensional systems. LQG-balanced realizations are those for which the smallest nonnegative self-adjoint solutions of the control and filter Riccati equations are equal. We show
Modeling Repeatable Events Using Discrete-Time Data: Predicting Marital Dissolution
Teachman, Jay
2011-01-01
I join two methodologies by illustrating the application of multilevel modeling principles to hazard-rate models with an emphasis on procedures for discrete-time data that contain repeatable events. I demonstrate this application using data taken from the 1995 National Survey of Family Growth (NSFG) to ascertain the relationship between multiple…
Huang, David Y. C.; Murphy, Debra A.; Hser, Yih-Ing
2011-01-01
We used discrete-time survival mixture modeling to examine 5,305 adolescents from the 1997 National Longitudinal Survey of Youth regarding the impact of parental monitoring during early adolescence (ages 14-16) on initiation of sexual intercourse and problem behavior engagement (ages 14-23). Four distinctive parental-monitoring groups were…
A Lyapunov-Krasovskii methodology for asymptotic stability of discrete time delay systems
Stojanović Sreten B.
2007-01-01
Full Text Available This paper presents a Lyapunov-Krasovskii methodology for asymptotic stability of discrete time delay systems. Based on the methods, delay-independent stability condition is derived. A numerical example has been working out to show the applicability of results derived.
DISCRETE-TIME STOCHASTIC EQUILIBRIUM WITH INFINITE HORIZON INCOMPLETE ASSET MARKETS
ZhangShunming
2001-01-01
Abstract. This paper examines the existence of general equilibrium in a discrete time economywith the infinite horizon incomplete markets. There is a single good at each node in the eventtree. The existence of general equilibrium for the infinite horizon economy is proved by takinglimit of equilibria in truncated economies in which trade stops at a sequence of dates.
AN APPROACH TO DESIGN OBSERVER FOR A CLASS OF DISCRETE CONTROL SYSTEMS WITH TIME-DELAY
Xue Liu; Cunchen Gao
2009-01-01
The design of functional observer for a class of discrete systems with time-delay is concerned. The solution to Sylvester function is given. An improved method for the functional observer design is proposed by the condition of linear matrix inequality. In the end, an example is given to illustrate the feasibility of the method.
Tenreiro Machado, J. A.; Galhano, Alexandra M.; Oliveira, Anabela M.; Tar, József K.
2010-03-01
This study addresses the optimization of rational fraction approximations for the discrete-time calculation of fractional derivatives. The article starts by analyzing the standard techniques based on Taylor series and Padé expansions. In a second phase the paper re-evaluates the problem in an optimization perspective by tacking advantage of the flexibility of the genetic algorithms.
MINIMAL INVERSION AND ITS ALGORITHMS OF DISCRETE-TIME NONLINEAR SYSTEMS
ZHENG Yufan
2005-01-01
The left-inverse system with minimal order and its algorithms of discrete-time nonlinear systems are studied in a linear algebraic framework. The general structure of left-inverse system is described and computed in symbolic algorithm. Two algorithms are given for constructing left-inverse systems with minimal order.
Xinggui Liu
2011-01-01
Full Text Available In this paper, by using Mawhin's continuation theorem of coincidence degree theory, we establish the existence of at least four positive periodic solutions for a discrete time Lotka-Volterra competitive system with harvesting terms. An example is given to illustrate the effectiveness of our results.
Hick Samuelson Keynes Dynamic Economic Model with Discrete Time and Consumer Sentiment
Dobrescu, Loretti I.; Neamå#U, Mihaela; Opriş, Dumitru
The paper describes the Hick Samuelson Keynes dynamical economic model with discrete time and consumer sentiment. We seek to demonstrate that consumer sentiment may create fluctuations in the economical activities. The model possesses a flip bifurcation and a Neimark-Sacker bifurcation, after which the stable state is replaced by a (quasi-) periodic motion.
Design of nonlinear discrete-time controllers using a parameter space sampling procedure
Young, G. E.; Auslander, D. M.
1983-01-01
The design of nonlinear discrete-time controllers is investigated where the control algorithm assumes a special form. State-dependent control actions are obtained from tables whose values are the design parameters. A new design methodology capable of dealing with nonlinear systems containing parameter uncertainty is used to obtain the controller design. Various controller strategies are presented and illustrated through an example.
Outer-(J1,J2)-lossless factorizations of linear discrete time-varying systems
Yu, Xiaode; Scherpen, Jacqueline M.A.; Veen, Allejan van der; Dewilde, Patrick
1996-01-01
In this paper the outer-J-lossless factorization for linear discrete time-varying systems is treated. Lossless operators and its corresponding J-lossless chain-scattering operators are studied. Then the factorization is treated by first 'taking out' the anticausal part, and then considering the
Robust observer-based fault estimation and accommodation of discrete-time piecewise linear systems
Tabatabaeipour, Mojtaba; Bak, Thomas
2013-01-01
In this paper a new integrated observer-based fault estimation and accommodation strategy for discrete-time piecewise linear (PWL) systems subject to actuator faults is proposed. A robust estimator is designed to simultaneously estimate the state of the system and the actuator fault. Then, the es...
Optimizing the morphological design of discrete-time cellular neural networks
terBrugge, MH; Spaanenburg, L; Jansen, WJ; Nijhuis, JAG
1996-01-01
The morphological design of Discrete-Time Cellular Neural Networks (DTCNNs) has been presented in a companion paper [1]. DTCNN templates have been given for the elemental morphological operators. One way to obtain realizations for more complex operators is cascading the DTCNN equivalences of the
Tabatabaeipour, Seyed Mojtaba; Bak, Thomas
2012-01-01
In this paper we consider the problem of fault estimation and accommodation for discrete time piecewise linear systems. A robust fault estimator is designed to estimate the fault such that the estimation error converges to zero and H∞ performance of the fault estimation is minimized. Then...
Homogeneous Discrete Time Alternating Compound Renewal Process: A Disability Insurance Application
Guglielmo D’Amico
2015-01-01
Full Text Available Discrete time alternating renewal process is a very simple tool that permits solving many real life problems. This paper, after the presentation of this tool, introduces the compound environment in the alternating process giving a systematization to this important tool. The claim costs for a temporary disability insurance contract are presented. The algorithm and an example of application are also provided.
Outer-(J1,J2)-lossless factorizations of linear discrete time-varying systems
Yu, Xiaode; Scherpen, Jacqueline M.A.; Veen, Allejan van der; Dewilde, Patrick
1996-01-01
In this paper the outer-J-lossless factorization for linear discrete time-varying systems is treated. Lossless operators and its corresponding J-lossless chain-scattering operators are studied. Then the factorization is treated by first 'taking out' the anticausal part, and then considering the oute
The ruin probability of a discrete time risk model under constant interest rate with heavy tails
Tang, Q.
2004-01-01
This paper investigates the ultimate ruin probability of a discrete time risk model with a positive constant interest rate. Under the assumption that the gross loss of the company within one year is subexponentially distributed, a simple asymptotic relation for the ruin probability is derived and co
Long-time asymptotics for the defocusing integrable discrete nonlinear Schr\\"odinger equation
YAMANE, HIDESHI
2011-01-01
We investigate the long-time asymptotics for the defocusing integrable discrete nonlinear Schr\\"odinger equation by means of the Deift-Zhou nonlinear steepest descent method. The leading term is a sum of two terms that oscillate with decay of order $t^{-1/2}$.
Long-time asymptotics for the defocusing integrable discrete nonlinear Schrödinger equation
YAMANE, HIDESHI
2014-01-01
We investigate the long-time asymptotics for the defocusing integrable discrete nonlinear Schrödinger equation of Ablowitz-Ladik by means of the inverse scattering transform and the Deift-Zhou nonlinear steepest descent method. The leading part is a sum of two terms that oscillate with decay of order $t^{-1/2}$.
Statistical inference for discrete-time samples from affine stochastic delay differential equations
Küchler, Uwe; Sørensen, Michael
2013-01-01
Statistical inference for discrete time observations of an affine stochastic delay differential equation is considered. The main focus is on maximum pseudo-likelihood estimators, which are easy to calculate in practice. A more general class of prediction-based estimating functions is investigated...
On the Riccati Equations of the H∞ Control Problem for Discrete Time-Varying Systems
Verhaegen, Michel; Scherpen, Jacquelien M.A.; Benedetto, Maria Domenica Di; Bittanti, Sergio; Isidori, Alberto; Luca, Alessandro De; Mosca, Edoardo; Oriolo, Giuseppe
1995-01-01
In this paper we investigate the relationship between the different Riccati equations that appear in the H∞ control problem for linear discrete time-varying systems. Once we obtain this relation we can reformulate the conditions under which the H∞ output feedback problem is solvable. In contrary to
Modeling Repeatable Events Using Discrete-Time Data: Predicting Marital Dissolution
Teachman, Jay
2011-01-01
I join two methodologies by illustrating the application of multilevel modeling principles to hazard-rate models with an emphasis on procedures for discrete-time data that contain repeatable events. I demonstrate this application using data taken from the 1995 National Survey of Family Growth (NSFG) to ascertain the relationship between multiple…
Large-time behaviour of some fully discrete kinetic models in bounded domains
Ester Gabetta
1991-05-01
Full Text Available We investigate the large-time behaviour of the fully discretized version both of the three velocity Broadwell model and of the four velocity model in a strip. We analyze the different behaviours on the light of some recent results by M. Slemrod [7] and C. Cercignani [3].
Codimension-Two Bifurcation, Chaos and Control in a Discrete-Time Information Diffusion Model
Ren, Jingli; Yu, Liping
2016-07-01
In this paper, we present a discrete model to illustrate how two pieces of information interact with online social networks and investigate the dynamics of discrete-time information diffusion model in three types: reverse type, intervention type and mutualistic type. It is found that the model has orbits with period 2, 4, 6, 8, 12, 16, 20, 30, quasiperiodic orbit, and undergoes heteroclinic bifurcation near 1:2 point, a homoclinic structure near 1:3 resonance point and an invariant cycle bifurcated by period 4 orbit near 1:4 resonance point. Moreover, in order to regulate information diffusion process and information security, we give two control strategies, the hybrid control method and the feedback controller of polynomial functions, to control chaos, flip bifurcation, 1:2, 1:3 and 1:4 resonances, respectively, in the two-dimensional discrete system.
Robust H∞ control for discrete-time polytopic uncertain systems with linear fractional vertices
Shaosheng ZHOU; James LAM; Shengyuan XU
2004-01-01
The robust H∞ control problem for discrete-time uncertain systems is investigated in this paper. The uncertain systems are modelled as a polytopic type with linear fractional uncertainty in the vertices. A new linear matrix inequality (LMI) characterization of the H∞ performance for discrete systems is given by introducing a matrix slack variable which decouples the matrix of a Lyapunov function candidate and the parametric matrices of the system. This feature enables one to derive sufficient conditions for discrete uncertain systems by using parameter-dependent Lyapunov functions with less conservativeness. Based on the result, H∞ performance analysis and controller design are carried out. A numerical example is included to demonstrate the effectiveness of the proposed results.
Codimension-Two Bifurcation, Chaos and Control in a Discrete-Time Information Diffusion Model
Ren, Jingli; Yu, Liping
2016-12-01
In this paper, we present a discrete model to illustrate how two pieces of information interact with online social networks and investigate the dynamics of discrete-time information diffusion model in three types: reverse type, intervention type and mutualistic type. It is found that the model has orbits with period 2, 4, 6, 8, 12, 16, 20, 30, quasiperiodic orbit, and undergoes heteroclinic bifurcation near 1:2 point, a homoclinic structure near 1:3 resonance point and an invariant cycle bifurcated by period 4 orbit near 1:4 resonance point. Moreover, in order to regulate information diffusion process and information security, we give two control strategies, the hybrid control method and the feedback controller of polynomial functions, to control chaos, flip bifurcation, 1:2, 1:3 and 1:4 resonances, respectively, in the two-dimensional discrete system.
LIU MeiQin
2007-01-01
A novel model, termed the standard neural network model (SNNM), is advanced to describe some delayed (or non-delayed) discrete-time intelligent systems composed of neural networks and Takagi and Sugeno (T-S) fuzzy models. The SNNM is composed of a discrete-time linear dynamic system and a bounded static nonlinear operator. Based on the global asymptotic stability analysis of the SNNMs, linear and nonlinear dynamic output feedback controllers are designed for the SNNMs to stabilize the closed-loop systems, respectively. The control design equations are shown to be a set of linear matrix inequalities (LMIs) which can be easily solved by various convex optimization algorithms to determine the control signals. Most neural-network-based (or fuzzy) discrete-time intelligent systems with time delays or without time delays can be transformed into the SNNMs for controller synthesis in a unified way. Three application examples show that the SNNMs not only make controller synthesis of neural-network-based (or fuzzy) discrete-time intelligent systems much easier, but also provide a new approach to the synthesis of the controllers for the other type of nonlinear systems.
Robust passivity analysis for discrete-time recurrent neural networks with mixed delays
Huang, Chuan-Kuei; Shu, Yu-Jeng; Chang, Koan-Yuh; Shou, Ho-Nien; Lu, Chien-Yu
2015-02-01
This article considers the robust passivity analysis for a class of discrete-time recurrent neural networks (DRNNs) with mixed time-delays and uncertain parameters. The mixed time-delays that consist of both the discrete time-varying and distributed time-delays in a given range are presented, and the uncertain parameters are norm-bounded. The activation functions are assumed to be globally Lipschitz continuous. Based on new bounding technique and appropriate type of Lyapunov functional, a sufficient condition is investigated to guarantee the existence of the desired robust passivity condition for the DRNNs, which can be derived in terms of a family of linear matrix inequality (LMI). Some free-weighting matrices are introduced to reduce the conservatism of the criterion by using the bounding technique. A numerical example is given to illustrate the effectiveness and applicability.
Analysis of Phase-Type Stochastic Petri Nets With Discrete and Continuous Timing
Jones, Robert L.; Goode, Plesent W. (Technical Monitor)
2000-01-01
The Petri net formalism is useful in studying many discrete-state, discrete-event systems exhibiting concurrency, synchronization, and other complex behavior. As a bipartite graph, the net can conveniently capture salient aspects of the system. As a mathematical tool, the net can specify an analyzable state space. Indeed, one can reason about certain qualitative properties (from state occupancies) and how they arise (the sequence of events leading there). By introducing deterministic or random delays, the model is forced to sojourn in states some amount of time, giving rise to an underlying stochastic process, one that can be specified in a compact way and capable of providing quantitative, probabilistic measures. We formalize a new non-Markovian extension to the Petri net that captures both discrete and continuous timing in the same model. The approach affords efficient, stationary analysis in most cases and efficient transient analysis under certain restrictions. Moreover, this new formalism has the added benefit in modeling fidelity stemming from the simultaneous capture of discrete- and continuous-time events (as opposed to capturing only one and approximating the other). We show how the underlying stochastic process, which is non-Markovian, can be resolved into simpler Markovian problems that enjoy efficient solutions. Solution algorithms are provided that can be easily programmed.
Time-discrete higher order ALE formulations: a priori error analysis
Bonito, Andrea
2013-03-16
We derive optimal a priori error estimates for discontinuous Galerkin (dG) time discrete schemes of any order applied to an advection-diffusion model defined on moving domains and written in the Arbitrary Lagrangian Eulerian (ALE) framework. Our estimates hold without any restrictions on the time steps for dG with exact integration or Reynolds\\' quadrature. They involve a mild restriction on the time steps for the practical Runge-Kutta-Radau methods of any order. The key ingredients are the stability results shown earlier in Bonito et al. (Time-discrete higher order ALE formulations: stability, 2013) along with a novel ALE projection. Numerical experiments illustrate and complement our theoretical results. © 2013 Springer-Verlag Berlin Heidelberg.
Continuous-Time Discrete-Distribution Theory for Activity-Driven Networks
Zino, Lorenzo; Rizzo, Alessandro; Porfiri, Maurizio
2016-11-01
Activity-driven networks are a powerful paradigm to study epidemic spreading over time-varying networks. Despite significant advances, most of the current understanding relies on discrete-time computer simulations, in which each node is assigned an activity potential from a continuous distribution. Here, we establish a continuous-time discrete-distribution framework toward an analytical treatment of the epidemic spreading, from its onset to the endemic equilibrium. In the thermodynamic limit, we derive a nonlinear dynamical system to accurately model the epidemic spreading and leverage techniques from the fields of differential inclusions and adaptive estimation to inform short- and long-term predictions. We demonstrate our framework through the analysis of two real-world case studies, exemplifying different physical phenomena and time scales.
Robust admissibility and admissibilisation of uncertain discrete singular time-delay systems
Cui, Yukang; Lam, James; Feng, Zhiguang; Shen, Jun
2016-11-01
This paper is concerned with the characterisation of robust admissibility and admissibilisation for uncertain discrete-time singular system with interval time-varying delay. Considering the norm-bounded uncertainty and the interval time-varying delay, a new comparison model is introduced to transform the original singular system into two connected subsystems. After this transformation, a singular system without uncertainty and delay can be handled by the Lyapunov-Krasovskii functional method. By virtue of the scaled small gain theorem, an admissibility condition of the original singular system is proposed in terms of linear matrix inequalities. Moreover, the problem of robust admissibilisation of uncertain discrete singular time-varying system is also studied by iterative linear matrix inequality algorithm with initial condition optimisation. Several numerical examples are used to illustrate that the results are less conservative than existing ones.
Autonomous learning by simple dynamical systems with a discrete-time formulation
Bilen, Agustín M.; Kaluza, Pablo
2017-05-01
We present a discrete-time formulation for the autonomous learning conjecture. The main feature of this formulation is the possibility to apply the autonomous learning scheme to systems in which the errors with respect to target functions are not well-defined for all times. This restriction for the evaluation of functionality is a typical feature in systems that need a finite time interval to process a unit piece of information. We illustrate its application on an artificial neural network with feed-forward architecture for classification and a phase oscillator system with synchronization properties. The main characteristics of the discrete-time formulation are shown by constructing these systems with predefined functions.
Bürger, Raimund; Diehl, Stefan; Mejías, Camilo
2016-01-01
The main purpose of the recently introduced Bürger-Diehl simulation model for secondary settling tanks was to resolve spatial discretization problems when both hindered settling and the phenomena of compression and dispersion are included. Straightforward time integration unfortunately means long computational times. The next step in the development is to introduce and investigate time-integration methods for more efficient simulations, but where other aspects such as implementation complexity and robustness are equally considered. This is done for batch settling simulations. The key findings are partly a new time-discretization method and partly its comparison with other specially tailored and standard methods. Several advantages and disadvantages for each method are given. One conclusion is that the new linearly implicit method is easier to implement than another one (semi-implicit method), but less efficient based on two types of batch sedimentation tests.
Reliable gain-scheduled control of discrete-time systems and its application to CSTR model
Sakthivel, R.; Selvi, S.; Mathiyalagan, K.; Shi, Y.
2016-10-01
This paper is focused on reliable gain-scheduled controller design for a class of discrete-time systems with randomly occurring nonlinearities and actuator fault. Further, the nonlinearity in the system model is assumed to occur randomly according to a Bernoulli distribution with measurable time-varying probability in real time. The main purpose of this paper is to design a gain-scheduled controller by implementing a probability-dependent Lyapunov function and linear matrix inequality (LMI) approach such that the closed-loop discrete-time system is stochastically stable for all admissible randomly occurring nonlinearities. The existence conditions for the reliable controller is formulated in terms of LMI constraints. Finally, the proposed reliable gain-scheduled control scheme is applied on continuously stirred tank reactor model to demonstrate the effectiveness and applicability of the proposed design technique.
Zhou, Ji; Castellanos, Michelle
2013-01-01
Utilizing longitudinal data of 3477 students from 28 institutions, we examine the effects of structural diversity and quality of interracial relation on students' persistence towards graduation within six years. We utilize multilevel discrete-time survival analysis to account for the longitudinal persistence patterns as well as the nested…
G. Chesi
2013-01-01
This paper addresses the problem of establishing robust asymptotical stability of discrete-time systems affected by time-varying parametric uncertainty. Specifically, it is supposed that the coefficients of the system depend linearly on the uncertainty, and that the uncertainty is confined into a polytope. In the continuous-time case, the problem can be addressed by imposing that the system admits a common homogeneous polynomial Lyapunov function (HPLF) at the vertices of the polytope. Unfort...
HR approximation of FIR filters via discrete-time hybrid-domain vector fitting
2009-01-01
We present a discrete-time hybrid-domain vector fitting algorithm, called HD-VFz, for the HR approximation of FIR filters with an arbitrary combination of time- and frequency-sampled responses. The core routine involves a two-step pole refinement process based on a linear least-squares solve and an eigenvalue problem. Through hybrid-domain data approximation and digital partial fraction basis with relative stability consideration, HD-VFz exhibits fast computation and remarkable fitting accura...
Self-adjoint Time Operator is the Rule for Discrete Semibounded Hamiltonians
Galapon, E A
2002-01-01
We prove explicitly that to every discrete, semibounded Hamiltonian with constant degeneracy and with finite sum of the squares of the reciprocal of its eigenvalues and whose eigenvectors span the entire Hilbert space there exists a characteristic self-adjoint time operator which is canonically conjugate to the Hamiltonian in a dense subspace of the Hilbert space. Moreover, we show that each characteristic time operator generates an uncountable class of self- adjoint operators canonically conjugate with the same Hamiltonian.
Arbitrary Dimension Convection-Diffusion Schemes for Space-Time Discretizations
Bank, Randolph E. [Univ. of California, San Diego, CA (United States); Vassilevski, Panayot S. [Lawrence Livermore National Lab. (LLNL), Livermore, CA (United States); Zikatanov, Ludmil T. [Bulgarian Academy of Sciences, Sofia (Bulgaria)
2016-01-20
This note proposes embedding a time dependent PDE into a convection-diffusion type PDE (in one space dimension higher) with singularity, for which two discretization schemes, the classical streamline-diffusion and the EAFE (edge average finite element) one, are investigated in terms of stability and error analysis. The EAFE scheme, in particular, is extended to be arbitrary order which is of interest on its own. Numerical results, in combined space-time domain demonstrate the feasibility of the proposed approach.
Reconstruction of the modified discrete Langevin equation from persistent time series.
Czechowski, Zbigniew
2016-05-01
The discrete Langevin-type equation, which can describe persistent processes, was introduced. The procedure of reconstruction of the equation from time series was proposed and tested on synthetic data, with short and long-tail distributions, generated by different Langevin equations. Corrections due to the finite sampling rates were derived. For an exemplary meteorological time series, an appropriate Langevin equation, which constitutes a stochastic macroscopic model of the phenomenon, was reconstructed.
Su Weiwei; Chen Yiming
2008-01-01
Delay-dependent robust stability of cellular neural networks with time-varying discrete and distributed time-varying delays is considered. Based on Lyapunov stability theory and the linear matrix inequality (LMIs) technique, delay-dependent stability criteria are derived in terms of LMIs avoiding bounding certain cross terms, which often leads to conservatism. The effectiveness of the proposed stability criteria and the improvement over the existing results are illustrated in the numerical examples.
2000-01-01
We propose in this paper two methods to compute Markovian bounds for monotone functions of a discrete time homogeneous Markov chain evolving in a totally ordered state space. The main interest of such methods is to propose algorithms to simplify analysis of transient characteristics such as the output process of a queue, or sojourn time in a subset of states. Construction of bounds are based on two kinds of results: well-known results on stochastic comparison between Markov cha...
Restricted feedback control in discrete-time dynamical systems with memory
Workman, Kathryn G.; Zhao, Shuang; Cain, John W.
2014-04-01
When an equilibrium state of a physical or biological system suffers a loss of stability (e.g., via a bifurcation), it may be both possible and desirable to stabilize the equilibrium via closed-loop feedback control. Significant effort has been devoted towards using such control to prevent oscillatory or chaotic behavior in dynamical systems, both continuous-time and discrete-time. Regarding control in discrete-time systems, most prior attempts to stabilize unstable equilibria require that the system be perturbed once during each time step. However, there are examples of systems for which this is neither feasible nor possible. In this paper, we analyze a restricted feedback control method for discrete-time systems (restricted in the sense that the controller's perturbations may be applied only in every other time step). We apply our theoretical analysis to a specific example from cardiac electrophysiology in which this sort of restricted feedback control is especially relevant. The example is a useful test case for the theory, and one for which an experimental setup is rather straightforward.
Analysis of Streamline Separation at Infinity Using Time-Discrete Markov Chains.
Reich, W; Scheuermann, G
2012-12-01
Existing methods for analyzing separation of streamlines are often restricted to a finite time or a local area. In our paper we introduce a new method that complements them by allowing an infinite-time-evaluation of steady planar vector fields. Our algorithm unifies combinatorial and probabilistic methods and introduces the concept of separation in time-discrete Markov-Chains. We compute particle distributions instead of the streamlines of single particles. We encode the flow into a map and then into a transition matrix for each time direction. Finally, we compare the results of our grid-independent algorithm to the popular Finite-Time-Lyapunov-Exponents and discuss the discrepancies.
Observation of discrete time-crystalline order in a disordered dipolar many-body system
Choi, Soonwon; Landig, Renate; Kucsko, Georg; Zhou, Hengyun; Isoya, Junichi; Jelezko, Fedor; Onoda, Shinobu; Sumiya, Hitoshi; Khemani, Vedika; von Keyserlingk, Curt; Yao, Norman Y; Demler, Eugene; Lukin, Mikhail D
2016-01-01
Understanding quantum dynamics away from equilibrium is an outstanding challenge in the modern physical sciences. It is well known that out-of-equilibrium systems can display a rich array of phenomena, ranging from self-organized synchronization to dynamical phase transitions. More recently, advances in the controlled manipulation of isolated many-body systems have enabled detailed studies of non-equilibrium phases in strongly interacting quantum matter. As a particularly striking example, the interplay of periodic driving, disorder, and strong interactions has recently been predicted to result in exotic "time-crystalline" phases, which spontaneously break the discrete time-translation symmetry of the underlying drive. Here, we report the experimental observation of such discrete time-crystalline order in a driven, disordered ensemble of $\\sim 10^6$ dipolar spin impurities in diamond at room-temperature. We observe long-lived temporal correlations at integer multiples of the fundamental driving period, experi...
El-Amin, Mohamed F.
2017-06-06
Recently, applications of nanoparticles have been considered in many branches of petroleum engineering, especially, enhanced oil recovery. The current paper is devoted to investigate the problem of nanoparticles transport in fractured porous media, numerically. We employed the discrete-fracture model (DFM) to represent the flow and transport in the fractured formations. The system of the governing equations consists of the mass conservation law, Darcy\\'s law, nanoparticles concentration in water, deposited nanoparticles concentration on the pore-wall, and entrapped nanoparticles concentration in the pore-throat. The variation of porosity and permeability due to the nanoparticles deposition/entrapment on/in the pores is also considered. We employ the multiscale time-splitting strategy to control different time-step sizes for different physics, such as pressure and concentration. The cell-centered finite difference (CCFD) method is used for the spatial discretization. Numerical examples are provided to demonstrate the efficiency of the proposed multiscale time splitting approach.
Hu, Jin; Wang, Jun
2015-06-01
In recent years, complex-valued recurrent neural networks have been developed and analysed in-depth in view of that they have good modelling performance for some applications involving complex-valued elements. In implementing continuous-time dynamical systems for simulation or computational purposes, it is quite necessary to utilize a discrete-time model which is an analogue of the continuous-time system. In this paper, we analyse a discrete-time complex-valued recurrent neural network model and obtain the sufficient conditions on its global exponential periodicity and exponential stability. Simulation results of several numerical examples are delineated to illustrate the theoretical results and an application on associative memory is also given.
Robust Moving Horizon H∞ Control of Discrete Time-Delayed Systems with Interval Time-Varying Delays
F. Yıldız Tascikaraoglu
2014-01-01
Full Text Available In this study, design of a delay-dependent type moving horizon state-feedback control (MHHC is considered for a class of linear discrete-time system subject to time-varying state delays, norm-bounded uncertainties, and disturbances with bounded energies. The closed-loop robust stability and robust performance problems are considered to overcome the instability and poor disturbance rejection performance due to the existence of parametric uncertainties and time-delay appeared in the system dynamics. Utilizing a discrete-time Lyapunov-Krasovskii functional, some delay-dependent linear matrix inequality (LMI based conditions are provided. It is shown that if one can find a feasible solution set for these LMI conditions iteratively at each step of run-time, then we can construct a control law which guarantees the closed-loop asymptotic stability, maximum disturbance rejection performance, and closed-loop dissipativity in view of the actuator limitations. Two numerical examples with simulations on a nominal and uncertain discrete-time, time-delayed systems, are presented at the end, in order to demonstrate the efficiency of the proposed method.
Guangli Jiang; Leibo Liu; Wenping Zhu; Shouyi Yin; Shaojun Wei
2015-01-01
This paper proposes a real-time feature extraction VLSI architecture for high-resolution images based on the accelerated KAZE algorithm. Firstly, a new system architecture is proposed. It increases the system throughput, provides flexibility in image resolution, and offers trade-offs between speed and scaling robustness. The architecture consists of a two-dimensional pipeline array that fully utilizes computational similarities in octaves. Secondly, a substructure (block-serial discrete-time...
New Delay-Dependent Stability of Uncertain Discrete-Time Switched Systems with Time-Varying Delays
Liang Lin XIONG; Shou Ming ZHONG; Mao YE
2011-01-01
This paper deals with the issues of robust stability for uncertain discrete-time switched systems with mode-dependent time delays. Based on a novel difference inequality and a switched Lyapunov function, new delay-dependent stability criteria are formulated in terms of linear matrix inequalities (LMIs) which are not contained in known literature. A numerical example is given to demonstrate that the proposed criteria improves some existing results significantly with much less computational effort.
Delay-Dependent Exponential Stability for Discrete-Time BAM Neural Networks with Time-Varying Delays
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.
Multilayer discrete-time neural-net controller with guaranteed performance.
Jagannathan, S; Lewis, F L
1996-01-01
A family of novel multilayer discrete-time neural-net (NN) controllers is presented for the control of a class of multi-input multi-output (MIMO) dynamical systems. The neural net controller includes modified delta rule weight tuning and exhibits a learning while-functioning-features. The structure of the NN controller is derived using a filtered error/passivity approach. Linearity in the parameters is not required and certainty equivalence is not used. This overcomes several limitations of standard adaptive control. The notion of persistency of excitation (PE) for multilayer NN is defined and explored. New online improved tuning algorithms for discrete-time systems are derived, which are similar to sigma or epsilon-modification for the case of continuous-time systems, that include a modification to the learning rate parameter plus a correction term. These algorithms guarantee tracking as well as bounded NN weights in nonideal situations so that PE is not needed. An extension of these novel weight tuning updates to NN with an arbitrary number of hidden layers is discussed. The notions of discrete-time passive NN, dissipative NN, and robust NN are introduced. The NN makes the closed-loop system passive.
Riccati discrete time transfer matrix method for elastic beam undergoing large overall motion
He Bin [Sun Yat-sen University, College of Engineering (China)], E-mail: njhebin@gmail.com; Rui Xiaoting, E-mail: ruixt@163.net; Wang Guoping [Nanjing University of Science and Technology, Institute of Power Engineering (China)
2007-11-15
An efficient method for dynamics simulation for elastic beam with large overall spatial motion and nonlinear deformation, namely, the Riccati discrete time transfer matrix method (Riccati-DT-TMM), is proposed in this investigation. With finite segments, continuous deformation field of a beam can be decomposed into many rigid bodies connected by rotational springs. Discrete time transfer matrices of rigid bodies and rotational springs are used to analyze the dynamic characteristic of the beam, and the Riccati transform is used to improve the numerical stability of discrete time transfer matrix method of multibody system dynamics. A predictor-corrector method is used to improve the numerical accuracy of the Riccati-DT-TMM. Using the Riccati-DT-TMM in dynamics analysis, the global dynamics equations of the system are not needed and the computation time required increases linearly with the system's number of degrees of freedom. Three numerical examples are given to validate the method for the dynamic simulation of a geometric nonlinear beam undergoing large overall motion.
Chen, Yao; Ho, Daniel W C; Lü, Jinhu; Lin, Zongli
2016-01-01
Multiagent systems (MASs) are ubiquitous in our real world. There is an increasing attention focusing on the consensus (or synchronization) problem of MASs over the past decade. Although there are numerous results reported on the convergence of a discrete-time MAS based on the infinite products of matrices, few results are on the convergence rate. Because of the switching topology, the traditional eigenvalue analysis and the Lyapunov function methods are both invalid for the convergence rate analysis of an MAS with a switching topology. Therefore, the estimation of the convergence rate for a discrete-time MAS with time-varying delays remains a difficult problem. To overcome the essential difficulty of switching topology, this paper aims at developing a contractive-set approach to analyze the convergence rate of a discrete-time MAS in the presence of time-varying delays and generalized coupling coefficients. Using the proposed approach, we obtain an upper bound of the convergence rate under the condition of joint connectivity. In particular, the proposed method neither requires the nonnegative property of the coupling coefficients nor the basic assumption of a uniform lower bound for all positive coupling coefficients, which have been widely applied in the existing works on this topic. As an application of the main results, we will show that the classical Vicsek model with time delays can realize synchronization if the initial topology is connected.
He Jiang
2015-01-01
Full Text Available This paper deals with the output consensus regulation problem for discrete-time multiagent systems with state-unmeasurable agents and external disturbances under directed communication network topologies. Firstly, the mathematical model for the output consensus problem of discrete-time multiagent systems is deduced and formulated via making matrix transformation. Then, based on state observers, a novel output consensus protocol with dynamic compensator which is used as observer for the exosystem is proposed to solve this problem. Some knowledge of matrix theory and graph theory is introduced to design protocol parameters and the convergence of output consensus errors is proved. Finally, a numerical simulation example is shown to verify the effectiveness of the proposed protocol design.
LS-based discrete-time adaptive nonlinear control——Feasibility and limitations
郭雷; 魏晨Institute of Systems Science; Chinese Academy of Sciences; Beijing 100080; China
1996-01-01
Global stability and instability of a class of discrete-time adaptive nonlinear control systems are investigated.The systems to be controlled are assumed to be linear in unknown parameters but nonlinear in dynamics which are characterizEd by a nonlinear function f(x).It is shown that in the scalar parameter case,when the standard least-squares (LS) method is used in estimation,the certainty equivalence adaptive control is globally stable whenever f(x) has a growth rate |f(x)| =0(||x||b) with b<8.Moreover,in the case where b≥8,it is also shown that the dosed-loop adaptive control system does not have global stability in general.Both the results found and the new analytical methods introduced may be regarded as a basic step for further study of discrete-time adaptive nonlinear control systems.
A discrete-time chaos synchronization system for electronic locking devices
Minero-Ramales, G.; López-Mancilla, D.; Castañeda, Carlos E.; Huerta Cuellar, G.; Chiu Z., R.; Hugo García López, J.; Jaimes Reátegui, R.; Villafaña Rauda, E.; Posadas-Castillo, C.
2016-11-01
This paper presents a novel electronic locking key based on discrete-time chaos synchronization. Two Chen chaos generators are synchronized using the Model-Matching Approach, from non-linear control theory, in order to perform the encryption/decryption of the signal to be transmitted. A model/transmitter system is designed, generating a key of chaotic pulses in discrete-time. A plant/receiver system uses the above mentioned key to unlock the mechanism. Two alternative schemes to transmit the private chaotic key are proposed. The first one utilizes two transmission channels. One channel is used to encrypt the chaotic key and the other is used to achieve output synchronization. The second alternative uses only one transmission channel for obtaining synchronization and encryption of the chaotic key. In both cases, the private chaotic key is encrypted again with chaos to solve secure communication-related problems. The results obtained via simulations contribute to enhance the electronic locking devices.
Robust stability analysis of uncertain discrete-time systems with state delay
任正云; 张立群; 邵惠鹤
2004-01-01
The sufficient conditions of stability for uncertain discrete-time systems with state delay have been proposed by some researchers in the past few years, yet these results may be conservative in application. The stability analysis of these systems is discussed, and the necessary and sufficient condition of stability is derived by method other than constructing Lyapunov function and solving Riccati inequality. The root locations of system characteristic polynomial, which is obtained by augmentation approach and Laplace expansion, determine the stability of uncertain discrete-time systems with state delay, the system is stable if and only if all roots lie within the unit circle. In order to analyze robust stability of system characteristic polynomial effectively, Kharitonov theorem and edge theorem are applied. Example shows the practicability of these methods.
H∞ output tracking control of discrete-time nonlinear systems via standard neural network models.
Liu, Meiqin; Zhang, Senlin; Chen, Haiyang; Sheng, Weihua
2014-10-01
This brief proposes an output tracking control for a class of discrete-time nonlinear systems with disturbances. A standard neural network model is used to represent discrete-time nonlinear systems whose nonlinearity satisfies the sector conditions. H∞ control performance for the closed-loop system including the standard neural network model, the reference model, and state feedback controller is analyzed using Lyapunov-Krasovskii stability theorem and linear matrix inequality (LMI) approach. The H∞ controller, of which the parameters are obtained by solving LMIs, guarantees that the output of the closed-loop system closely tracks the output of a given reference model well, and reduces the influence of disturbances on the tracking error. Three numerical examples are provided to show the effectiveness of the proposed H∞ output tracking design approach.
Engineering Stable Discrete-Time Quantum Dynamics via a Canonical QR Decomposition
Bolognani, Saverio
2009-01-01
We analyze the asymptotic behavior of discrete-time, Markovian quantum systems with respect to a subspace of interest. Global asymptotic stability of subspaces is relevant to quantum information processing, in particular for initializing the system in pure states or subspace codes. We provide a linear-algebraic characterization of the dynamical properties leading to invariance and attractivity of a given quantum subspace. We then construct a design algorithm for discrete-time feedback control that allows to stabilize a target subspace, proving that if the control problem is feasible, then the algorithm returns an effective control choice. In order to prove this result, a canonical QR matrix decomposition is derived, and also used to establish the control scheme potential for the simulation of open-system dynamics.
Frequency Weighted Model Order Reduction Technique and Error Bounds for Discrete Time Systems
Muhammad Imran
2014-01-01
for whole frequency range. However, certain applications (like controller reduction require frequency weighted approximation, which introduce the concept of using frequency weights in model reduction techniques. Limitations of some existing frequency weighted model reduction techniques include lack of stability of reduced order models (for two sided weighting case and frequency response error bounds. A new frequency weighted technique for balanced model reduction for discrete time systems is proposed. The proposed technique guarantees stable reduced order models even for the case when two sided weightings are present. Efficient technique for frequency weighted Gramians is also proposed. Results are compared with other existing frequency weighted model reduction techniques for discrete time systems. Moreover, the proposed technique yields frequency response error bounds.
Robust exponential stability analysis of a larger class of discrete-time recurrent neural networks
无
2007-01-01
The robust exponential stability of a larger class of discrete-time recurrent neural networks (RNNs) is explored in this paper. A novel neural network model, named standard neural network model (SNNM), is introduced to provide a general framework for stability analysis of RNNs. Most of the existing RNNs can be transformed into SNNMs to be analyzed in a unified way.Applying Lyapunov stability theory method and S-Procedure technique, two useful criteria of robust exponential stability for the discrete-time SNNMs are derived. The conditions presented are formulated as linear matrix inequalities (LMIs) to be easily solved using existing efficient convex optimization techniques. An example is presented to demonstrate the transformation procedure and the effectiveness of the results.
Dynamic Tracking with Zero Variation and Disturbance Rejection Applied to Discrete-Time Systems
Renato de Aguiar Teixeira Mendes
2010-01-01
Full Text Available The problem of signal tracking in discrete linear time invariant systems, in the presence of a disturbance signal in the plant, is solved using a new zero-variation methodology. A discrete-time dynamic output feedback controller is designed in order to minimize the H∞ norm between the exogen input and the output signal of the system, such that the effect of the disturbance is attenuated. Then, the zeros modification is used to minimize the H∞ norm from the reference input signal to the error signal. The error is taken as the difference between the reference and the output signal. The proposed design is formulated in linear matrix inequalities (LMIs framework, such that the optimal solution of the stated problem is obtained. The method can be applied to plants with delay. The control of a delayed system illustrates the effectiveness of the proposed method.
Stability analysis of discrete-time BAM neural networks based on standard neural network models
ZHANG Sen-lin; LIU Mei-qin
2005-01-01
To facilitate stability analysis of discrete-time bidirectional associative memory (BAM) neural networks, they were converted into novel neural network models, termed standard neural network models (SNNMs), which interconnect linear dynamic systems and bounded static nonlinear operators. By combining a number of different Lyapunov functionals with S-procedure, some useful criteria of global asymptotic stability and global exponential stability of the equilibrium points of SNNMs were derived. These stability conditions were formulated as linear matrix inequalities (LMIs). So global stability of the discrete-time BAM neural networks could be analyzed by using the stability results of the SNNMs. Compared to the existing stability analysis methods, the proposed approach is easy to implement, less conservative, and is applicable to other recurrent neural networks.
Bifurcation Analysis and Chaos Control in a Discrete-Time Parasite-Host Model
Xueli Chen
2017-01-01
Full Text Available A discrete-time parasite-host system with bifurcation is investigated in detail in this paper. The existence and stability of nonnegative fixed points are explored and the conditions for the existence of flip bifurcation and Neimark-Sacker bifurcation are derived by using the center manifold theorem and bifurcation theory. And we also prove the chaos in the sense of Marotto. The numerical simulations not only illustrate the consistence with the theoretical analysis, but also exhibit other complex dynamical behaviors, such as bifurcation diagrams, Maximum Lyapunov exponents, and phase portraits. More specifically, when the integral step size is chosen as a bifurcation parameter, this paper presents the finding of period orbits, attracting invariant cycles and chaotic attractors of the discrete-time parasite-host system. Specifically, we have stabilized the chaotic orbits at an unstable fixed point by using the feedback control method.
A simple method of chaos control for a class of chaotic discrete-time systems
Jiang Guoping E-mail: jianggp@njupt.edu.cn; Zheng Weixing E-mail: w.zheng@uws.edu.au
2005-02-01
In this paper, a simple method is proposed for chaos control for a class of discrete-time chaotic systems. The proposed method is built upon the state feedback control and the characteristic of ergodicity of chaos. The feedback gain matrix of the controller is designed using a simple criterion, so that control parameters can be selected via the pole placement technique of linear control theory. The new controller has a feature that it only uses the state variable for control and does not require the target equilibrium point in the feedback path. Moreover, the proposed control method cannot only overcome the so-called 'odd eigenvalues number limitation' of delayed feedback control, but also control the chaotic systems to the specified equilibrium points. The effectiveness of the proposed method is demonstrated by a two-dimensional discrete-time chaotic system.
Shih-Wei Lin
2014-01-01
Full Text Available Berth allocation is the forefront operation performed when ships arrive at a port and is a critical task in container port optimization. Minimizing the time ships spend at berths constitutes an important objective of berth allocation problems. This study focuses on the discrete dynamic berth allocation problem (discrete DBAP, which aims to minimize total service time, and proposes an iterated greedy (IG algorithm to solve it. The proposed IG algorithm is tested on three benchmark problem sets. Experimental results show that the proposed IG algorithm can obtain optimal solutions for all test instances of the first and second problem sets and outperforms the best-known solutions for 35 out of 90 test instances of the third problem set.
Lin, Shih-Wei; Ying, Kuo-Ching; Wan, Shu-Yen
2014-01-01
Berth allocation is the forefront operation performed when ships arrive at a port and is a critical task in container port optimization. Minimizing the time ships spend at berths constitutes an important objective of berth allocation problems. This study focuses on the discrete dynamic berth allocation problem (discrete DBAP), which aims to minimize total service time, and proposes an iterated greedy (IG) algorithm to solve it. The proposed IG algorithm is tested on three benchmark problem sets. Experimental results show that the proposed IG algorithm can obtain optimal solutions for all test instances of the first and second problem sets and outperforms the best-known solutions for 35 out of 90 test instances of the third problem set.
Chaos communication based on synchronization of discrete-time chaotic systems
Lu Jun-Guo; Xi Yu-Geng
2005-01-01
A novel chaos communication method is proposed based on synchronization of discrete-time chaotic systems. This method uses a full-order state observer to achieve synchronization and secure communication between the transmitter and the receiver. Further, we present a multiple-access chaotic digital communication method by combining the observer with the on-line least square method. Simulation results are also given for illustration.
Dissipativity analysis for discrete singular systems with time-varying delay.
Feng, Zhiguang; Li, Wenxing; Lam, James
2016-09-01
In this paper, the issue of dissipativity analysis for discrete singular systems with time-varying delay is investigated. By using a recently developed inequality, which is less conservative than the Jensen inequality, and the improved reciprocally convex combination approach, sufficient criteria are established to guarantee the admissibility and dissipativity of the considered system. Moreover, H∞ performance characterization and passivity analysis are carried out. Numerical examples are presented to illustrate the effectiveness of the proposed method.
Observers design for one-sided Lipschitz discrete-time systems
Benallouch, Mohamed; Boutayeb, Mohamed; Zasadzinski, Michel
2012-01-01
International audience; This note focuses on state observer design for a general class of nonlinear discrete-time systems that satisfies the one-sided Lipschitz condition. It has been shown that this condition may encompass a large class of nonlinearities. However, challenging problems arise such as relevant choice of the Lyapunov function or non convexity of the obtained stability conditions. Both full-order and reduced-order observer design are considered. In this work, the main contributio...
Zhu Jin; Xi Hongsheng; Xiao Xiaobo; Ji Haibo
2007-01-01
Robust LQG problems of discrete-time Markovian jump systems with uncertain noises are investigated.The problem addressed is the construction of perturbation upper bounds on the uncertain noise covariances so as to guarantee that the deviation of the control performance remains within the precision prescribed in actual problems.Furthermore, this regulator is capable of minimizing the worst performance in an uncertain case. A numerical example is exploited to show the validity of the method.
Dynamic output feedback for discrete-time systems under amplitude and rate actuator constraints
Silva Junior, Joao Manoel Gomes da; Limon Marruedo, Daniel; Alamo Cantarero, Teodoro Rafael; Camacho, Eduardo F.
2008-01-01
This work proposes a technique for the design of stabilizing dynamic output feedback controllers for discrete-time linear systems with rate and amplitude saturating actuators. The nonlinear effects introduced by the saturations in the closed-loop system are taken into account by using a generalized sector condition, which leads to theoretical conditions for solving the problem directly in the form of linear matrix inequalities.
On invariant ellipsoids for discrete-time systems by saturated optimal controls
Bin ZHOU; Guangren DUAN
2008-01-01
Analytical approximation of the maximal invariant ellipsoid for discrete-time linear systems with saturated optimal control is established, which is less conservative than existing computationally un-intensive results. Simultaneously, necessary and sufficient conditions for such approximation being equal to the real maximal invariant ellipsoid is presented.All results are given analytically and can easily be implemented in practice.An illustrative example is given to show the effectiveness of the proposed approach.
Tightened Exponential Bounds for Discrete-Time Conditionally Symmetric Martingales and Applications
Sason, Igal
2012-01-01
This paper revisits the derivation of some exponential bounds for discrete-time and real-valued martingales with bounded jumps in order to improve these bounds for conditionally symmetric martingales. The new bounds are extended to conditionally symmetric sub or super-martingales, and they are also considered in connection to some previously reported bounds in the literature. Two applications of these bounds are exemplified in the context of gambling, and the number of up-crossings of a super-martingale.
Control design for discrete-time state-multiplicative noise stochastic systems
Krokavec, Dušan; Filasová, Anna
2015-11-01
Design conditions for existence of the H∞ linear state feedback control for discretetime stochastic systems with state-multiplicative noise and polytopic uncertainties are presented in the paper. Using an enhanced form of the bounded real lemma for discrete-time stochastic systems with state-multiplicative noise, the LMI-based procedure is provided for computation of the gains of linear, as well as nonlinear, state control law. The approach is illustrated on an example demonstrating the validity of the proposed method.
Xianming ZHANG; Min WU; Jinhua SHE; Dongsheng HAN
2007-01-01
This paper addresses the problems of the robust stability and robust stabilization of a discrete-time system with polytopic uncertainties.A new and simple method is presented to directly decouple the Lyapunov matrix and the system dynamic matrix.Combining this method with the parameter-dependent Lyapunov function approach yields new criteria that include some existing ones as special cases.A numerical example illustrates the improvement over the existing ones.
Chen Di-Lan; Zhang Wei-Dong
2008-01-01
This paper is concerned with the problem of robust H∞ control for structured uncertain stochastic neural networks with both discrete and distributed time varying delays. A sufficient condition is presented for the existence of H∞ control based on the Lyapunov stability theory. The stability criterion is described in terms of linear matrix inequalities (LMIs),which can be easily checked in practice. An example is provided to demonstrate the effectiveness of the proposed result.
Impulsive synchronization of discrete-time chaotic systems under communication constraints
Gao, Yanbo; Zhang, Xiaomei; Lu, Guoping; Zheng, Yufan
2011-03-01
This paper investigates the problem of impulsive synchronization of discrete-time chaotic systems subject to limited communication capacity. Control laws with impulses are derived by using measurement feedback, where the effect of quantization errors is considered. Sufficient conditions for asymptotic stability of synchronization error systems are given in terms of linear matrix inequalities and algebraic inequalities. Some numerical simulations are given to demonstrate the effectiveness of the method.
Stabilization of a class of discrete-time switched systems via observer-based output feedback
Jiao LI; Yuzhong LIU
2007-01-01
In this paper, observer-based static output feedback control problem for discrete-time uncertain switched systems is investigated under an arbitrary switching rule. The main method used in this note is combining switched. Lyapunov function (SLF) method with Finsler's Lemma. Based on linear matrix inequality (LMI) a less conservative stability condition is established and this condition allows extra degree of freedom for stability analysis. Finally, a simulation example is given to illustrate the efficiency of the result.
Discrete Time McKean–Vlasov Control Problem: A Dynamic Programming Approach
Pham, Huyên, E-mail: pham@math.univ-paris-diderot.fr; Wei, Xiaoli, E-mail: tyswxl@gmail.com [Laboratoire de Probabilités et Modèles Aléatoires, CNRS, UMR 7599, Université Paris Diderot (France)
2016-12-15
We consider the stochastic optimal control problem of nonlinear mean-field systems in discrete time. We reformulate the problem into a deterministic control problem with marginal distribution as controlled state variable, and prove that dynamic programming principle holds in its general form. We apply our method for solving explicitly the mean-variance portfolio selection and the multivariate linear-quadratic McKean–Vlasov control problem.
Discrete-Time Chaotic Circuits for Implementation of Tent Map and Bernoulli Map
LI Zhi-zhong; QIU Shui-sheng
2005-01-01
Discrete-time chaotic circuit implementations of a tent map and a Bernoulli map using switched-current (SI) techniques are presented. The two circuits can be constructed with 16MOSFET's and 2 capacitors. The simulations and experiments built with commercially available IC's for the circuits have demonstrated the validity of the circuit designs. The experiment results also indicate that the proposed circuits are integrable by a standard CMOS technology. The implementations are useful for studies and applications of chaos.
Asymptotic stability of monostable wavefronts in discrete-time integral recursions
无
2010-01-01
The aim of this work is to study the traveling wavefronts in a discrete-time integral recursion with a Gauss kernel in R2.We first establish the existence of traveling wavefronts as well as their precise asymptotic behavior.Then,by employing the comparison principle and upper and lower solutions technique,we prove the asymptotic stability and uniqueness of such monostable wavefronts in the sense of phase shift and circumnutation.We also obtain some similar results in R.
Anticontrol of chaos for discrete-time fuzzy hyperbolic model with uncertain parameters
Zhao Yan; Zhang Hua-Guang; Zheng Cheng-De
2008-01-01
This paper proposes a new method to chaotify the discrete-time fuzzy hyperbolic model (DFHM) with uncertain parameters.A simple nonlinear state feedback controller is designed for this purpose.By revised Marotto theorem,it is proven that the chaos generated by this controller satisfies the Li-Yorke definition.An example is presented to demonstrate the effectiveness of the approach.
Glatt-Holtz, Nathan; Temam, Roger; Wang, Chuntian
2014-01-01
As a first step towards the numerical analysis of the stochastic primitive equations of the atmosphere and oceans, we study their time discretization by an implicit Euler scheme. From deterministic viewpoint the 3D Primitive Equations are studied with physically realistic boundary conditions. From probabilistic viewpoint we consider a wide class of nonlinear, state dependent, white noise forcings. The proof of convergence of the Euler scheme covers the equations for the oceans, atmosphere, co...
Parametrization of Minimal Spectral Factors of Discrete-Time Rational Spectral Densities
Baggio, Giacomo; Ferrante, Augusto
2016-01-01
In this paper, the problem of providing a complete parametrization of the minimal spectral factors of a discrete-time rational spectral density is considered. The desired parametrization is given in terms of the all-pass divisors of an all-pass function, related to the so-called phase function, under very mild assumptions on the given spectral density. This result provides a partial answer to a conjecture raised in [3].
Peter Arcidiacono; Patrick Bayer; Jason R. Blevins; Paul B. Ellickson
2012-01-01
This paper develops a dynamic model of retail competition and uses it to study the impact of the expansion of a new national competitor on the structure of urban markets. In order to accommodate substantial heterogeneity (both observed and unobserved) across agents and markets, the paper first develops a general framework for estimating and solving dynamic discrete choice models in continuous time that is computationally light and readily applicable to dynamic games. In the proposed framework...
Yurong Liu
2013-01-01
Full Text Available This paper is concerned with the leader-following consensus problem in mean-square for a class of discrete-time multiagent systems. The multiagent systems under consideration are the directed and contain arbitrary discrete time-delays. The communication links are assumed to be time-varying and stochastic. It is also assumed that some agents in the network are well informed and act as leaders, and the others are followers. By introducing novel Lyapunov functionals and employing some new analytical techniques, sufficient conditions are derived to guarantee the leader-following consensus in mean-square for the concerned multiagent systems, so that all the agents are steered to an anticipated state target. A numerical example is presented to illustrate the main results.
Stabilizing Solution for a Discrete-Time Modified Algebraic Riccati Equation in Infinite Dimensions
Viorica Mariela Ungureanu
2015-01-01
Full Text Available We provide necessary and sufficient conditions for the existence of stabilizing solutions for a class of modified algebraic discrete-time Riccati equations (MAREs defined on ordered Banach spaces of sequences of linear and bounded operators. These MAREs arise in the study of linear quadratic (LQ optimal control problems for infinite-dimensional discrete-time linear systems (DTLSs affected simultaneously by multiplicative white noise (MN and Markovian jumps (MJs. Unlike most of the previous works, where the detectability and observability notions are key tools for studying the global solvability of MAREs, in this paper the conditions of existence of mean-square stabilizing solutions are given directly in terms of system parameters. The methods we have used are based on the spectral theory of positive operators and the properties of trace class and compact operators. Our results generalise similar ones obtained for finite-dimensional MAREs associated with stochastic DTLSs without MJs. Also they complete and extend (in the autonomous case former investigations concerning the existence of certain global solutions (as minimal, maximal, and stabilizing solutions for generalized discrete-time Riccati type equations defined on infinite-dimensional ordered Banach spaces.
Jiao Li; Jun Zhao
2017-05-01
This paper investigates incremental passivity and output regulation for switched discrete-time systems. We develop the results in two parts. First of all, a concept of incremental passivity is proposed to describe the overall incremental passivity property of a switched discrete-time system in the absence of the classic incremental passivity property of the subsystems. A condition for incremental passivity is given. A certain negative output feedback is designed to produce asymptotic stability. Incremental passivity is shown to be preserved under feedback interconnection. The second part of this paper is concerned with an application of the incremental passivity theory to the output regulation problem for switched discrete-time systems. The key idea is to construct a switched internal model with incremental passivity, which closely links the solvability of the output regulation problem. A characteristic of the switched internal model is that it does not necessarily switch synchronously with the controlled plant, which greatly increases the freedom of design. Once such a switched internal model is established, the output regulation problem is then solved by construction of the feedback interconnection between the controlled plant and the switched internal model. The main usefulness of the strategy is to get rid of the solvability of the output regulation problem for the subsystems.
Anssari-Benam, Afshin; Bucchi, Andrea; Bader, Dan L
2015-09-18
Discrete element models have often been the primary tool in investigating and characterising the viscoelastic behaviour of soft tissues. However, studies have employed varied configurations of these models, based on the choice of the number of elements and the utilised formation, for different subject tissues. This approach has yielded a diverse array of viscoelastic models in the literature, each seemingly resulting in different descriptions of viscoelastic constitutive behaviour and/or stress-relaxation and creep functions. Moreover, most studies do not apply a single discrete element model to characterise both stress-relaxation and creep behaviours of tissues. The underlying assumption for this disparity is the implicit perception that the viscoelasticity of soft tissues cannot be described by a universal behaviour or law, resulting in the lack of a unified approach in the literature based on discrete element representations. This paper derives the constitutive equation for different viscoelastic models applicable to soft tissues with two characteristic times. It demonstrates that all possible configurations exhibit a unified and universal behaviour, captured by a single constitutive relationship between stress, strain and time as: σ+Aσ̇+Bσ¨=Pε̇+Qε¨. The ensuing stress-relaxation G(t) and creep J(t) functions are also unified and universal, derived as [Formula: see text] and J(t)=c2+(ε0-c2)e(-PQt)+σ0Pt, respectively. Application of these relationships to experimental data is illustrated for various tissues including the aortic valve, ligament and cerebral artery. The unified model presented in this paper may be applied to all tissues with two characteristic times, obviating the need for employing varied configurations of discrete element models in preliminary investigation of the viscoelastic behaviour of soft tissues. Copyright © 2015 Elsevier Ltd. All rights reserved.
[Prevalence of dry eye in Hansen's disease patients from a colony hospital in Goiânia, Brazil].
Frazão, Karys Carvalho; Picolo, Naira Bernardes; Hanouche, Rosana Zacarias; Santos, Procópio Miguel dos; Santos, Regina Cândido Ribeiro dos
2005-01-01
To determine the prevalence of dry eye in Hansen's disease patients from the "Hospital de Dermatologia Sanitária de Goiânia". The sample of the present study included 70 patients with Hansen's disease, from the "Hospital de Dermatologia Sanitária de Goiânia", and 30 controls, from the "Fundação Banco de Olhos de Goiás", both located in Goiânia-GO, Brazil. Ophthalmologic examination and Schirmer I, break-up time (BUT) and rose Bengal staining tests were carried out for all patients in a single evaluation. For the diagnosis of dry eye the Schirmer I equal or less than 5 mm and rose Bengal grade II or III, in at least one eye were considered. Forty-four (63.0%) patients with Hansen's disease were male and 22 (73.3%) controls were female (p=0.001). The mean age of the patients with Hansen's disease was 61.1+/-12.5 years and in the control group, it was 55.7+/-9.6 years. Fifteen (21.4%) patients with Hansen's disease and four (13.3%) controls presented with dry eye diagnosis (p=0.429). The lepromatous type (74.2%) of Hansen's disease was the most prevalent and dry eye (66.7%) was more frequent in this clinical form of the disease. The dry eye disease was more prevalent in patients with Hansen's disease, although the difference was not statistically significant.
Optical force on a discrete invisibility cloak in time-dependent fields
Chaumet, Patrick C.; Zolla, Frederic; Nicolet, Andre; Belkebir, Kamal [Institut Fresnel, CNRS, Aix-Marseille Universite, Campus de St-Jerome 13013 Marseille (France); Rahmani, Adel [Department of Mathematical Sciences, University of Technology, Sydney, Broadway NSW 2007 (Australia)
2011-09-15
We study, in time domain, the exchange of momentum between an electromagnetic pulse and a three-dimensional, discrete, spherical invisibility cloak. We find that a discrete cloak, initially at rest, would experience an electromagnetic force due to the pulse but would acquire zero net momentum and net displacement. On the other hand, we find that while the cloak may manage to conceal an object and shroud it from the electromagnetic forces associated with the pulse, the cloak itself can experience optomechanical stress on a scale much larger than the object would in the absence of the cloak. We also consider the effects of material dispersion and losses on the electromagnetic forces experienced by the cloak and show that they lead to a transfer of momentum from the pulse to the cloak.
Bifurcation and complex dynamics of a discrete-time predator-prey system involving group defense
S. M. Sohel Rana
2015-09-01
Full Text Available In this paper, we investigate the dynamics of a discrete-time predator-prey system involving group defense. The existence and local stability of positive fixed point of the discrete dynamical system is analyzed algebraically. It is shown that the system undergoes a flip bifurcation and a Neimark-Sacker bifurcation in the interior of R+2 by using bifurcation theory. Numerical simulation results not only show the consistence with the theoretical analysis but also display the new and interesting dynamical behaviors, including phase portraits, period-7, 20-orbits, attracting invariant circle, cascade of period-doubling bifurcation from period-20 leading to chaos, quasi-periodic orbits, and sudden disappearance of the chaotic dynamics and attracting chaotic set. The Lyapunov exponents are numerically computed to characterize the complexity of the dynamical behaviors.
Consensus of Discrete Multiagent System with Various Time Delays and Environmental Disturbances
Zheping Yan
2014-12-01
Full Text Available In this paper, the consensus problem of discrete multiagent systems with time varying sampling periods is studied. Firstly, with thorough analysis of various delays among agents, the control input of each agent is designed with consideration of sending delay and receiving delay. With construction of discrete dynamics of state error vector, it is proved by applying Halanay inequality that consensus of the system can be reached. Further, the definition of bounded consensus is proposed in the situation where environmental disturbances exist. In order to handle this problem, the Halanay inequality is extended into a more general one with boundedness property. Based on the new Halanay inequality obtained, the boundedness of consensus error is guaranteed. At last, simulation examples are presented to demonstrate the theoretical conclusions.
Discretizing of linear systems with time-delay Using method of Euler’s and Tustin’s approximations
Bemri H’mida
2015-03-01
Full Text Available Delays deteriorate the control performance and could destabilize the overall system in the theory of discretetime signals and dynamic systems. Whenever a computer is used in measurement, signal processing or control applications, the data as seen from the computer and systems involved are naturally discrete-time because a computer executes program code at discrete points of time. Theory of discrete-time dynamic signals and systems is useful in design and analysis of control systems, signal filters, state estimators and model estimation from time-series of process data system identification. In this paper, a new approximated discretization method and digital design for control systems with delays is proposed. System is transformed to a discrete-time model with time delays. To implement the digital modeling, we used the z-transfer functions matrix which is a useful model type of discrete-time systems, being analogous to the Laplace-transform for continuous-time systems. The most important use of the z-transform is for defining z-transfer functions matrix is employed to obtain an extended discrete-time. The proposed method can closely approximate the step response of the original continuous timedelayed control system by choosing various of energy loss level. Illustrative example is simulated to demonstrate the effectiveness of the developed method.
Modelling and real-time simulation of continuous-discrete systems in mechatronics
Lindow, H. [Rostocker, Magdeburg (Germany)
1996-12-31
This work presents a methodology for simulation and modelling of systems with continuous - discrete dynamics. It derives hybrid discrete event models from Lagrange`s equations of motion. This method combines continuous mechanical, electrical and thermodynamical submodels on one hand with discrete event models an the other hand into a hybrid discrete event model. This straight forward software development avoids numeric overhead.
Real-Time Discrete Adaptive Control of Robot Arm Based on Digital Signal Processing
无
2008-01-01
A discrete model reference adaptive controller of robot arm is obtained by integrating the reduced dynamic model of robot, model reference adaptive control (MRAC) and digital signal processing (DSP) computer system into an electromechanical system. With the DSP computer system, the control signal of each joint of the robot arm can be processed in real time and independently. The simulation and experiment results show that with the control strategy, the robot achieved a good trajectory following precision, a good decoupling performance and a high real-time adaptivity.
Ohkubo, Jun
2011-12-01
A scheme is developed for estimating state-dependent drift and diffusion coefficients in a stochastic differential equation from time-series data. The scheme does not require to specify parametric forms for the drift and diffusion coefficients in advance. In order to perform the nonparametric estimation, a maximum likelihood method is combined with a concept based on a kernel density estimation. In order to deal with discrete observation or sparsity of the time-series data, a local linearization method is employed, which enables a fast estimation.
The turnpike property for dynamic discrete time zero-sum games
Alexander J. Zaslavski
1999-01-01
Full Text Available We consider a class of dynamic discrete-time two-player zero-sum games. We show that for a generic cost function and each initial state, there exists a pair of overtaking equilibria strategies over an infinite horizon. We also establish that for a generic cost function f, there exists a pair of stationary equilibria strategies (xf,yf such that each pair of “approximate” equilibria strategies spends almost all of its time in a small neighborhood of (xf,yf.
John Cortés-Romero
2013-01-01
Full Text Available The problem of active disturbance rejection control of induction motors is tackled by means of a generalized PI observer based discrete-time control, using the delta operator approach as the methodology of analyzing the sampled time process. In this scheme, model uncertainties and external disturbances are included in a general additive disturbance input which is to be online estimated and subsequently rejected via the controller actions. The observer carries out the disturbance estimation, thus reducing the complexity of the controller design. The controller efficiency is tested via some experimental results, performing a trajectory tracking task under load variations.
Gibson, J. S.; Rosen, I. G.
1988-01-01
An abstract approximation framework is developed for the finite and infinite time horizon discrete-time linear-quadratic regulator problem for systems whose state dynamics are described by a linear semigroup of operators on an infinite dimensional Hilbert space. The schemes included the framework yield finite dimensional approximations to the linear state feedback gains which determine the optimal control law. Convergence arguments are given. Examples involving hereditary and parabolic systems and the vibration of a flexible beam are considered. Spline-based finite element schemes for these classes of problems, together with numerical results, are presented and discussed.
Xia Zhou
2013-01-01
Full Text Available The problem of bounded-input bounded-output (BIBO stabilization in mean square for a class of discrete-time stochastic control systems with mixed time-varying delays and nonlinear perturbations is investigated. Some novel delay-dependent stability conditions for the previously mentioned system are established by constructing a novel Lyapunov-Krasovskii function. These conditions are expressed in the forms of linear matrix inequalities (LMIs, whose feasibility can be easily checked by using MATLAB LMI Toolbox. Finally, a numerical example is given to illustrate the validity of the obtained results.
Xianming ZHANG; Min WU; Jinhua SHE; Dongsheng HAN
2006-01-01
This paper examines the delay-dependent H-infinity control problem for discrete-time linear systems with time-varying state delays and norm-bounded uncertainties. A new inequality for the finite sum of quadratic terms is first established. Then, some new delay-dependent criteria are derived by employing the new inequality to guarantee the robust stability of a closed-loop system with a prescribed H-infinity norm bound for all admissible uncertainties and bounded time-vary delays. A numerical example demonstrates that the proposed method is an improvement over existing ones.
On the Einstein-Podolsky-Rosen paradox using discrete time physics
Riek, Roland
2017-08-01
The Einstein-Podolski-Rosen paradox highlights several strange properties of quantum mechanics including the super position of states, the non locality and its limitation to determine an experiment only statistically. Here, this well known paradox is revisited theoretically for a pair of spin {\\scriptstyle \\frac{1}{2}} systems in a singlet state under the assumption that in classical physics time evolves in discrete time steps t while in quantum mechanics the individual spin system(s) evolve(s) between the eigenstates harmonically with a period of 4 t. It is further assumed that time is a single variable, that the quantum mechanics time evolution and the classical physics discrete time evolution are coherent to each other, and that the precision of the start of the experiment and of the measurement time point are much less than t. Under these conditions, it is demonstrated for a spin {\\scriptstyle \\frac{1}{2}} system that the fast oscillation between the eigen states spin up | ↑> and spin down | ↓> reproduce the expected outcome of a single measurement as well as ensemble measurements without the need of postulating a simultaneous superposition of the spin system in its quantum state. When this concept is applied to a spin {\\scriptstyle \\frac{1}{2}} system pair in a singlet state it is shown that no entanglement between the two spins is necessary to describe the system resolving the Einstein-Podolski-Rosen paradox.
A Reply to Hansen's Cultural Humanism
Lemberger, Matthew E.
2012-01-01
Hansen (2012b) responds to the author's (Lemberger, 2012) critique of his humanistic vision by dividing their arguments as either individual or cultural in design. In this reply, the author contends that the individual cannot be extracted from her or his culture and, therefore, what is sufficient for a humanistic counseling culture must also be…
A Reply to Hansen's Cultural Humanism
Lemberger, Matthew E.
2012-01-01
Hansen (2012b) responds to the author's (Lemberger, 2012) critique of his humanistic vision by dividing their arguments as either individual or cultural in design. In this reply, the author contends that the individual cannot be extracted from her or his culture and, therefore, what is sufficient for a humanistic counseling culture must also be…
Legendre, Davey P; Muzny, Christina A; Swiatlo, Edwin
2012-01-01
Hansen's disease, also known as leprosy, remains an important public health problem throughout the world, including North America. The causative microbe in Hansen's disease is Mycobacterium leprae, an acid-fast organism that is difficult to grow in vitro. The nine-banded armadillo is the major animal reservoir in the United States. Manifestations of disease vary based on host immune response and can range from tuberculoid to lepromatous leprosy (paucibacillary to multibacillary disease). Hansen's disease typically affects the skin, nerves, and eyes, and patients may present with skin lesions, weakness, numbness, eye pain, or loss of vision. Definitive diagnosis is based on a combination of physical examination findings and skin biopsy and/or smear. Modern antibacterial therapy typically consists of combinations of dapsone and rifampin with or without clofazimine. Clofazimine is available only as an investigational drug through the National Hansen's Disease Program. Other options include moxifloxacin, ofloxacin, minocycline, and clarithromycin. Hansen's disease is associated with type 1 (reversal) and type 2 (erythema nodosum leprosum) immunologic reactions, during which the disease process appears to worsen dramatically. These reactions may occur at any time before, during, or after treatment. Antibacterial therapy should usually be continued during these reactions. Treatment options for these reactions differ based on clinical manifestations and include corticosteroids, thalidomide, pentoxiphylline, tumor necrosis factor inhibitors, and T cell inhibitors. Prompt diagnosis, antimicrobial therapy, and treatment of reactions dramatically reduce complications of the disease. © 2012, Pharmacotherapy Publications, Inc.
ANALYSIS OF A DISCRETE-TIME GI/GEO/1/N QUEUE WITH MULTIPLE WORKING VACATIONS
Veena GOSWAMI; G.B.MUND
2010-01-01
This paper analyzes a finite-buffer renewal input single server discrete-time queneing system with multiple working vacations.The server works at a different rate rather than completely stopping working during the multiple working vacations.The service times during a service period,service time during a vacation period and vacation times are geometrically distributed.The queue is analyzed using the supplementary variable and the imbedded Markov-chain techniques.We obtain steady-state system length distributions at pre-arrival,arbitrary and outside observer's observation epochs.The analysis of actual waiting-time distribution and some performance measures are carried out.We present some numerical results and discuss special cases of the model.
Legal time limits vs. discretional limits of administrative judicial review in Albania
Gerti Shella
2016-11-01
Full Text Available Administrative courts in Albania were established in 2012, as a separate branch of the court system, following enactment of the Law No. 49/2012 “On the Organization and Functioning of the Administrative Courts and Adjudication of Administrative Disputes”. One of the main features of the administrative adjudication is the swiftness at which it should be carried out. The law provides carefully for many time limits and procedural deadlines, to achieve such intended effect. This article focuses specifically on the time limits of concluding (1 the judicial review in administrative courts and 2 on due delivery of the final decision in court secretariat. These two distinct procedural phases constitute 98% of the length of a court case in time terms. The main thesis of this paper is that time limits which are explicitly written and required by the law produce better results in terms of compliance of judges with law and higher efficiency compared to discretional time limits.
Cai, Chao-Ran; Wu, Zhi-Xi; Guan, Jian-Yue
2014-11-01
Recently, Gómez et al. proposed a microscopic Markov-chain approach (MMCA) [S. Gómez, J. Gómez-Gardeñes, Y. Moreno, and A. Arenas, Phys. Rev. E 84, 036105 (2011)PLEEE81539-375510.1103/PhysRevE.84.036105] to the discrete-time susceptible-infected-susceptible (SIS) epidemic process and found that the epidemic prevalence obtained by this approach agrees well with that by simulations. However, we found that the approach cannot be straightforwardly extended to a susceptible-infected-recovered (SIR) epidemic process (due to its irreversible property), and the epidemic prevalences obtained by MMCA and Monte Carlo simulations do not match well when the infection probability is just slightly above the epidemic threshold. In this contribution we extend the effective degree Markov-chain approach, proposed for analyzing continuous-time epidemic processes [J. Lindquist, J. Ma, P. Driessche, and F. Willeboordse, J. Math. Biol. 62, 143 (2011)JMBLAJ0303-681210.1007/s00285-010-0331-2], to address discrete-time binary-state (SIS) or three-state (SIR) epidemic processes on uncorrelated complex networks. It is shown that the final epidemic size as well as the time series of infected individuals obtained from this approach agree very well with those by Monte Carlo simulations. Our results are robust to the change of different parameters, including the total population size, the infection probability, the recovery probability, the average degree, and the degree distribution of the underlying networks.
Adaptive control for a class of discrete-time time-delay systems with regard to delay parameter
Chai Lin; Cheng Ming; Fei Shumin; Zhai Junyong
2009-01-01
The memory state feedback control problem for a class of discrete-time systems with input delay and unknown state delay is addressed based on LMIs and Lyapunov-Krasovskii functional method. Under the action of our designed adaptive control law, the unknown time-delay parameter is included in memory state feedback controller. Using LMI technique, delay-dependent sufficient conditions for the existence of the feedback controller are obtained. Finally, the effectiveness of the proposed design method is demonstrated by a numerical example.
Zhang, Huaguang; Song, Ruizhuo; Wei, Qinglai; Zhang, Tieyan
2011-12-01
In this paper, a novel heuristic dynamic programming (HDP) iteration algorithm is proposed to solve the optimal tracking control problem for a class of nonlinear discrete-time systems with time delays. The novel algorithm contains state updating, control policy iteration, and performance index iteration. To get the optimal states, the states are also updated. Furthermore, the "backward iteration" is applied to state updating. Two neural networks are used to approximate the performance index function and compute the optimal control policy for facilitating the implementation of HDP iteration algorithm. At last, we present two examples to demonstrate the effectiveness of the proposed HDP iteration algorithm.
Further Result on Passivity for Discrete-Time Stochastic T-S Fuzzy Systems with Time-Varying Delays
Ting Lei
2014-01-01
Full Text Available The passivity for discrete-time stochastic T-S fuzzy systems with time-varying delays is investigated. By constructing appropriate Lyapunov-Krasovskii functionals and employing stochastic analysis method and matrix inequality technique, a delay-dependent criterion to ensure the passivity for the considered T-S fuzzy systems is established in terms of linear matrix inequalities (LMIs that can be easily checked by using the standard numerical software. An example is given to show the effectiveness of the obtained result.
Global Discrete Artificial Boundary Conditions for Time-Dependent Wave Propagation
Ryaben'kii, V. S.; Tsynkov, S. V.; Turchaninov, V. I.
2001-12-01
We construct global artificial boundary conditions (ABCs) for the numerical simulation of wave processes on unbounded domains using a special nondeteriorating algorithm that has been developed previously for the long-term computation of wave-radiation solutions. The ABCs are obtained directly for the discrete formulation of the problem; in so doing, neither a rational approximation of “nonreflecting kernels” nor discretization of the continuous boundary conditions is required. The extent of temporal nonlocality of the new ABCs appears fixed and limited; in addition, the ABCs can handle artificial boundaries of irregular shape on regular grids with no fitting/adaptation needed and no accuracy loss induced. The nondeteriorating algorithm, which is the core of the new ABCs, is inherently three-dimensional, it guarantees temporally uniform grid convergence of the solution driven by a continuously operating source on arbitrarily long time intervals and provides unimprovable linear computational complexity with respect to the grid dimension. The algorithm is based on the presence of lacunae, i.e., aft fronts of the waves, in wave-type solutions in odd-dimensional spaces. It can, in fact, be built as a modification on top of any consistent and stable finite-difference scheme, making its grid convergence uniform in time and at the same time keeping the rate of convergence the same as that of the unmodified scheme. In this paper, we delineate the construction of the global lacunae-based ABCs in the framework of a discretized wave equation. The ABCs are obtained for the most general formulation of the problem that involves radiation of waves by moving sources (e.g., radiation of acoustic waves by a maneuvering aircraft). We also present systematic numerical results that corroborate the theoretical design properties of the ABC algorithm.
Design of RLS Wiener Fixed-Lag Smoother in Linear Discrete-Time Stochastic Systems
2015-01-01
This paper newly presents the recursive least-squares (RLS) fixed-lag smoother using the covariance information and then the RLS Wiener fixed-lag smoother in linear discrete-time wide-sense stationary stochastic systems. Here, the additional disturbance in the measurement of the signal is white noise. The signal is uncorrelated with observed noise. It is assumed that the signal process is fitted to the autoregressive (AR) model of order NN. For this AR model of order NN, in the proposed fixed...
ROBUST STABILITY WITH GUARANTEEING COST FOR DISCRETE TIME-DELAY SYSTEMS WITH NONLINEAR PERTURBATION
JIA Xinchun; ZHENG Nanning; LIU Yuehu
2005-01-01
The problems of robust stability and robust stability with a guaranteeing cost for discrete time-delay systems with nonlinear perturbation are discussed. A sufficient criterion for robust stability is established in an LMI framework and a linear convex optimization problem with LMI constraints for computing maximal perturbation bound is proposed. Meanwhile, a sufficient criterion for robust stability with a guaranteeing cost for such systems is obtained, and an optimal procedure for decreasing the value of guaranteeing cost is put forward. Two examples are used to illustrate the efficiency of the results.
Bahi, J M; Guyeux, C; Richard, A
2011-01-01
Chaotic functions are characterized by sensitivity to initial conditions, transitivity, and regularity. Providing new functions with such properties is a real challenge. This work shows that one can associate with any Boolean network a continuous function, whose discrete-time iterations are chaotic if and only if the iteration graph of the Boolean network is strongly connected. Then, sufficient conditions for this strong connectivity are expressed on the interaction graph of this network, leading to a constructive method of chaotic function computation. The whole approach is evaluated in the chaos-based pseudo-random number generation context.
Indirect adaptive fuzzy control for a class of nonlinear discrete-time systems
无
2008-01-01
An indirect adaptive fuzzy control scheme is developed for a class of nonlinear discrete-time systems. In this method, two fuzzy logic systems are used to approximate the unknown functions, and the parameters of membership functions in fuzzy logic systems are adjusted according to adaptive laws for the purpose of controlling the plant to track a reference trajectory. It is proved that the scheme can not only guarantee the boundedness of the input and output of the closed-loop system, but also make the tracking error converge to a small neighborhood of the origin. Simulation results indicate the effectiveness of this scheme.
Dynamical behavior of a discrete time Hogg-Huberman model with three resources
Inoue, M.; Tanaka, T.; Takagi, N.; Shibata, J.
2002-09-01
The dynamical behavior of a discrete time Hogg-Huberman model with three resources 1-3 is investigated. The payoff function of resource 3 is assumed to be the same function as that of resource 2. It is found that when the control parameter takes certain values there are various states which are called the monopoly state of resource 1, and synchronized and asynchronized chaotic states with respect to the fractions of agents using resources 2 and 3. The effect of a reward mechanism based on the actual performance of agents is also calculated in this system.
H∞ Enhanced Control Design of Discrete-Time Takagi-Sugeno State-Multiplicative Noisy Systems
Dušan Krokavec
2014-01-01
Full Text Available Design conditions for existence of the H∞ state feedback control for Takagi-Sugeno fuzzy discrete-time stochastic systems with state-multiplicative noise, stabilizing the closed-loop in such way that the quadratic performance in the mean is satisfied, are presented in the paper. Using newly introduced enhanced form of the bounded real lemma for such stochastic systems, the LMI-based procedure is provided for computation of gain matrices of the state control law, realized in the parallel distributed compensation structure. The approach is illustrated on an example, demonstrating the validity of the proposed method.
Passive Fault-tolerant Control of Discrete-time Piecewise Affine Systems against Actuator Faults
Tabatabaeipour, Seyed Mojtaba; Izadi-Zamanabadi, Roozbeh; Bak, Thomas
2012-01-01
In this paper, we propose a new method for passive fault-tolerant control of discrete time piecewise affine systems. Actuator faults are considered. A reliable piecewise linear quadratic regulator (LQR) state feedback is designed such that it can tolerate actuator faults. A sufficient condition...... for the exis- tence of a passive fault-tolerant controller is derived and formulated as the feasibility of a set of linear matrix inequalities (LMIs). The upper bound on the performance cost can be minimized using a convex optimization problem with LMI constraints which can be solved efficiently. The approach...
Synchronization of discrete-time spatiotemporal chaos via adaptive fuzzy control
Xue Yue Ju
2003-01-01
A discrete-time adaptive fuzzy control scheme is presented to synchronize model-unknown coupled Henon-map lattices (CHMLs). The proposed method is robust to approximate errors, parameter mismatches and disturbances, because it integrates the merits of the adaptive fuzzy systems and the variable structure control with a sector. The simulation results of synchronization of CHMLs show that it not only can synchronize model-unknown CHMLs but also is robust against parameter mismatches and noise of the systems. These merits are advantageous for engineering realization.
Bosch, Jessica
2014-04-01
We consider the efficient solution of the Cahn-Hilliard variational inequality using an implicit time discretization, which is formulated as an optimal control problem with pointwise constraints on the control. By applying a semi-smooth Newton method combined with a Moreau-Yosida regularization technique for handling the control constraints we show superlinear convergence in function space. At the heart of this method lies the solution of large and sparse linear systems for which we propose the use of preconditioned Krylov subspace solvers using an effective Schur complement approximation. Numerical results illustrate the competitiveness of this approach. © 2014 Elsevier Inc.
On the Internal Multi-Model Control of Uncertain Discrete-Time Systems
Chakra Othman
2016-09-01
Full Text Available In this paper, new approaches of internal multi-model control are proposed to be applied for the case of the discrete-time systems with parametric uncertainty. In this sense, two implantation structures of the internal multi-model control are adopted; the first is based on the principle of switching and the second on the residues techniques. The stability’s study of these control structures is based on the Kharitonov theorem, thus two extensions of this theorem have been applied to define the internal models. To illustrate these approaches, simulation results are presented at the end of this article.
Repelling, binding, and oscillating of two-particle discrete-time quantum walks
Wang, Qinghao; Li, Zhi-Jian
2016-10-01
In this paper, we investigate the effects of particle-particle interaction and static force on the propagation of probability distribution in two-particle discrete-time quantum walk, where the interaction and static force are expressed as a collision phase and a linear position-dependent phase, respectively. It is found that the interaction can lead to boson repelling and fermion binding. The static force also induces Bloch oscillation and results in a continuous transition from boson bunching to fermion anti-bunching. The interplays of particle-particle interaction, quantum interference, and Bloch oscillation provide a versatile framework to study and simulate many-particle physics via quantum walks.
ZHANG Yan-hu; YAN Wen-jun; LU Jian-ning; ZHAO Guang-zhou
2005-01-01
Multi-objective robust state-feedback controller synthesis problems for linear discrete-time uncertain systems are addressed. Based on parameter-dependent Lyapunov functions, the Gl2 and GH2 norm expressed in terms of LMI (Linear Matrix Inequality) characterizations are further generalized to cope with the robust analysis for convex polytopic uncertain system.Robust state-feedback controller synthesis conditions are also derived for this class of uncertain systems. Using the above results,multi-objective state-feedback controller synthesis procedures which involve the LMI optimization technique are developed and less conservative than the existing one. An illustrative example verified the validity of the approach.
Romá, Federico; Cugliandolo, Leticia F; Lozano, Gustavo S
2014-08-01
We introduce a numerical method to integrate the stochastic Landau-Lifshitz-Gilbert equation in spherical coordinates for generic discretization schemes. This method conserves the magnetization modulus and ensures the approach to equilibrium under the expected conditions. We test the algorithm on a benchmark problem: the dynamics of a uniformly magnetized ellipsoid. We investigate the influence of various parameters, and in particular, we analyze the efficiency of the numerical integration, in terms of the number of steps needed to reach a chosen long time with a given accuracy.
Dynamical Properties of Discrete-Time Background Neural Networks with Uniform Firing Rate
Min Wan
2013-01-01
Full Text Available The dynamics of a discrete-time background network with uniform firing rate and background input is investigated. The conditions for stability are firstly derived. An invariant set is then obtained so that the nondivergence of the network can be guaranteed. In the invariant set, it is proved that all trajectories of the network starting from any nonnegative value will converge to a fixed point under some conditions. In addition, bifurcation and chaos are discussed. It is shown that the network can engender bifurcation and chaos with the increase of background input. The computations of Lyapunov exponents confirm the chaotic behaviors.
Yueyang Li
2014-01-01
Full Text Available This paper investigates the H∞ fixed-lag fault estimator design for linear discrete time-varying (LDTV systems with intermittent measurements, which is described by a Bernoulli distributed random variable. Through constructing a novel partially equivalent dynamic system, the fault estimator design is converted into a deterministic quadratic minimization problem. By applying the innovation reorganization technique and the projection formula in Krein space, a necessary and sufficient condition is obtained for the existence of the estimator. The parameter matrices of the estimator are derived by recursively solving two standard Riccati equations. An illustrative example is provided to show the effectiveness and applicability of the proposed algorithm.
Neimark-Sacker bifurcation of a two-dimensional discrete-time predator-prey model.
Khan, A Q
2016-01-01
In this paper, we study the dynamics and bifurcation of a two-dimensional discrete-time predator-prey model in the closed first quadrant [Formula: see text]. The existence and local stability of the unique positive equilibrium of the model are analyzed algebraically. It is shown that the model can undergo a Neimark-Sacker bifurcation in a small neighborhood of the unique positive equilibrium and an invariant circle will appear. Some numerical simulations are presented to illustrate our theocratical results and numerically it is shown that the unique positive equilibrium of the system is globally asymptotically stable.
Non-divergence of stochastic discrete time algorithms for PCA neural networks.
Lv, Jian Cheng; Yi, Zhang; Li, Yunxia
2015-02-01
Learning algorithms play an important role in the practical application of neural networks based on principal component analysis, often determining the success, or otherwise, of these applications. These algorithms cannot be divergent, but it is very difficult to directly study their convergence properties, because they are described by stochastic discrete time (SDT) algorithms. This brief analyzes the original SDT algorithms directly, and derives some invariant sets that guarantee the nondivergence of these algorithms in a stochastic environment by selecting proper learning parameters. Our theoretical results are verified by a series of simulation examples.
Synchronization and Bifurcation Analysis in Coupled Networks of Discrete-Time Systems
无
2007-01-01
Synchronization and bifurcation analysis in coupled networks of discrete-time systems are investigated in the present paper. We mainly focus on some special coupling matrix, i.e., the sum of each row equals a nonzero constant u and the network connection is directed. A result that the network can reach a new synchronous state, which is not the asymptotic limit set determined by the node state equation, is derived. It is interesting that the network exhibits bifurcation if we regard the constant u as a bifurcation parameter at the synchronous state. Numerical simulations are given to show the efficiency of our derived conclusions.
Robust reliable H∞ control for discrete-time Markov jump linear systems with actuator failures
Chen Jiaorong; Liu Fei
2008-01-01
The robust reliable H∞ control problem for discrete-time Markovian jump systems with actuator failures is studied.A more practical model of actuator failures than outage is considered.Based on the state feedback method,the resulting closed-loop systems are reliable in that they remain robust stochastically stable and satisfy a certain level of Hex disturbance attenuation not only when all actuators are operational,but also in case of some actuator failures.The solvability condition of controllers can be equivalent to a feasibility problem of coupled linear matrix inequalities (LMIs).A numerical example is also given to illustrate the design procedures and their effectiveness.
Geometric tools for solving the FDI problem for linear periodic discrete-time systems
Longhi, Sauro; Monteriù, Andrea
2013-07-01
This paper studies the problem of detecting and isolating faults in linear periodic discrete-time systems. The aim is to design an observer-based residual generator where each residual is sensitive to one fault, whilst remaining insensitive to the other faults that can affect the system. Making use of the geometric tools, and in particular of the outer observable subspace notion, the Fault Detection and Isolation (FDI) problem is formulated and necessary and solvability conditions are given. An algorithmic procedure is described to determine the solution of the FDI problem.
On Optimal Fault Detection for Discrete-time Markovian Jump Linear Systems
LI Yue-Yang; ZHONG Mai-Ying
2013-01-01
This paper deals with the problem of fault detection for discrete-time Markovian jump linear systems (MJLS).Using an observer-based fault detection filter (FDF) as a residual generator,the design of the FDF is formulated as an optimization problem for maximizing stochastic H_/H∞ or H∞/H∞ performance index.With the aid of an operator optimization method,it is shown that a unified optimal solution can be derived by solving a coupled Riccati equation.Numerical examples are given to show the effectiveness of the proposed method.
H-infinity filtering for discrete-time switched linear systems under arbitrary switching
无
2011-01-01
This paper is concerned with the problem of H-infinity filtering for discrete-time switched linear systems under arbitrary switching laws.New sufficient conditions for the solvability of the problem are given via switched quadratic Lyapunov functions.Based on Finsler's lemma,two sets of slack variables with special structure are introduced to provide extra degrees of freedom in optimizing the guaranteed H-infinity performance.Compared to the existing methods,the proposed one has better performances and less...
Capacity of Discrete-Time Wiener Phase Noise Channels to Within a Constant Gap
Barletta, Luca; Rini, Stefano
2017-01-01
The capacity of the discrete-time channel affected by both additive Gaussian noise and Wiener phase noise is studied. Novel inner and outer bounds are presented, which differ of at most $6.65$ bits per channel use for all channel parameters. The capacity of this model can be subdivided in three regimes: (i) for large values of the frequency noise variance, the channel behaves similarly to a channel with circularly uniform iid phase noise; (ii) when the frequency noise variance is small, the e...
Use of discrete Fourier transform to sum spectra in measurements with long counting times
Pilar Rubio Montero, M. [Departamento de Fisica, Universidad de Extremadura, Sta. Teresa de Jornet 38, E-06800, Merida (Spain); Garcia-Torano, Eduardo [Laboratorio de Metrologia de Radiaciones Ionizantes, CIEMAT, Avenida Complutense 22, 28040 Madrid (Spain)]. E-mail: E.garciatorano@ciemat.es
2007-07-11
When measuring nuclear spectra for long counting times, it is usual to split the acquisition in a set of spectra of shorter duration that are later added after correcting by drift during the measurements. We describe a method to determine the shifting correction by using the properties of the Discrete Fourier Transform (DFT). The method does not require assuming a particular spectral shape and the implementation is essentially independent of the kind of spectra being analyzed. The drift correction is defined for an integer number of channels. We present the results of the application to alpha-particle spectroscopy of long-lived nuclides.
Saïda Bedoui
2013-01-01
Full Text Available This paper addresses the problem of simultaneous identification of linear discrete time delay multivariable systems. This problem involves both the estimation of the time delays and the dynamic parameters matrices. In fact, we suggest a new formulation of this problem allowing defining the time delay and the dynamic parameters in the same estimated vector and building the corresponding observation vector. Then, we use this formulation to propose a new method to identify the time delays and the parameters of these systems using the least square approach. Convergence conditions and statistics properties of the proposed method are also developed. Simulation results are presented to illustrate the performance of the proposed method. An application of the developed approach to compact disc player arm is also suggested in order to validate simulation results.
H{sup {infinity}} State Feedback Control for Generalized Continuous/Discrete Time Delay System
Kim, J.H.; Lee, S.K.; Park, H.B. [Kyungpook National University, Taegu (Korea, Republic of); Jeung, E.T. [Changwon National University, Changwon (Korea, Republic of)
1998-04-01
In this paper, we consider the problem of designing H{sup {infinity}} state feedback controller for the generalized time delay systems with delayed states and control inputs in continuous and discrete time cases, respectively. The generalized time delay system problems are solved on the basis of LMI(linear matrix inequality) technique considering time delays. The sufficient condition for the existence of controller and H{sup {infinity}} state feedback controller design methods are presented. Also, using some changes of variables and Schur complements, the obtained sufficient condition can be rewritten as a LMI form in terms of transformed variables. The proposed controller design method can be extended into the problem of robust H{sup {infinity}} state feedback controller design method easily. (author). 15 refs.
Discrete-time control of a spacecraft with retargetable flexible antennas
Meirovitch, Leonard; France, Martin E. B.
This paper is concerned with the control of a spacecraft consisting of a rigid platform and retargetable flexible antennas. The mission consists of a minimum-time maneuver of the antenna(s) to coincide with predetermined line(s) of sight, while stabilizing the platform in an inertial space and suppressing the elastic vibration of the antenna(s). The system is modeled by a set of linearized, time-varying equations of motion. A discrete-time approach permits consideration of the time-varying nature of the system in designing the digital control law. Several control techniques were investigateed and results from numerical examples involving a spacecraft with a single flexible antena are presented.
Ji Xu; Jing hai Li; Hua biao Qi; Xiao jian Fang; Li qiang Lu; Wei Ge; Xiao wei Wang; Ming Xu; Fei guo Chen; Xian feng He
2011-01-01
Real-time simulation of industrial equipment is a huge challenge nowadays.The high performance and fine-grained parallel computing provided by graphics processing units (GPUs) bring us closer to our goals.In this article,an industrial-scale rotating drum is simulated using simplified discrete element method (DEM) without consideration of the tangential components of contact force and particle rotation.A single GPU is used first to simulate a small model system with about 8000 particles in real-time,and the simulation is then scaled up to industrial scale using more than 200 GPUs in a 1D domain-decomposition parallelization mode.The overall speed is about 1/11 of the real-time.Optimization of the communication part of the parallel GPU codes can speed up the simulation further,indicating that such real-time simulations have not only methodological but also industrial implications in the near future.
A Discrete Heterogeneous-Group Economic Growth Model with Endogenous Leisure Time
Wei-Bin Zhang
2009-01-01
Full Text Available This paper proposes a one-sector multigroup growth model with endogenous labor supply in discrete time. Proposing an alternative approach to behavior of households, we examine the dynamics of wealth and income distribution in a competitive economy with capital accumulation as the main engine of economic growth. We show how human capital levels, preferences, and labor force of heterogeneous households determine the national economic growth, wealth, and income distribution and time allocation of the groups. By simulation we demonstrate, for instance, that in the three-group economy when the rich group's human capital is improved, all the groups will economically benefit, and the leisure times of all the groups are reduced but when any other group's human capital is improved, the group will economically benefit, the other two groups economically lose, and the leisure times of all the groups are increased.
Discrete-time retrial queue with Bernoulli vacation, preemptive resume and feedback customers
Peishu Chen
2015-09-01
Full Text Available Purpose: We consider a discrete-time Geo/G/1 retrial queue where the retrial time follows a general distribution, the server subject to Bernoulli vacation policy and the customer has preemptive resume priority, Bernoulli feedback strategy. The main purpose of this paper is to derive the generating functions of the stationary distribution of the system state, the orbit size and some important performance measures. Design/methodology: Using probability generating function technique, some valuable and interesting performance measures of the system are obtained. We also investigate two stochastic decomposition laws and present some numerical results. Findings: We obtain the probability generating functions of the system state distribution as well as those of the orbit size and the system size distributions. We also obtain some analytical expressions for various performance measures such as idle and busy probabilities, mean orbit and system sizes. Originality/value: The analysis of discrete-time retrial queues with Bernoulli vacation, preemptive resume and feedback customers is interesting and to the best of our knowledge, no other scientific journal paper has dealt with this question. This fact gives the reason why efforts should be taken to plug this gap.
HERMITE WENO SCHEMES WITH LAX-WENDROFF TYPE TIME DISCRETIZATIONS FOR HAMILTON-JACOBI EQUATIONS
Jianxian Qiu
2007-01-01
In this paper, we use Hermite weighted essentially non-oscillatory (HWENO) schemes with a Lax-Wendroff time discretization procedure, termed HWENO-LW schemes, to solve Hamilton-Jacobi equations. The idea of the reconstruction in the HWENO schemes comes from the original WENO schemes, however both the function and its first derivative values are evolved in time and are used in the reconstruction. One major advantage of HWENO schemes is its compactness in the reconstruction. We explore the possibility in avoiding the nonlinear weights for part of the procedure, hence reducing the cost but still maintaining non-oscillatory properties for problems with strong discontinuous derivative. As a result,comparing with HWENO with Runge-Kutta time discretizations schemes (HWENO-RK) of Qiu and Shu [19] for Hamilton-Jacobi equations, the major advantages of HWENO-LW schemes are their saving of computational cost and their compactness in the reconstruction.Extensive numerical experiments are performed to illustrate the capability of the method.
Formal Reasoning About Finite-State Discrete-Time Markov Chains in HOL
Liya Liu; Osman Hasan; Sofiène Tahar
2013-01-01
Markov chains are extensively used in modeling different aspects of engineering and scientific systems,such as performance of algorithms and reliability of systems.Different techniques have been developed for analyzing Markovian models,for example,Markov Chain Monte Carlo based simulation,Markov Analyzer,and more recently probabilistic modelchecking.However,these techniques either do not guarantee accurate analysis or are not scalable.Higher-order-logic theorem proving is a formal method that has the ability to overcome the above mentioned limitations.However,it is not mature enough to handle all sorts of Markovian models.In this paper,we propose a formalization of Discrete-Time Markov Chain (DTMC) that facilitates formal reasoning about time-homogeneous finite-state discrete-time Markov chain.In particular,we provide a formal verification on some of its important properties,such as joint probabilities,Chapman-Kolmogorov equation,reversibility property,using higher-order logic.To demonstrate the usefulness of our work,we analyze two applications:a simplified binary communication channel and the Automatic Mail Quality Measurement protocol.
Policy iteration adaptive dynamic programming algorithm for discrete-time nonlinear systems.
Liu, Derong; Wei, Qinglai
2014-03-01
This paper is concerned with a new discrete-time policy iteration adaptive dynamic programming (ADP) method for solving the infinite horizon optimal control problem of nonlinear systems. The idea is to use an iterative ADP technique to obtain the iterative control law, which optimizes the iterative performance index function. The main contribution of this paper is to analyze the convergence and stability properties of policy iteration method for discrete-time nonlinear systems for the first time. It shows that the iterative performance index function is nonincreasingly convergent to the optimal solution of the Hamilton-Jacobi-Bellman equation. It is also proven that any of the iterative control laws can stabilize the nonlinear systems. Neural networks are used to approximate the performance index function and compute the optimal control law, respectively, for facilitating the implementation of the iterative ADP algorithm, where the convergence of the weight matrices is analyzed. Finally, the numerical results and analysis are presented to illustrate the performance of the developed method.
Observation of discrete time-crystalline order in a disordered dipolar many-body system
Choi, Soonwon; Choi, Joonhee; Landig, Renate; Kucsko, Georg; Zhou, Hengyun; Isoya, Junichi; Jelezko, Fedor; Onoda, Shinobu; Sumiya, Hitoshi; Khemani, Vedika; von Keyserlingk, Curt; Yao, Norman Y.; Demler, Eugene; Lukin, Mikhail D.
2017-03-01
Understanding quantum dynamics away from equilibrium is an outstanding challenge in the modern physical sciences. Out-of-equilibrium systems can display a rich variety of phenomena, including self-organized synchronization and dynamical phase transitions. More recently, advances in the controlled manipulation of isolated many-body systems have enabled detailed studies of non-equilibrium phases in strongly interacting quantum matter; for example, the interplay between periodic driving, disorder and strong interactions has been predicted to result in exotic ‘time-crystalline’ phases, in which a system exhibits temporal correlations at integer multiples of the fundamental driving period, breaking the discrete time-translational symmetry of the underlying drive. Here we report the experimental observation of such discrete time-crystalline order in a driven, disordered ensemble of about one million dipolar spin impurities in diamond at room temperature. We observe long-lived temporal correlations, experimentally identify the phase boundary and find that the temporal order is protected by strong interactions. This order is remarkably stable to perturbations, even in the presence of slow thermalization. Our work opens the door to exploring dynamical phases of matter and controlling interacting, disordered many-body systems.
Suzuki, Yasuhiko; Yamaguchi, Tomoyuki; Kim, Hyun; Yokoyama, Kazumasa; Nakajima, Chie
2014-12-01
As for the Mycobacterium leprae which is a causative agent of Hansen's disease, many studies had been done since it was identified in 1873. However, those studies, at the same time, experienced many struggles because of the difficulty of culture of M. leprae on the artificial growth media. Hence, the study of Hansen's disease progressed by taking the knowledge from the study of tuberculosis caused by the bacteria belonging to the same genus, genus Mycobacterium. For instance, the knowledge of mutations in specific genes responsible for rifampicin- and quinolone-resistance in M. tuberculosis led the elucidation of drug-resistant acquisition mechanism of M. leprae. Similarly, it is necessary for the researcher of Hansen's disease to get important information from the latest topic of the tuberculosis study and utilize them to the study of the disease.
Kaczorek Tadeusz
2016-06-01
Full Text Available The minimum energy control problem for the descriptor discrete-time linear systems by the use of Weierstrass-Kronecker decomposition is formulated and solved. Necessary and sufficient conditions for the reachability of descriptor discrete-time linear systems are given. A procedure for computation of optimal input and a minimal value of the performance index is proposed and illustrated by a numerical example.
Qi, Donglian; Liu, Meiqin; Qiu, Meikang; Zhang, Senlin
2010-08-01
This brief studies exponential H(infinity) synchronization of a class of general discrete-time chaotic neural networks with external disturbance. On the basis of the drive-response concept and H(infinity) control theory, and using Lyapunov-Krasovskii (or Lyapunov) functional, state feedback controllers are established to not only guarantee exponential stable synchronization between two general chaotic neural networks with or without time delays, but also reduce the effect of external disturbance on the synchronization error to a minimal H(infinity) norm constraint. The proposed controllers can be obtained by solving the convex optimization problems represented by linear matrix inequalities. Most discrete-time chaotic systems with or without time delays, such as Hopfield neural networks, cellular neural networks, bidirectional associative memory networks, recurrent multilayer perceptrons, Cohen-Grossberg neural networks, Chua's circuits, etc., can be transformed into this general chaotic neural network to be H(infinity) synchronization controller designed in a unified way. Finally, some illustrated examples with their simulations have been utilized to demonstrate the effectiveness of the proposed methods.
Ely, Gregory
2013-01-01
In this work we propose a novel algorithm for multiple-event localization for Hydraulic Fracture Monitoring (HFM) through the exploitation of the sparsity of the observed seismic signal when represented in a basis consisting of space time propagators. We provide explicit construction of these propagators using a forward model for wave propagation which depends non-linearly on the problem parameters - the unknown source location and mechanism of fracture, time and extent of event, and the locations of the receivers. Under fairly general assumptions and an appropriate discretization of these parameters we first build an over-complete dictionary of generalized Radon propagators and assume that the data is well represented as a linear superposition of these propagators. Exploiting this structure we propose sparsity penalized algorithms and workflow for super-resolution extraction of time overlapping multiple seismic events from single well data.
Approximately optimal tracking control for discrete time-delay systems with disturbances
Gongyou Tang; Huiying Sun; Haiping Pang
2008-01-01
Optimal tracking control (OTC) for discrete time-delay systems affected by persistent disturbances with quadratic performance index is considered. By introducing a sensitivity parameter, the original OTC problem is transformed into a series of two-point boundary value (TPBV) problems without time-advance or time-delay terms. The obtained OTC law consists of analytic feedforward and feedback terms and a compensation term which is the sum of an infinite series of adjoint vectors. The analytic feedforward and feedback terms can be found by solving a Riccati matrix equation and two Stein matrix equations. The compensation term can be obtained by using an iteration formula of the adjoint vectors. Observers are constructed to make the approximate OTC law physically realizable. A simulation example shows that the approximate approach is effective in tracking the reference input and robust with respect to exogenous persistent disturbances.
Adaptive learning with guaranteed stability for discrete-time recurrent neural networks
无
2007-01-01
To avoid unstable learning, a stable adaptive learning algorithm was proposed for discrete-time recurrent neural networks. Unlike the dynamic gradient methods, such as the backpropagation through time and the real time recurrent learning, the weights of the recurrent neural networks were updated online in terms of Lyapunov stability theory in the proposed learning algorithm, so the learning stability was guaranteed. With the inversion of the activation function of the recurrent neural networks, the proposed learning algorithm can be easily implemented for solving varying nonlinear adaptive learning problems and fast convergence of the adaptive learning process can be achieved. Simulation experiments in pattern recognition show that only 5 iterations are needed for the storage of a 15X15 binary image pattern and only 9 iterations are needed for the perfect realization of an analog vector by an equilibrium state with the proposed learning algorithm.
A Discrete-Time Queue with Balking, Reneging, and Working Vacations
Veena Goswami
2014-01-01
Full Text Available This paper presents an analysis of balking and reneging in finite-buffer discrete-time single server queue with single and multiple working vacations. An arriving customer may balk with a probability or renege after joining according to a geometric distribution. The server works with different service rates rather than completely stopping the service during a vacation period. The service times during a busy period, vacation period, and vacation times are assumed to be geometrically distributed. We find the explicit expressions for the stationary state probabilities. Various system performance measures and a cost model to determine the optimal service rates are presented. Moreover, some queueing models presented in the literature are derived as special cases of our model. Finally, the influence of various parameters on the performance characteristics is shown numerically.
A DISCRETE TIME TWO-LEVEL MIXED SERVICE PARALLEL POLLING MODEL
Guan Zheng; Zhao Dongfeng; Zhao Yifan
2012-01-01
We present a discrete time single-server two-level mixed service polling systems with two queue types,one center queue and N normal queues.Two-level means the center queue will be successive served after each normal queue.In the first level,server visits between the center queue and the normal queue.In the second level,normal queues are polled by a cyclic order.Mixed service means the service discipline are exhaustive for center queue,and parallel i-limited for normal queues.We propose an imbedded Markov chain framework to drive the closed-form expressions for the mean cycle time,mean queue length,and mean waiting time.Numerical examples demonstrate that theoretical and simulation results are identical the new system efficiently differentiates priorities.
He, Jianbin; Yu, Simin; Cai, Jianping
2016-12-01
Lyapunov exponent is an important index for describing chaotic systems behavior, and the largest Lyapunov exponent can be used to determine whether a system is chaotic or not. For discrete-time dynamical systems, the Lyapunov exponents are calculated by an eigenvalue method. In theory, according to eigenvalue method, the more accurate calculations of Lyapunov exponent can be obtained with the increment of iterations, and the limits also exist. However, due to the finite precision of computer and other reasons, the results will be numeric overflow, unrecognized, or inaccurate, which can be stated as follows: (1) The iterations cannot be too large, otherwise, the simulation result will appear as an error message of NaN or Inf; (2) If the error message of NaN or Inf does not appear, then with the increment of iterations, all Lyapunov exponents will get close to the largest Lyapunov exponent, which leads to inaccurate calculation results; (3) From the viewpoint of numerical calculation, obviously, if the iterations are too small, then the results are also inaccurate. Based on the analysis of Lyapunov-exponent calculation in discrete-time systems, this paper investigates two improved algorithms via QR orthogonal decomposition and SVD orthogonal decomposition approaches so as to solve the above-mentioned problems. Finally, some examples are given to illustrate the feasibility and effectiveness of the improved algorithms.
Fault-tolerant Control of Discrete-time LPV systems using Virtual Actuators and Sensors
Tabatabaeipour, Mojtaba; Stoustrup, Jakob; Bak, Thomas
2015-01-01
This paper proposes a new fault-tolerant control (FTC) method for discrete-time linear parameter varying (LPV) systems using a reconfiguration block. The basic idea of the method is to achieve the FTC goal without re-designing the nominal controller by inserting a reconfiguration block between th....... Finally, the effectiveness of the method is demonstrated via a numerical example and stator current control of an induction motor.......This paper proposes a new fault-tolerant control (FTC) method for discrete-time linear parameter varying (LPV) systems using a reconfiguration block. The basic idea of the method is to achieve the FTC goal without re-designing the nominal controller by inserting a reconfiguration block between......, it transforms the output of the controller for the faulty system such that the stability and performance goals are preserved. Input-to-state stabilizing LPV gains of the virtual actuator and sensor are obtained by solving linear matrix inequalities (LMIs). We show that separate design of these gains guarantees...
Balancing order and some other discrete-time properties of multiwavelets
Lebrun, Jerome; Vetterli, Martin
1999-10-01
This paper deals with multiwavelets and the different properties of approximation and smoothness that are associated with them. In particular, we focus on the important issue of the preservation of discrete time polynomial signals by multiwavelet based filter banks. We give here a precise definition of balancing for higher degree discrete time polynomial signals and link it to a very natural factorization of the lowpass refinement mask that is the counterpart of the well-known zeros at (pi) condition on the scaling function in the usual wavelet framework. This property of balancing proves them to be central to the issues of the preservation of smooth signals by the filter bank, the approximation power of the multiresolution analysis and the smoothness of the scaling functions and wavelets. Using these new results, we are able to construct a family of orthogonal multiwavelets with symmetries and compact support that is indexed by the order of balancing. We also give the minimum length orthogonal multiwavelets for any balancing order.
A discrete geometric approach to solving time independent Schrödinger equation
Specogna, Ruben; Trevisan, Francesco
2011-02-01
The time independent Schrödinger equation stems from quantum theory axioms as a partial differential equation. This work aims at providing a novel discrete geometric formulation of this equation in terms of integral variables associated with precise geometric elements of a pair of three-dimensional interlocked grids, one of them based on tetrahedra. We will deduce, in a purely geometric way, a computationally efficient discrete counterpart of the time independent Schrödinger equation in terms of a standard symmetric eigenvalue problem. Moreover boundary and interface conditions together with non homogeneity and anisotropy of the media involved are accounted for in a straightforward manner. This approach yields to a sensible computational advantage with respect to the finite element method, where a generalized eigenvalue problem has to be solved instead. Such a modeling tool can be used for analyzing a number of quantum phenomena in modern nano-structured devices, where the accounting of the real 3D geometry is a crucial issue.
Set-membership fuzzy filtering for nonlinear discrete-time systems.
Yang, Fuwen; Li, Yongmin
2010-02-01
This paper is concerned with the set-membership filtering (SMF) problem for discrete-time nonlinear systems. We employ the Takagi-Sugeno (T-S) fuzzy model to approximate the nonlinear systems over the true value of state and to overcome the difficulty with the linearization over a state estimate set rather than a state estimate point in the set-membership framework. Based on the T-S fuzzy model, we develop a new nonlinear SMF estimation method by using the fuzzy modeling approach and the S-procedure technique to determine a state estimation ellipsoid that is a set of states compatible with the measurements, the unknown-but-bounded process and measurement noises, and the modeling approximation errors. A recursive algorithm is derived for computing the ellipsoid that guarantees to contain the true state. A smallest possible estimate set is recursively computed by solving the semidefinite programming problem. An illustrative example shows the effectiveness of the proposed method for a class of discrete-time nonlinear systems via fuzzy switch.
Dynamics in a Discrete-time Predator-prey System with Allee Effect
Xian-wei Chen; Xiang-ling Fu; Zhu-jun Jing
2013-01-01
In this paper,dynamics of the discrete-time predator-prey system with Allee effect are investigated in detail.Conditions of the existence for flip bifurcation and Hopf bifurcation are derived by using the center manifold theorem and bifurcation theory,and then further illustrated by numerical simulations.Chaos in the sense of Marotto is proved by both analytical and numerical methods.Numerical simulations included bifurcation diagrams,Lyapunov exponents,phase portraits,fractal dimensions display new and rich dynamical behavior.More specifically,apart from stable dynamics,this paper presents the finding of chaos in the sense of Marotto together with a host of interesting phenomena connected to it.The analytic results and numerical simulations demostrates that the Allee constant plays a very important role for dynamical behavior.The dynamical behavior can move from complex instable states to stable states as the Allee constant increases (within a limited value).Combining the existing results in the current literature with the new results reported in this paper,a more complete understanding of the discrete-time predator-prey with Allee effect is given.
Maginnis, P. A.; West, M.; Dullerud, G. E.
2016-10-01
We propose an algorithm to accelerate Monte Carlo simulation for a broad class of stochastic processes. Specifically, the class of countable-state, discrete-time Markov chains driven by additive Poisson noise, or lattice discrete-time Markov chains. In particular, this class includes simulation of reaction networks via the tau-leaping algorithm. To produce the speedup, we simulate pairs of fair-draw trajectories that are negatively correlated. Thus, when averaged, these paths produce an unbiased Monte Carlo estimator that has reduced variance and, therefore, reduced error. Numerical results for three example systems included in this work demonstrate two to four orders of magnitude reduction of mean-square error. The numerical examples were chosen to illustrate different application areas and levels of system complexity. The areas are: gene expression (affine state-dependent rates), aerosol particle coagulation with emission and human immunodeficiency virus infection (both with nonlinear state-dependent rates). Our algorithm views the system dynamics as a "black-box", i.e., we only require control of pseudorandom number generator inputs. As a result, typical codes can be retrofitted with our algorithm using only minor changes. We prove several analytical results. Among these, we characterize the relationship of covariances between paths in the general nonlinear state-dependent intensity rates case, and we prove variance reduction of mean estimators in the special case of affine intensity rates.
Controlling influenza disease: Comparison between discrete time Markov chain and deterministic model
Novkaniza, F.; Ivana, Aldila, D.
2016-04-01
Mathematical model of respiratory diseases spread with Discrete Time Markov Chain (DTMC) and deterministic approach for constant total population size are analyzed and compared in this article. Intervention of medical treatment and use of medical mask included in to the model as a constant parameter to controlling influenza spreads. Equilibrium points and basic reproductive ratio as the endemic criteria and it level set depend on some variable are given analytically and numerically as a results from deterministic model analysis. Assuming total of human population is constant from deterministic model, number of infected people also analyzed with Discrete Time Markov Chain (DTMC) model. Since Δt → 0, we could assume that total number of infected people might change only from i to i + 1, i - 1, or i. Approximation probability of an outbreak with gambler's ruin problem will be presented. We find that no matter value of basic reproductive ℛ0, either its larger than one or smaller than one, number of infection will always tends to 0 for t → ∞. Some numerical simulation to compare between deterministic and DTMC approach is given to give a better interpretation and a better understanding about the models results.
System for time-discretized vacuum ultraviolet spectroscopy of spark breakdown in air
Ryberg, D.; Fierro, A.; Dickens, J.; Neuber, A. [Center for Pulsed Power and Power Electronics, Department of Electrical and Computer Engineering and Department of Physics, Texas Tech University, Lubbock, Texas 79409 (United States)
2014-10-15
A system for time-discretized spectroscopic measurements of the vacuum ultraviolet (VUV) emission from spark discharges in the 60-160 nm range has been developed for the study of early plasma-forming phenomena. The system induces a spark discharge in an environment close to atmospheric conditions created using a high speed puff value, but is otherwise kept at high vacuum to allow for the propagation of VUV light. Using a vertical slit placed 1.5 mm from the discharge the emission from a small cross section of the discharge is allowed to pass into the selection chamber consisting of a spherical grating, with 1200 grooves/mm, and an exit slit set to 100 μm. Following the exit slit is a photomultiplier tube with a sodium salicylate scintillator that is used for the time discretized measurement of the VUV signal with a temporal resolution limit of 10 ns. Results from discharges studied in dry air, Nitrogen, SF{sub 6}, and Argon indicate the emission of light with wavelengths shorter than 120 nm where the photon energy begins to approach the regime of direct photoionization.
System for time-discretized vacuum ultraviolet spectroscopy of spark breakdown in air
Ryberg, D.; Fierro, A.; Dickens, J.; Neuber, A.
2014-10-01
A system for time-discretized spectroscopic measurements of the vacuum ultraviolet (VUV) emission from spark discharges in the 60-160 nm range has been developed for the study of early plasma-forming phenomena. The system induces a spark discharge in an environment close to atmospheric conditions created using a high speed puff value, but is otherwise kept at high vacuum to allow for the propagation of VUV light. Using a vertical slit placed 1.5 mm from the discharge the emission from a small cross section of the discharge is allowed to pass into the selection chamber consisting of a spherical grating, with 1200 grooves/mm, and an exit slit set to 100 μm. Following the exit slit is a photomultiplier tube with a sodium salicylate scintillator that is used for the time discretized measurement of the VUV signal with a temporal resolution limit of 10 ns. Results from discharges studied in dry air, Nitrogen, SF6, and Argon indicate the emission of light with wavelengths shorter than 120 nm where the photon energy begins to approach the regime of direct photoionization.
Ma, Yuechao; Fu, Lei
2016-10-01
This study employs the multiple Lyapunov-like function method and the average dwell-time concept of switching signal to investigate the finite-time H∞ static output-feedback (SOF) control problem for a class of discrete-time switched singular time-delay systems subject to actuator saturation. First, sufficient conditions are presented to guarantee the discrete-time switched singular time-delay system regular, causal and finite-time boundedness. Meanwhile, sufficient conditions are presented to ensure the H∞ disturbance attenuation level, and the design method of H∞ SOF controller is developed by solving matrix inequalities optimisation problem without any decompositions of system matrices and equivalent transformation. Finally, the effectiveness and merit of the theoretical results are shown through some numerical examples and several vivid illustrations.
Yujian Guo
2016-01-01
Full Text Available A design strategy of optimal output regulators for dual-rate discrete-time systems, whose output sampling period is an integer multiple of the input updating period, is proposed. At first, by using the discrete lifting technique, the dual-rate discrete-time system is converted to a single-rate augmented system in form and the lifted state-space model is constructed. Correspondingly, the performance index of the original system is modified to the performance index of the single-rate augmented system. And the original problem is transformed into an output regulation problem for the augmented system. Then, according to the optimal regulator theory, an optimal output regulator for the dual-rate discrete-time system is derived. In the meantime, the existence conditions of the optimal output regulator are discussed. Finally, a numerical example is included to illustrate the effectiveness of the proposed method.
Syed Asif Ali Shah
2012-01-01
Full Text Available Flow time analysis is a powerful concept to analyze the flow time of any arriving customer in any system at any instant. A load management mechanism can be employed very effectively in any queueing system by utilizing a system which provides probability of dual service rate. In this paper, we develop and demonstrate the flow and service processes transition diagram to determine the flow time of a customer in a load management late arrival state dependent finite discrete time queueing system with dual service rate where customers are hypogeometrically distributed. We compute the probability mass function of each starting state and total probability mass function. The obtained analytical results are validated with simulation results for varying values of arrival and service probabilities.
Modeling commodity salam contract between two parties for discrete and continuous time series
Hisham, Azie Farhani Badrol; Jaffar, Maheran Mohd
2017-08-01
In order for Islamic finance to remain competitive as the conventional, there needs a new development of Islamic compliance product such as Islamic derivative that can be used to manage the risk. However, under syariah principles and regulations, all financial instruments must not be conflicting with five syariah elements which are riba (interest paid), rishwah (corruption), gharar (uncertainty or unnecessary risk), maysir (speculation or gambling) and jahl (taking advantage of the counterparty's ignorance). This study has proposed a traditional Islamic contract namely salam that can be built as an Islamic derivative product. Although a lot of studies has been done on discussing and proposing the implementation of salam contract as the Islamic product however they are more into qualitative and law issues. Since there is lack of quantitative study of salam contract being developed, this study introduces mathematical models that can value the appropriate salam price for a commodity salam contract between two parties. In modeling the commodity salam contract, this study has modified the existing conventional derivative model and come out with some adjustments to comply with syariah rules and regulations. The cost of carry model has been chosen as the foundation to develop the commodity salam model between two parties for discrete and continuous time series. However, the conventional time value of money results from the concept of interest that is prohibited in Islam. Therefore, this study has adopted the idea of Islamic time value of money which is known as the positive time preference, in modeling the commodity salam contract between two parties for discrete and continuous time series.
[Immune response of Hansen's disease. Review].
Rada, Elsa; Aranzazu, Nacarid; Convit, Jacinto
2009-12-01
Hansen's disease presents a wide spectrum of clinical and histopathological manifestations that reflect the nature of the immunological response of the host towards diverse Mycobacterium leprae components. The immunological system, composed by both innate and adaptive immunology, offers protection towards infections of various etiologies, among them bacterial. Bacteria, of course, have developed multiple strategies for evading host defenses, based on either very complex or simple mechanisms, but with a single purpose: to "resist" host attacks and to be able to survive. We have tried to summarize some recent studies in Hansen's disease, with more emphasis in the inmunology area. We think that in the future, all illnesses should also be very strongly related to other important aspects such as the social, environmental and economic, and whose development is not solved in a laboratory.
42 CFR 32.91 - Purchase of services for Hansen's disease patients.
2010-10-01
... 42 Public Health 1 2010-10-01 2010-10-01 false Purchase of services for Hansen's disease patients... MEDICAL CARE AND EXAMINATIONS MEDICAL CARE FOR PERSONS WITH HANSEN'S DISEASE AND OTHER PERSONS IN EMERGENCIES Persons with Hansen's Disease § 32.91 Purchase of services for Hansen's disease patients. Hansen's...
Hansen's disease mimicking a systemic vasculitis.
Sampaio, L; Silva, L; Terroso, G; Pimenta, S; Brandão, F; Pinto, J; Prisca, A; Brito, J; Ventura, F
2011-01-01
Hansen's disease, caused by Mycobacterium leprae, classically presents with cutaneous and neurological manifestations. Rheumatologic manifestations present in 1 to 5% of the patients, and include arthritis, arthralgias, Charcot arthropathy, erythema nodosum and vasculitis. We report a case of a 86 year old woman with polyarthritis, subcutaneous nodules and leg ulcers whose differential diagnosis included primary vasculitis and diffuse connective tissue diseases and ended to be leprosy in a non endemic country.
Survival, extinction and approximation of discrete-time branching random walks
Zucca, Fabio
2010-01-01
We consider a general discrete-time branching random walk on a countable set X. We relate local and global survival with suitable inequalities involving the first-moment matrix M of the process. In particular we prove that, while the local behavior is characterized by M, the global behavior cannot be completely described in terms of properties involving M alone. Moreover we show that locally surviving branching random walks can be approximated by sequences of spatially confined branching random walks which eventually survive locally if the (possibly finite) state space is large enough. An analogous result can be achieved by approximating a branching random walk by a sequence of multitype contact processes and allowing a sufficiently large number of particles per site. We compare these results with the ones obtained in the continuous-time case and we give some examples and counterexamples.
Performance limitations in the tracking and regulation problem for discrete-time systems.
Jiang, Xiao-Wei; Guan, Zhi-Hong; Yuan, Fu-Shun; Zhang, Xian-He
2014-03-01
In this paper, the optimal tracking and regulation performance of discrete-time, multi-input multi-output, linear time-invariant systems is investigated. The control signal is influenced by the external disturbance, and the output feedback is subjected to an additive white Gaussian noise (AWGN) corruption. The tracking error with channel input power constraint and the output regulation with control energy constraint are adopted as the measure of tracking and regulation performance respectively, which can be obtained by searching through all stabilizing two-parameter controllers. Both results demonstrate that the performance is closely related to locations and directions of the nonminimum phase zeros, unstable poles of the plant and may be badly degraded by external disturbance and AWGN.
Khandekar, A A; Malwatkar, G M; Patre, B M
2013-01-01
In this paper, a discrete time sliding mode controller (DSMC) is proposed for higher order plus delay time (HOPDT) processes. A sliding mode surface is selected as a function of system states and error and the tuning parameters of sliding mode controller are determined using dominant pole placement strategy. The condition for the existence of stable sliding mode is obtained by using Lyapunov function. The proposed method is applicable to HOPDT processes with oscillatory and integrating behavior, open loop instability or non-minimum phase characteristics and works satisfactory under the effect of parametric uncertainty. The method does not require reduced order model and provides simple way to design the controllers. The simulation and experimentation results show that the proposed method ensures desired tracking dynamics.
Discrete-time filtering for nonlinear polynomial systems over linear observations
Hernandez-Gonzalez, M.; Basin, M. V.
2014-07-01
This paper designs a discrete-time filter for nonlinear polynomial systems driven by additive white Gaussian noises over linear observations. The solution is obtained by computing the time-update and measurement-update equations for the state estimate and the error covariance matrix. A closed form of this filter is obtained by expressing the conditional expectations of polynomial terms as functions of the estimate and the error covariance. As a particular case, a third-degree polynomial is considered to obtain the finite-dimensional filtering equations. Numerical simulations are performed for a third-degree polynomial system and an induction motor model. Performance of the designed filter is compared with the extended Kalman one to verify its effectiveness.
Tang Yang; Zhong Hui-Huang; Fang Jian-An
2008-01-01
A general model of linearly stochastically coupled identical connected neural networks with hybrid coupling is proposed,which is composed of constant coupling,coupling discrete time-varying delay and coupling distributed timevarying delay.All the coupling terms are subjected to stochastic disturbances described in terms of Brownian motion,which reflects a more realistic dynamical behaviour of coupled systems in practice.Based on a simple adaptive feedback controller and stochastic stability theory,several sufficient criteria are presented to ensure the synchronization of linearly stochastically coupled complex networks with coupling mixed time-varying delays.Finally,numerical simulatious illustrated by scale-free complex networks verify the effectiveness of the proposed controllers.
Simultaneous Robust Fault and State Estimation for Linear Discrete-Time Uncertain Systems
Feten Gannouni
2017-01-01
Full Text Available We consider the problem of robust simultaneous fault and state estimation for linear uncertain discrete-time systems with unknown faults which affect both the state and the observation matrices. Using transformation of the original system, a new robust proportional integral filter (RPIF having an error variance with an optimized guaranteed upper bound for any allowed uncertainty is proposed to improve robust estimation of unknown time-varying faults and to improve robustness against uncertainties. In this study, the minimization problem of the upper bound of the estimation error variance is formulated as a convex optimization problem subject to linear matrix inequalities (LMI for all admissible uncertainties. The proportional and the integral gains are optimally chosen by solving the convex optimization problem. Simulation results are given in order to illustrate the performance of the proposed filter, in particular to solve the problem of joint fault and state estimation.
Decentralized Observer with a Consensus Filter for Distributed Discrete-Time Linear Systems
Acikmese, Behcet; Mandic, Milan
2011-01-01
This paper presents a decentralized observer with a consensus filter for the state observation of a discrete-time linear distributed systems. In this setup, each agent in the distributed system has an observer with a model of the plant that utilizes the set of locally available measurements, which may not make the full plant state detectable. This lack of detectability is overcome by utilizing a consensus filter that blends the state estimate of each agent with its neighbors' estimates. We assume that the communication graph is connected for all times as well as the sensing graph. It is proven that the state estimates of the proposed observer asymptotically converge to the actual plant states under arbitrarily changing, but connected, communication and sensing topologies. As a byproduct of this research, we also obtained a result on the location of eigenvalues, the spectrum, of the Laplacian for a family of graphs with self-loops.
SU Cheng-li; WANG Shu-qing
2006-01-01
An extended robust model predictive control approach for input constrained discrete uncertain nonlinear systems with time-delay based on a class of uncertain T-S fuzzy models that satisfy sector bound condition is presented. In this approach, the minimization problem of the "worst-case" objective function is converted into the linear objective minimization problem involving linear matrix inequalities (LMIs) constraints. The state feedback control law is obtained by solving convex optimization of a set of LMIs. Sufficient condition for stability and a new upper bound on robust performance index are given for these kinds of uncertain fuzzy systems with state time-delay. Simulation results of CSTR process show that the proposed robust predictive control approach is effective and feasible.
Infinite horizon self-learning optimal control of nonaffine discrete-time nonlinear systems.
Wei, Qinglai; Liu, Derong; Yang, Xiong
2015-04-01
In this paper, a novel iterative adaptive dynamic programming (ADP)-based infinite horizon self-learning optimal control algorithm, called generalized policy iteration algorithm, is developed for nonaffine discrete-time (DT) nonlinear systems. Generalized policy iteration algorithm is a general idea of interacting policy and value iteration algorithms of ADP. The developed generalized policy iteration algorithm permits an arbitrary positive semidefinite function to initialize the algorithm, where two iteration indices are used for policy improvement and policy evaluation, respectively. It is the first time that the convergence, admissibility, and optimality properties of the generalized policy iteration algorithm for DT nonlinear systems are analyzed. Neural networks are used to implement the developed algorithm. Finally, numerical examples are presented to illustrate the performance of the developed algorithm.
Perturbed dynamics of discrete-time switched nonlinear systems with delays and uncertainties.
Liu, Xingwen; Cheng, Jun
2016-05-01
This paper addresses the dynamics of a class of discrete-time switched nonlinear systems with time-varying delays and uncertainties and subject to perturbations. It is assumed that the nominal switched nonlinear system is robustly uniformly exponentially stable. It is revealed that there exists a maximal Lipschitz constant, if perturbation satisfies a Lipschitz condition with any Lipschitz constant less than the maximum, then the perturbed system can preserve the stability property of the nominal system. In situations where the perturbations are known, it is proved that there exists an upper bound of coefficient such that the perturbed system remains exponentially stable provided that the perturbation is scaled by any coefficient bounded by the upper bound. A numerical example is provided to illustrate the proposed theoretical results.
A multi-objective dynamic programming approach to constrained discrete-time optimal control
Driessen, B.J.; Kwok, K.S.
1997-09-01
This work presents a multi-objective differential dynamic programming approach to constrained discrete-time optimal control. In the backward sweep of the dynamic programming in the quadratic sub problem, the sub problem input at a stage or time step is solved for in terms of the sub problem state entering that stage so as to minimize the summed immediate and future cost subject to minimizing the summed immediate and future constraint violations, for all such entering states. The method differs from previous dynamic programming methods, which used penalty methods, in that the constraints of the sub problem, which may include terminal constraints and path constraints, are solved exactly if they are solvable; otherwise, their total violation is minimized. Again, the resulting solution of the sub problem is an input history that minimizes the quadratic cost function subject to being a minimizer of the total constraint violation. The expected quadratic convergence of the proposed algorithm is demonstrated on a numerical example.
M. A. Hussain
2014-01-01
Full Text Available This paper discusses the discrete-time stability analysis of a neural network inverse model control strategy for a relative order two nonlinear system. The analysis is done by representing the closed loop system in state space format and then analyzing the time derivative of the state trajectory using Lyapunov’s direct method. The analysis shows that the tracking output error of the states is confined to a ball in the neighborhood of the equilibrium point where the size of the ball is partly dependent on the accuracy of the neural network model acting as the controller. Simulation studies on the two-tank-in-series system were done to complement the stability analysis and to demonstrate some salient results of the study.
A discrete adaptive near-time optimum control for the plasma vertical position in a Tokamak
Scibile, L
2001-01-01
A nonlinear controller for the plasma vertical position in a Tokamak, based on a discrete-time adaptive near time optimum control algorithm (DANTOC) is designed to stabilize the system and to maximize the state-space region over which stability can be guaranteed. The controller is also robust to the edge localized modes (ELMs) and the 600 Hz noise from the thyristor power supplies that are the primary source of disturbances and measurement noise. The controller is tested in simulation for the JET Tokamak and the results confirm its efficacy in controlling the vertical position for different plasma configurations. The controller is also tested experimentally on a real Tokamak, COMPASS-D, and the results demonstrate the improvement with respect to a simple linear PD controller in the presence of disturbances and measurement noise. The emphasis of the is on the development of the design methodology. (38 refs).
Liyun Su
2011-01-01
Full Text Available In order to suppress the interference of the strong fractional noise signal in discrete-time ultrawideband (UWB systems, this paper presents a new UWB multi-scale Kalman filter (KF algorithm for the interference suppression. This approach solves the problem of the narrowband interference (NBI as nonstationary fractional signal in UWB communication, which does not need to estimate any channel parameter. In this paper, the received sampled signal is transformed through multiscale wavelet to obtain a state transition equation and an observation equation based on the stationarity theory of wavelet coefficients in time domain. Then through the Kalman filter method, fractional signal of arbitrary scale is easily figured out. Finally, fractional noise interference is subtracted from the received signal. Performance analysis and computer simulations reveal that this algorithm is effective to reduce the strong fractional noise when the sampling rate is low.
Novel l2-l∞ controller design for LPV discrete time-delay systems
Wang Junling; Wang Changhong; Li Yanhui; Gao Huijun
2005-01-01
One of the first attempts to derive energy-to-peak performance criteria and state-feedback controller design problem for linear parameter-varying discrete time systems with time delay is provided. Firstly, we present a parameterdependent l2-l∞ performance criterion using a parameter-dependent Lyapunov function. Upon the conditions addressed,an improved parameter-dependent l2-l∞ performance criterion is established by the introduction of a slack variable,which exhibits a kind of decoupling between Lyapunov functions and system matrices. This kind of decoupling enables us to obtain more easily tractable conditions for analysis and synthesis problems. Then, the corresponding parameter-dependent state-feedback controller design is investigated upon these performance criteria, with sufficient conditions obtained for the existence of admissible controllers in terms of parameterized linear matrix inequalities. Finally, a numerical example is provided to illustrate the feasibility and advantage of the proposed controller design procedure.
Discrete-time dynamic network model for the spread of susceptible-infective-recovered diseases
Chauhan, Sanjeev Kumar
2017-07-01
We propose a discrete-time dynamic network model describing the spread of susceptible-infective-recovered diseases in a population. We consider the case in which the nodes in the network change their links due to social mixing dynamics as well as in response to the disease. The model shows the behavior that, as we increase social mixing, disease spread is inhibited in certain cases, while in other cases it is enhanced. We also extend this dynamic network model to take into account the case of hidden infection. Here we find that, as expected, the disease spreads more readily if there is a time period after contracting the disease during which an individual is infective but is not known to have the disease.
A Discrete Time Markov Chain Model for High Throughput Bidirectional Fano Decoders
Xu, Ran; Morris, Kevin; Kocak, Taskin
2010-01-01
The bidirectional Fano algorithm (BFA) can achieve at least two times decoding throughput compared to the conventional unidirectional Fano algorithm (UFA). In this paper, bidirectional Fano decoding is examined from the queuing theory perspective. A Discrete Time Markov Chain (DTMC) is employed to model the BFA decoder with a finite input buffer. The relationship between the input data rate, the input buffer size and the clock speed of the BFA decoder is established. The DTMC based modelling can be used in designing a high throughput parallel BFA decoding system. It is shown that there is a tradeoff between the number of BFA decoders and the input buffer size, and an optimal input buffer size can be chosen to minimize the hardware complexity for a target decoding throughput in designing a high throughput parallel BFA decoding system.
Bifurcation and complex dynamics of a discrete-time predator-prey system
S. M. Sohel Rana
2015-06-01
Full Text Available In this paper, we investigate the dynamics of a discrete-time predator-prey system of Holling-I type in the closed first quadrant R+2. The existence and local stability of positive fixed point of the discrete dynamical system is analyzed algebraically. It is shown that the system undergoes a flip bifurcation and a Neimark-Sacker bifurcation in the interior of R+2 by using bifurcation theory. It has been found that the dynamical behavior of the model is very sensitive to the parameter values and the initial conditions. Numerical simulation results not only show the consistence with the theoretical analysis but also display the new and interesting dynamic behaviors, including phase portraits, period-9, 10, 20-orbits, attracting invariant circle, cascade of period-doubling bifurcation from period-20 leading to chaos, quasi-periodic orbits, and sudden disappearance of the chaotic dynamics and attracting chaotic set. In particular, we observe that when the prey is in chaotic dynamic, the predator can tend to extinction or to a stable equilibrium. The Lyapunov exponents are numerically computed to characterize the complexity of the dynamical behaviors. The analysis and results in this paper are interesting in mathematics and biology.
Qiu Bo
2008-01-01
Full Text Available Binaural cue coding (BCC is an efficient technique for spatial audio rendering by using the side information such as interchannel level difference (ICLD, interchannel time difference (ICTD, and interchannel correlation (ICC. Of the side information, the ICTD plays an important role to the auditory spatial image. However, inaccurate estimation of the ICTD may lead to the audio quality degradation. In this paper, we develop a novel ICTD estimation algorithm based on the nonuniform discrete Fourier transform (NDFT and integrate it with the BCC approach to improve the decoded auditory image. Furthermore, a new subjective assessment method is proposed for the evaluation of auditory image widths of decoded signals. The test results demonstrate that the NDFT-based scheme can achieve much wider and more externalized auditory image than the existing BCC scheme based on the discrete Fourier transform (DFT. It is found that the present technique, regardless of the image width, does not deteriorate the sound quality at the decoder compared to the traditional scheme without ICTD estimation.
Bo Qiu
2008-05-01
Full Text Available Binaural cue coding (BCC is an efficient technique for spatial audio rendering by using the side information such as interchannel level difference (ICLD, interchannel time difference (ICTD, and interchannel correlation (ICC. Of the side information, the ICTD plays an important role to the auditory spatial image. However, inaccurate estimation of the ICTD may lead to the audio quality degradation. In this paper, we develop a novel ICTD estimation algorithm based on the nonuniform discrete Fourier transform (NDFT and integrate it with the BCC approach to improve the decoded auditory image. Furthermore, a new subjective assessment method is proposed for the evaluation of auditory image widths of decoded signals. The test results demonstrate that the NDFT-based scheme can achieve much wider and more externalized auditory image than the existing BCC scheme based on the discrete Fourier transform (DFT. It is found that the present technique, regardless of the image width, does not deteriorate the sound quality at the decoder compared to the traditional scheme without ICTD estimation.
Flach, S
1998-01-01
Nonlinear classical Hamiltonian lattices exhibit generic solutions in the form of discrete breathers. These solutions are time-periodic and (typically exponentially) localized in space. The lattices exhibit discrete translational symmetry. Discrete breathers are not confined to certain lattice dimensions. Necessary ingredients for their occurence are the existence of upper bounds on the phonon spectrum (of small fluctuations around the groundstate) of the system as well as the nonlinearity in the differential equations. We will present existence proofs, formulate necessary existence conditions, and discuss structural stability of discrete breathers. The following results will be also discussed: the creation of breathers through tangent bifurcation of band edge plane waves; dynamical stability; details of the spatial decay; numerical methods of obtaining breathers; interaction of breathers with phonons and electrons; movability; influence of the lattice dimension on discrete breather properties; quantum lattic...
Dong, Shuai; Yu, Lingjie; Zhang, Wei; Wu, Junjie; Zhang, Weijun; You, Lixing; Huang, Yidong
2015-03-01
In this paper, a generation scheme for telecom band hyper-entanglement is proposed and demonstrated based on the vector spontaneous four wave mixing (SFWM) processes in optical fibers. Two kinds of two-photon states are generated, one is hyper-entangled in the degree of freedoms (DOFs) of energy-time and polarization, the other is hyper-entangled in DOFs of energy-time and discrete-frequency. Experiments of Franson-type interference, two-photon interference under non-orthogonal polarization bases and spatial quantum beating are realized to demonstrate the entanglement in energy-time, polarization and frequency, respectively. This scheme provides a simple way to realize telecom band hyper-entanglement, which has potential for large geographic-scale applications of quantum communication and quantum information over optical fibers.
无
2011-01-01
In this paper,a class of discrete time non-autonomous competing system with feedback controls is considered. With the help of differential equations with piecewise constant arguments,we first propose a discrete model of a continuous non-autonomous competing system with feedback controls. Then,using the coincidence degree and the related continuation theorem as well as some priori estimations,a suficient condition for the existence of positive solutions to difference equations is obtained.
Adaptive band-limited disturbance rejection in linear discrete-time systems
Foued Ben-Amara
1995-01-01
Full Text Available The problem of adaptively rejecting a disturbance consisting of a linear combination of sinusoids with unknown and/or time varying frequencies for SISO LTI discrete-time systems is considered. The rejection of the disturbance input is achieved by constructing the set of stabilizing controllers using the Youla parametrization and adjusting the Youla parameter to achieve asymptotic disturbance rejection. The first main result in this paper concerns off-line controller design where a controller that achieves regulation is numerically designed off-line based on the assumption that only the sequence of discrete disturbance input values (as opposed to a model of the disturbance is available. A least squares based optimization algorithm is used in the controller design. As expected, it is shown, under some mild assumptions, that if the off-line designed controller achieves regulation, then it must include a model of the disturbance input. The second main result concerns on-line controller design where recursive versions of the off-line algorithm used above for controller design are presented and their convergence properties analyzed. Conditions under which the on-line algorithms yield an asymptotic controller that achieves regulation are presented. Conditions both for the case where the disturbance input properties are constant but unknown and for the case where they are unknown and time-varying are given. The on-line controller construction amounts to an adaptive implementation of the Internal Model Principle. The performance robustness of the off-line designed controller in the face of plant model uncertainties is investigated. It is shown, under some mild assumptions, that performance robustness is realized provided internal stability is maintained. The performance of the adaptation algorithms is illustrated through a simulation example.
Use of Hansen Solubility Parameters in Fuel Treatment Processes
2014-03-17
Charts 3. DATES COVERED (From - To) Jan 2014- Mar 2014 4. TITLE AND SUBTITLE 5a. CONTRACT NUMBER In-House Use of Hansen Solubility Parameters in...distribution is unlimited. AFRL Public Affairs Clearance # USE OF HANSEN SOLUBILITY PARAMETERS IN FUEL TREATMENT PROCESSES 17 March 2014 Andrew J...Treatment Needs – Hansen Solubility Parameters • Dyes – Experimental HSP Determination – Extrapolation to Other Dyes • Predictions for Extraction Fluids
Incorporation of Time Delayed Measurements in a Discrete-time Kalman Filter
Larsen, Thomas Dall; Andersen, Nils Axel; Ravn, Ole;
1998-01-01
In many practical systems there is a delay in some of the sensor devices, for instance vision measurements that may have a long processing time. How to fuse these measurements in a Kalman filter is not a trivial problem if the computational delay is critical. Depending on how much time...... using past and present estimates of the Kalman filter and calculating an optimal gain for this extrapolated measurement...... there is at hand, the designer has to make trade offs between optimality and computational burden of the filter. In this paper various methods in the literature along with a new method proposed by the authors will be presented and compared. The new method is based on “extrapolating” the measurement to present time...
Cheiridium tetrophthalmum Daday, a new synonym of Larca lata (Hansen (Pseudoscorpiones, Larcidae
Harvey, Mark S.
2011-07-01
Full Text Available Cheiridium tetrophthalmum Daday, 1889 is removed from the synonymy of Geogarypus minor (L. Koch, 1873, and treated as a junior synonym of Larca lata (Hansen, 1884. The distribution of Larca lata and Geogarypus minor is documented, and L. lata is recorded from Hungary for the first time.
Schwarz, O.; Strumpf, M.
The literary assets of Peter Andreas Hansen are deposited in the Staatsarchiv Hamburg, the Forschungs- und Landesbibliothek Gotha and the Thüringer Staatsarchiv Gotha. They were never systematically investigated. The authors present here some results of a first evaluation. It was possible to reconstruct the historical events with regard to the maintenance of the Astronomische Nachrichten and the Altona observatory in 1854. Hansen was a successful teacher for many young astronomers. His way of stimulating the evolution of astronomy followed Zach's tradition.
Design and Stability of Discrete-Time Quantum Filters with Measurement Imperfections
Somaraju, Abhinav; Sayrin, Clement; Rouchon, Pierre
2011-01-01
This work considers the theory underlying a discrete-time quantum filter recently used in a quantum feedback experiment. It proves that this filter taking into account decoherence and measurement errors is optimal and stable. We present the general framework underlying this filter and show that it corresponds to a recursive expression of the least-square optimal estimation of the density operator in the presence of measurement imperfections. By measurement imperfections, we mean in a very general sense unread measurement performed by the environment (decoherence) and active measurement performed by non-ideal detectors. However, we assume to know precisely all the Kraus operators and also the detection error rates. Such recursive expressions combine well known methods from quantum filtering theory and classical probability theory (Bayes' law). We then demonstrate that such a recursive filter is always stable with respect to its initial condition: the fidelity between the optimal filter state (when the initial ...
Yunjie Wu
2013-01-01
Full Text Available In order to improve the tracking accuracy of flight simulator and expend its frequency response, a multirate-sampling-method-based discrete-time chattering free sliding mode control is developed and imported into the systems. By constructing the multirate sampling sliding mode controller, the flight simulator can perfectly track a given reference signal with an arbitrarily small dynamic tracking error, and the problems caused by a contradiction of reference signal period and control period in traditional design method can be eliminated. It is proved by theoretical analysis that the extremely high dynamic tracking precision can be obtained. Meanwhile, the robustness is guaranteed by sliding mode control even though there are modeling mismatch, external disturbances and measure noise. The validity of the proposed method is confirmed by experiments on flight simulator.
Zhizheng Wu
2012-01-01
Full Text Available Motivated by a class of contact vibration control problems in mechanical systems, this paper considers a regulation problem for discrete-time switched bimodal linear systems where it is desired to achieve output regulation against partially known deterministic and unknown random exogenous signals. First, a set of observer-based Youla parameterized stabilizing controllers is constructed, based on which the regulation conditions for the switched system against the deterministic signals along with an H2 performance constraint against the unknown random signals are derived. Then a corresponding regulator synthesis algorithm is developed based on solving properly formulated linear matrix inequalities. The proposed regulator is successfully evaluated on an experimental setup involving a switched bimodal mechanical system subject to contact vibrations, hence, demonstrating the effectiveness of the proposed regulation approach.
A Versatile Discrete-Time Approach for Modeling Switch-Mode Controllers
Risbo, Lars; Høyerby, Mikkel Christian Wendelboe; Andersen, Michael Andreas E.
2008-01-01
is demonstrated to allow very precise predictions of comparator frequency response in a variety of control schemes. In the presented work, the modeling method is exemplified for the standard PWM and two different self-oscillating (a.k.a. sliding mode) control schemes. The proposed method is believed......This paper presents a universal method for modeling the frequency response of comparators in switchmode controllers. As the main non-linearity in most switchmode controllers, understanding the comparator is the key to understanding the system. Based on discrete-time modeling, the proposed method...... by the authors to be the first method that is able to handle these fundamentally different control schemes within a single modeling framework. Experimentally measured output impedance and comparator magnitude responses are compared to the model results. Great accuracy is achieved from DC to frequencies far...
Sliding Mode Control for Discrete-Time Systems With Markovian Packet Dropouts.
Song, Heran; Chen, Shih-Chi; Yam, Yeung
2016-07-09
This paper presents the design of a sliding mode controller for networked control systems subject to successive Markovian packet dropouts. This paper adopts the Gilbert-Elliott channel model to describe the temporal correlation among packet losses, and proposes an update scheme to select the assumed available states for use in a sliding mode control law. A technique used in the theory of discrete-time Markov jump linear systems is applied to tackle the effect of the packet losses. This involves introducing a couple of Lyapunov functions dependent on the indicator functions of the instantaneous packet loss, and proving that the sliding mode controller is able to drive the system state trajectories into the neighborhood of the designed integral sliding surface in mean-square sense given that the corresponding Lyapunov inequalities are satisfied. The system is guaranteed thereafter to remain inside the neighborhood of the sliding surface. Simulated case studies are presented to illustrate the effectiveness of the control law.
Variable speed wind turbine control by discrete-time sliding mode approach.
Torchani, Borhen; Sellami, Anis; Garcia, Germain
2016-05-01
The aim of this paper is to propose a new design variable speed wind turbine control by discrete-time sliding mode approach. This methodology is designed for linear saturated system. The saturation constraint is reported on inputs vector. To this end, the back stepping design procedure is followed to construct a suitable sliding manifold that guarantees the attainment of a stabilization control objective. It is well known that the mechanisms are investigated in term of the most proposed assumptions to deal with the damping, shaft stiffness and inertia effect of the gear. The objectives are to synthesize robust controllers that maximize the energy extracted from wind, while reducing mechanical loads and rotor speed tracking combined with an electromagnetic torque. Simulation results of the proposed scheme are presented.
Approximate optimal control for a class of nonlinear discrete-time systems with saturating actuators
2008-01-01
In this paper, we solve the approximate optimal control problem for a class of nonlinear discrete-time systems with saturating actu- ators via greedy iterative Heuristic Dynamic Programming (GI-HDP) algorithm. In order to deal with the saturating problem of actu- ators, a novel nonquadratic functional is developed. Based on the nonquadratic functional, the GI-HDP algorithm is introduced to obtain the optimal saturated controller with a rigorous convergence analysis. For facilitating the implementation of the iterative algo- rithm, three neural networks are used to approximate the value function, compute the optimal control policy and model the unknown plant, respectively. An example is given to demonstrate the validity of the proposed optimal control scheme.
Transformation Matrix for Time Discretization Based on Tustin’s Method
Yiming Jiang
2014-01-01
Full Text Available This paper studies rules in transformation of transfer function through time discretization. A method of using transformation matrix to realize bilinear transform (also known as Tustin’s method is presented. This method can be described as the conversion between the coefficients of transfer functions, which are expressed as transform by certain matrix. For a polynomial of degree n, the corresponding transformation matrix of order n exists and is unique. Furthermore, the transformation matrix can be decomposed into an upper triangular matrix multiplied with another lower triangular matrix. And both have obvious regularity. The proposed method can achieve rapid bilinear transform used in automatic design of digital filter. The result of numerical simulation verifies the correctness of the theoretical results. Moreover, it also can be extended to other similar problems. Example in the last throws light on this point.
Tabatabaeipour, Seyed Mojtaba; Bak, Thomas
2012-01-01
In this paper we consider the problem of fault estimation and accommodation for discrete time piecewise linear systems. A robust fault estimator is designed to estimate the fault such that the estimation error converges to zero and H∞ performance of the fault estimation is minimized. Then......, the estimate of fault is used to compensate for the effect of the fault. Hence, using the estimate of fault, a fault tolerant controller using a piecewise linear static output feedback is designed such that it stabilizes the system and provides an upper bound on the H∞ performance of the faulty system....... Sufficient conditions for the existence of robust fault estimator and fault tolerant controller are derived in terms of linear matrix inequalities. Upper bounds on the H∞ performance can be minimized by solving convex optimization problems with linear matrix inequality constraints. The efficiency...
Fast state estimation subject to random data loss in discrete-time nonlinear stochastic systems
Mahdi Alavi, S. M.; Saif, Mehrdad
2013-12-01
This paper focuses on the design of the standard observer in discrete-time nonlinear stochastic systems subject to random data loss. By the assumption that the system response is incrementally bounded, two sufficient conditions are subsequently derived that guarantee exponential mean-square stability and fast convergence of the estimation error for the problem at hand. An efficient algorithm is also presented to obtain the observer gain. Finally, the proposed methodology is employed for monitoring the Continuous Stirred Tank Reactor (CSTR) via a wireless communication network. The effectiveness of the designed observer is extensively assessed by using an experimental tested-bed that has been fabricated for performance evaluation of the over wireless-network estimation techniques under realistic radio channel conditions.
Observer-based fault detection scheme for a class of discrete time-delay systems
Zhong Maiying(钟麦英); Zhang Chenghui(张承慧); Ding Steven X; Lam James
2004-01-01
In this contribution, robust fault detection problems for discrete time-delay systems with l2-norm bounded un-known inputs are studied. The basic idea of our study is first to introduce a state-memoryless observer-based fault detec-tion filter (FDF) as the residual generator and then to formulate such a FDF design problem as an H∞ optimization prob-lem in the sense of increasing the sensitivity of residual to the faults, while simultaneously enhancing the robustness of residual to unknown input as well as plant input. The main results consist of the formulation of such a residual generation optimization problem, solvability conditions and the derivation of an analytic solution. The residual evaluation problem is also considered, which includes the determination of residual evaluation function and threshold. A numerical example is used to demonstrate the proposed fault detection scheme.
Multiple periodic solutions for a discrete time model of plankton allelopathy
Zhang Jianbao; Fang Hui
2006-01-01
We study a discrete time model of the growth of two species of plankton with competitive and allelopathic effects on each other N1(k+1) = N1(k)exp{r1(k)-a11(k)N1(k)-a12(k)N2(k)-b1(k)N1(k)N2(k)}, N2(k+1) = N2(k)exp{r2(k)-a21(k)N2(k)-b2(k)N1(k)N1(k)N2(k)}. A set of sufficient conditions is obtained for the existence of multiple positive periodic solutions for this model. The approach is based on Mawhin's continuation theorem of coincidence degree theory as well as some a priori estimates. Some...
Guaranteed cost control with constructing switching law of uncertain discrete-time switched systems
Zhang Ying; Duan Guangren
2007-01-01
A guaranteed cost control problem for a class of linear discrete-time switched systems with normbounded uncertainties is considered in this article. The purpose is to construct a switching rule and design a state feedback control law, such that, the closed-loop system is asymptotically stable and the closed-loop cost function value is not more than a specified upper bound for all admissible uncertainties under the constructed switching rule.A sufficient condition for the existence of guaranteed cost controllers and switching rules is derived based on the Lyapunov theory together with the linear matrix inequality (LMI) approach. Furthermore, a convex optimization problem with LMI constraints is formulated to select the suboptimal guaranteed cost controller. A numerical example demonstrates the validity of the proposed design approach.
Guaranteed cost control with pole constraints for uncertain discrete-time switched systems
Ying ZHANG; Guangren DUAN; Liyan CHEN
2009-01-01
For a class of discrete-time switched systems with norm-bounded uncertainties and a quadratic cost index, the problem of designing a guaranteed cost state feedback controller with pole constraints is considered. A sufficient condition on the existence of robust guaranteed controllers is derived by a quadratic Lyapunov function approach together with linear matrix inequality (LMI)technique. Based on a constructed switching law, the closed-loop system is quadratic D-stable and the closedloop cost function value is not more than a specified upper bound. Furthermore, the design of suboptimal guaranteed cost controllers is turned into a convex optimization problem with linear matrix inequalities constraints. A numerical example demonstrates the effect of the proposed design approach.
Zhong, Xiangnan; He, Haibo; Zhang, Huaguang; Wang, Zhanshan
2014-12-01
In this paper, we develop and analyze an optimal control method for a class of discrete-time nonlinear Markov jump systems (MJSs) with unknown system dynamics. Specifically, an identifier is established for the unknown systems to approximate system states, and an optimal control approach for nonlinear MJSs is developed to solve the Hamilton-Jacobi-Bellman equation based on the adaptive dynamic programming technique. We also develop detailed stability analysis of the control approach, including the convergence of the performance index function for nonlinear MJSs and the existence of the corresponding admissible control. Neural network techniques are used to approximate the proposed performance index function and the control law. To demonstrate the effectiveness of our approach, three simulation studies, one linear case, one nonlinear case, and one single link robot arm case, are used to validate the performance of the proposed optimal control method.
New approaches to robust l2-l∞ and H∞ filtering for uncertain discrete-time systems
高会军; 王常虹
2003-01-01
The problems of robust l2-l∞ and H∞ filtering for discrete-time systems with parameter uncer- tainty residing in a polytope are investigated in this paper. The filtering strategies are based on new ro- bust performance criteria derived from a new result of parameter-dependent Lyapunov stability condition, which exhibit less conservativeness than previous results in the quadratic framework. The designed filters guaranteeing a prescribed l2-l∞ or H∞ noise attenuation level can be obtained from the solution of convex optimization problems, which can be solved via efficient interior point methods. Numerical examples have shown that the filter design procedures proposed in this paper are much less conservative than earlier results.
H2 control of discrete-time periodic systems with Markovian jumps and multiplicative noise
Ma, Hongji; Jia, Yingmin
2013-10-01
This paper addresses the problem of optimal and robust H2 control for discrete-time periodic systems with Markov jump parameters and multiplicative noise. To analyse the system performance in the presence of exogenous random disturbance, an H2 norm is firstly established on the basis of Gramian matrices. Further, under the condition of exact observability, a necessary and sufficient condition is presented for the solvability of H2 optimal control problem by means of a generalised Riccati equation. When the transition probabilities of jump parameter are incompletely measurable, an H2-guaranteed cost norm is exploited and the robust H2 controller is designed through a linear matrix inequality (LMI) optimisation approach. An example of a networked control system is supplied to illustrate the proposed results.
Approximation methods of mixed l 1/H2 optimization problems for MIMO discrete-time systems
李昇平
2004-01-01
The mixed l1/H2 optimization problem for MIMO (multiple input-multiple output) discrete-time systems is eonsidered. This problem is formulated as minimizing the l1-norm of a dosed-loop transfer matrix while maintaining the H2-norm of another closed-loop transfer matrix at prescribed level. The continuity property of the optimal value in respect to changes in the H2-norm constraint is studied. The existence of the optimal solutions of mixed l1/H2 problem is proved. Becatse the solution of the mixed l1/H2 problem is based on the scaled-Q method, it avoids the zero interpolation difficulties. The convergent upper and lower bounds can be obtained by solving a sequence of finite dimensional nonlinear programming for which many efficient numerical optimization algorithms exist.
Ruiz-Cruz, Riemann; Sanchez, Edgar N; Ornelas-Tellez, Fernando; Loukianov, Alexander G; Harley, Ronald G
2013-12-01
In this paper, the authors propose a particle swarm optimization (PSO) for a discrete-time inverse optimal control scheme of a doubly fed induction generator (DFIG). For the inverse optimal scheme, a control Lyapunov function (CLF) is proposed to obtain an inverse optimal control law in order to achieve trajectory tracking. A posteriori, it is established that this control law minimizes a meaningful cost function. The CLFs depend on matrix selection in order to achieve the control objectives; this matrix is determined by two mechanisms: initially, fixed parameters are proposed for this matrix by a trial-and-error method and then by using the PSO algorithm. The inverse optimal control scheme is illustrated via simulations for the DFIG, including the comparison between both mechanisms.
Allee effect in a discrete-time predator-prey system
Celik, Canan [TOBB Economics and Technology University, Faculty of Arts and Sciences, Department of Mathematics, Soeguetoezue 06530, Ankara (Turkey)], E-mail: canan.celik@etu.edu.tr; Duman, Oktay [TOBB Economics and Technology University, Faculty of Arts and Sciences, Department of Mathematics, Soeguetoezue 06530, Ankara (Turkey)], E-mail: oduman@etu.edu.tr
2009-05-30
In this paper, we study the stability of a discrete-time predator-prey system with and without Allee effect. By analyzing both systems, we first obtain local stability conditions of the equilibrium points without the Allee effect and then exhibit the impact of the Allee effect on stability when it is imposed on prey population. We also show the stabilizing effect of Allee effect by numerical simulations and verify that when the prey population is subject to an Allee effect, the trajectory of the solutions approximates to the corresponding equilibrium point much faster. Furthermore, for some fixed parameter values satisfying necessary conditions, we show that the corresponding equilibrium point moves from instability to stability under the Allee effect on prey population.
Xiao-Ting Rui; Edwin Kreuzer; Bao Rong; Bin He
2012-01-01
In this paper,by defining new state vectors and developing new transfer matrices of various elements moving in space,the discrete time transfer matrix method of multi-rigid-flexible-body system is expanded to study the dynamics of muhibody system with flexible beams moving in space.Formulations and numerical example of a rigidflexible-body three pendulums system moving in space are given to validate the method. Using the new method to study the dynamics of multi-rigid-flexible-body system mov ing in space,the global dynamics equations of system are not needed,the orders of involved matrices of the system are very low and the computational speed is high,irrespective of the size of the system.The new method is simple,straightforward,practical,and provides a powerful tool for multi-rigid-flexible-body system dynamics.
Automatic reconstruction of molecular and genetic networks from discrete time series data.
Durzinsky, Markus; Wagler, Annegret; Weismantel, Robert; Marwan, Wolfgang
2008-09-01
We apply a mathematical algorithm which processes discrete time series data to generate a complete list of Petri net structures containing the minimal number of nodes required to reproduce the data set. The completeness of the list as guaranteed by a mathematical proof allows to define a minimal set of experiments required to discriminate between alternative network structures. This in principle allows to prove all possible minimal network structures by disproving all alternative candidate structures. The dynamic behaviour of the networks in terms of a switching rule for the transitions of the Petri net is part of the result. In addition to network reconstruction, the algorithm can be used to determine how many yet undetected components at least must be involved in a certain process. The algorithm also reveals all alternative structural modifications of a network that are required to generate a predefined behaviour.
LQR-Based Optimal Distributed Cooperative Design for Linear Discrete-Time Multiagent Systems.
Zhang, Huaguang; Feng, Tao; Liang, Hongjing; Luo, Yanhong
2017-03-01
In this paper, a novel linear quadratic regulator (LQR)-based optimal distributed cooperative design method is developed for synchronization control of general linear discrete-time multiagent systems on a fixed, directed graph. Sufficient conditions are derived for synchronization, which restrict the graph eigenvalues into a bounded circular region in the complex plane. The synchronizing speed issue is also considered, and it turns out that the synchronizing region reduces as the synchronizing speed becomes faster. To obtain more desirable synchronizing capacity, the weighting matrices are selected by sufficiently utilizing the guaranteed gain margin of the optimal regulators. Based on the developed LQR-based cooperative design framework, an approximate dynamic programming technique is successfully introduced to overcome the (partially or completely) model-free cooperative design for linear multiagent systems. Finally, two numerical examples are given to illustrate the effectiveness of the proposed design methods.
Positive Filtering with l1-Gain for Discrete-Time Positive Systems
Xiaoming Chen
2016-01-01
Full Text Available This paper is concerned with the positive filtering problem for discrete-time positive systems under the l1-induced performance. We aim to propose a pair of positive filters with error-bounding features to estimate the output of positive systems. A novel characterization is first constructed so that the filtering error system is asymptotically stable with a prescribed l1-induced performance. Then, necessary and sufficient conditions for the existence of required filters are presented, and the obtained results are expressed as linear programming problems. Moreover, it is pointed out that the results can be easily checked by standard software. In addition, a numerical example is given to show the effectiveness of the proposed design procedures.
Attractors and the attraction basins of discrete-time cellular neural networks
Ma Runnian; Xi Youmin
2005-01-01
The dynamic behavior of discrete-time cellular neural networks(DTCNN), which is strict with zero threshold value, is mainly studied in asynchronous mode and in synchronous mode. In general, a k-attractor of DTCNN is not a convergent point.But in this paper, it is proved that a k-attractor is a convergent point if the strict DTCNN satisfies some conditions. The attraction basin of the strict DTCNN is studied, one example is given to illustrate the previous conclusions to be wrong, and several results are presented. The obtained results on k-attractor and attraction basin not only correct the previous results, but also provide a theoretical foundation of performance analysis and new applications of the DTCNN.
A VHDL Core for Intrinsic Evolution of Discrete Time Filters with Signal Feedback
Gwaltney, David A.; Dutton, Kenneth
2005-01-01
Evolution of a novel low-pass filter design has been presented along with an assessment of its capabilities. (1) Performed well with the two added sines used as input during the evolution. (2) Also performs well when the input includes more sine at frequencies between the two used during evolution. (3) Fails to perform when input is a sine sweep with wider bandwidth. (4) This illustrates the importance of designing the evolutionary process to be representative of the environment that will be seen by the evolved design during deployment. The use of non-standard operators and fewer resources should allow the EMVCore to implement more compact representations of digital filters and to provide fault tolerance by implementing a new solution in the remaining tiles after some are damaged. The EMVCore can be used to implement standard discrete time filters in addition to evolved components.
Quasi-Newton-type optimized iterative learning control for discrete linear time invariant systems
Yan GENG; Xiaoe RUAN
2015-01-01
In this paper, a quasi-Newton-type optimized iterative learning control (ILC) algorithm is investigated for a class of discrete linear time-invariant systems. The proposed learning algorithm is to update the learning gain matrix by a quasi-Newton-type matrix instead of the inversion of the plant. By means of the mathematical inductive method, the monotone convergence of the proposed algorithm is analyzed, which shows that the tracking error monotonously converges to zero after a finite number of iterations. Compared with the existing optimized ILC algorithms, due to the superlinear convergence of quasi-Newton method, the proposed learning law operates with a faster convergent rate and is robust to the ill-condition of the system model, and thus owns a wide range of applications. Numerical simulations demonstrate the validity and effectiveness.
Multiple periodic solutions for a discrete time model of plankton allelopathy
Zhang Jianbao; Fang Hui
2006-01-01
We study a discrete time model of the growth of two species of plankton with competitive and allelopathic effects on each other N1(k+1) = N1(k)exp{r1(k)-a11(k)N1(k)-a12(k)N2(k)-b1(k)N1(k)N2(k)}, N2(k+1) = N2(k)exp{r2(k)-a21(k)N2(k)-b2(k)N1(k)N1(k)N2(k)}. A set of sufficient conditions is obtained for the existence of multiple positive periodic solutions for this model. The approach is based on Mawhin's continuation theorem of coincidence degree theory as well as some a priori estimates. Some...
Jian Ding
2014-01-01
Full Text Available This paper addresses the problem of P-type iterative learning control for a class of multiple-input multiple-output linear discrete-time systems, whose aim is to develop robust monotonically convergent control law design over a finite frequency range. It is shown that the 2 D iterative learning control processes can be taken as 1 D state space model regardless of relative degree. With the generalized Kalman-Yakubovich-Popov lemma applied, it is feasible to describe the monotonically convergent conditions with the help of linear matrix inequality technique and to develop formulas for the control gain matrices design. An extension to robust control law design against systems with structured and polytopic-type uncertainties is also considered. Two numerical examples are provided to validate the feasibility and effectiveness of the proposed method.
Set-membership state estimation for discrete time piecewise affine systems using zonotopes
Tabatabaeipour, Mojtaba; Stoustrup, Jakob
2013-01-01
This paper presents a method for guaranteed state estimation of discrete time piecewise affine systems with unknown but bounded noise and disturbance. Using zonotopic set representations, the proposed method computes the set of states that are consistent with the model, observation, and bounds...... on the noise and disturbance such that the real state of the system is guaranteed to lie in this set. Because in piecewise affine systems, the state space is partitioned into a number of polyhedral sets, at each iteration the intersection of the zonotopes containing a set-valued estimation of the states...... with each of the polyhedral partitions must be computed. We use an analytic method to compute the intersection as a zonotope and minimize the size of the intersection. A numerical example is provided to illuminate the algorithm....
Finite frequency H_∞ filtering for uncertain discrete-time switched linear systems
Dawei Ding; Guanghong Yang
2009-01-01
This paper is concerned with the problem of robust H_∞ filtering for discrete-time switched linear systems with polytopic uncertainties in the finite frequency domain. Based on the generalized Kalman-Yakubovich-Popov (GKYP) iemma and switched parameter-depen-dent Lyapunov functions, a switched full-order filter is designed such that the corresponding filtering error system is asymptotically sta-ble and satisfies a prescribed finite frequency H_∞ performance index. Compared with the existing full frequency approaches, the proposed finite frequency one receives better results for the cases in which the frequency ranges of noises are known. A numerical exam-ple is given to illustrate the effectiveness of the proposed method.
Frequency-shaped and observer-based discrete-time sliding mode control
Mehta, Axaykumar
2015-01-01
It is well established that the sliding mode control strategy provides an effective and robust method of controlling the deterministic system due to its well-known invariance property to a class of bounded disturbance and parameter variations. Advances in microcomputer technologies have made digital control increasingly popular among the researchers worldwide. And that led to the study of discrete-time sliding mode control design and its implementation. This brief presents, a method for multi-rate frequency shaped sliding mode controller design based on switching and non-switching type of reaching law. In this approach, the frequency dependent compensator dynamics are introduced through a frequency-shaped sliding surface by assigning frequency dependent weighing matrices in a linear quadratic regulator (LQR) design procedure. In this way, the undesired high frequency dynamics or certain frequency disturbance can be eliminated. The states are implicitly obtained by measuring the output at a faster rate than th...
The critical node problem in stochastic networks with discrete-time Markov chain
Gholam Hassan Shirdel
2016-04-01
Full Text Available The length of the stochastic shortest path is defined as the arrival probability from a source node to a destination node. The uncertainty of the network topology causes unstable connections between nodes. A discrete-time Markov chain is devised according to the uniform distribution of existing arcs where the arrival probability is computed as a finite transition probability from the initial state to the absorbing state. Two situations are assumed, departing from the current state to a new state, or waiting in the current state while expecting better conditions. Our goal is to contribute to determining the critical node in a stochastic network, where its absence results in the greatest decrease of the arrival probability. The proposed method is a simply application for analyzing the resistance of networks against congestion and provides some crucial information of the individual nodes. Finally, this is illustrated using networks of various topologies.
Direct adaptive control for a class of MIMO nonlinear discrete-time systems
Lei Li; Zhizhong Mao
2014-01-01
This paper considers the problem of adaptive con-trol for a class of multiple input multiple output (MIMO) nonlinear discrete-time systems based on input-output model with unknown interconnections between subsystems. Based on the Taylor ex-pand technology, an equivalent model in affine-like form is derived for the original nonaffine nonlinear system. Then a direct adap-tive neural network (NN) control er is implemented based on the affine-like model. By finding an orthogonal matrix to tune the NN weights, the closed-loop system is proven to be semiglobal y uni-formly ultimately bounded. The σ-modification technique is used to remove the requirement of persistence excitation during the adaptation. The control performance of the closed-loop system is guaranteed by suitably choosing the design parameters.
Wang, Dong; Liu, Tao; Sun, Ximing; Zhong, Chongquan
2016-07-01
A discrete-time domain two-degree-of-freedom (2DOF) design method is proposed for integrating and unstable processes with time delay. Based on a 2DOF control structure recently developed, a controller is analytically designed in terms of the H2 optimal control performance specification for the set-point tracking, and another controller is derived by proposing the desired closed-loop transfer function for load disturbance rejection. Both controllers can be tuned relatively independent to realize control optimization. Analytical expression of the set-point response is given for quantitatively tuning the single adjustable parameter in the set-point tracking controller. At the meantime, sufficient and necessary conditions for holding robust stability of the closed-loop control system are established for tuning another adjustable parameter in the disturbance rejection controller, along with numerical tuning guidelines. Illustrative examples from the literature are used to demonstrate the effectiveness of the proposed method.
Park, Moon Kyu; Kim, Yong Hee; Cha, Kune Ho; Kim, Myung Ki [KEPCO, KEPRI, Taejon (Korea, Republic of)
1998-10-01
A method is described to develop an H{infinity} filtering method for the dynamic compensation of self-powered neutron detectors normally used for fixed incore instruments. An H{infinity} norm of the filter transfer matrix is used as the optimization criteria in the worst-case estimation error sense. Filter modeling is performed for discrete-time model. The filter gains are optimized in the sense of noise attenuation level of H{infinity} setting. By introducing Bounded Real Lemma, the conventional algebraic Riccati inequalities are converted into Linear Matrix Inequalities (LMIs). Finally, the filter design problem is solved via the convex optimization framework using LMIs. The simulation results show that remarkable improvements are achieved in view of the filter response time and the filter design efficiency.
Robust fault detection for discrete-time Markovian jump systems with mode-dependent time-delays
Hongru WANG; Changhong WANG; Shaoshuai MOU; Huijun GAO
2007-01-01
This paper investigates a fault detection problem for a class of discrete-time Markovian jump systems with norm-bounded uncertainties and mode-dependent time-delays. Attention is focused on constructing the residual generator based on the filter of which its parameters matrices are dependent on the system mode, that is, the fault detection filter is a Markovian jump system as well. The design of fault detection filter is reduced to H-infinity filtering problem by using H-infinity control theory, which can guarantee the difference between the residual and the fault (or, more generally weighted fault) as small as possible in the context of enhancing the robustness of residual to modeling errors, control inputs and unknown inputs. Sufficient condition for the existence of the above filters is established by means of linear matrix inequalities, which can be readily solved by using standard numerical software. A numerical example is given to illustrate the feasibility of the proposed method.
Jinxing Lin; Shumin Fei; Jiong Shen
2010-01-01
The problems of robust stability and stabilization via memoryless state feedback for a class of discrete-time switched singular systems with time-varying delays and linear fractional uncertainties are investigated.By constructing a novel switched Lyapunov-Krasovskii functional,a delay-dependent criterion for the unforced system to be regular,causal and uniformly asymptotically stable is established in terms of linear matrix inequalities(LMIs).An explicit expression for the desired memoryless state feedback stabilization controller is also given.The merits of the proposed criteria lie in their less conservativeness and relative simplicity,which are achieved by considering additionally useful terms(ignored in previous methods)when estimating the upper bound of the forward difference of the Lyapunov-Krasovskii functional and by avoiding utilizing any model augmentation transformation.Some numerical examples are provided to illustrate the validity of the proposed methods.
Ocular manifestation in treated multibacillary Hansen's disease.
Parikh, Rajul; Thomas, Saju; Muliyil, Jayaprakash; Parikh, Shefali; Thomas, Ravi
2009-11-01
To report the prevalence of ocular morbidity in patients with treated multibacillary Hansen's disease (HD) using modern ophthalmic diagnostic techniques in a rural community endemic for HD. Cross-sectional, observation study. All patients with multibacillary HD who had completed their multidrug therapy and who resided in 4 defined geographical areas in Vellore, Tamil Nadu, India. All participants underwent a complete eye examination that included slit-lamp examination, esthesiometry, gonioscopy, applanation tonometry, and dilated fundus examination, including a stereobiomicroscopic examination of the fundus at an ophthalmic center set up for that purpose. Glaucoma suspects underwent automated perimetry using a Humphrey Field Analyzer (Humphrey Instruments, San Leandro, CA). The prevalence of various ocular disease parameters were reported as mean value with 95% confidence interval. The difference of disease prevalence between various leprosy groups was compared using an unpaired t test. The association between eye symptoms and potentially sight-threatening complications was analyzed using the chi-square test. Three hundred eighty-six of the 446 patients with multibacillary HD residing in the defined areas were evaluated. Four patients (1.04%; 95% confidence interval [CI], 0.0%-2.0%) were bilaterally blind; 33 (8.55%; 95% CI, 5.8%-11.3%) had unilateral blindness. Mean intraocular pressure was 12 mmHg (standard deviation, 4.1 mmHg), and prevalence of glaucoma was 3.6% (95% CI, 1.8%-5.5%). Potentially sight-threatening (PST) pathologic features (corneal anesthesia, lagophthalmos, uveitis, scleritis, and advanced glaucoma) were present in 10.4% (95% CI, 7.4%-13.4%) of patients. Significant cataracts occurred 3 times more frequently in those with polar lepromatous leprosy. The odds ratio for PST pathology in the presence of patient-reported symptoms (pain, redness, inability to close eye, burning, and irritation) was 2.9 (95% CI, 1.34-6.26). Patients who have completed
Liu, Hongjian; Wang, Zidong; Shen, Bo; Alsaadi, Fuad E.
2016-07-01
This paper deals with the robust H∞ state estimation problem for a class of memristive recurrent neural networks with stochastic time-delays. The stochastic time-delays under consideration are governed by a Bernoulli-distributed stochastic sequence. The purpose of the addressed problem is to design the robust state estimator such that the dynamics of the estimation error is exponentially stable in the mean square, and the prescribed ? performance constraint is met. By utilizing the difference inclusion theory and choosing a proper Lyapunov-Krasovskii functional, the existence condition of the desired estimator is derived. Based on it, the explicit expression of the estimator gain is given in terms of the solution to a linear matrix inequality. Finally, a numerical example is employed to demonstrate the effectiveness and applicability of the proposed estimation approach.
Adaptive stabilization of discrete-time systems using linear periodically time varying controllers
Ortega, Romeo; Albertos, Pedro; Lozano, Rogelio
1988-01-01
A direct adaptive scheme based on the use of linear time-varying periodic controllers is proposed which estimates online the periodic coefficients of the controller. It is shown that adaptive stabilization is attained for all possibly nonstably invertible plants of known order but unknown delay. Although no appeal is made to persistency of excitation arguments, a provision is needed to avoid the singularity of an estimated matrix, this property being required only for the analysis and not the control calculations.
Kubatko, Ethan J.
2013-10-29
Discontinuous Galerkin (DG) spatial discretizations are often used in a method-of-lines approach with explicit strong-stability-preserving (SSP) Runge–Kutta (RK) time steppers for the numerical solution of hyperbolic conservation laws. The time steps that are employed in this type of approach must satisfy Courant–Friedrichs–Lewy stability constraints that are dependent on both the region of absolute stability and the SSP coefficient of the RK method. While existing SSPRK methods have been optimized with respect to the latter, it is in fact the former that gives rise to stricter constraints on the time step in the case of RKDG stability. Therefore, in this work, we present the development of new “DG-optimized” SSPRK methods with stability regions that have been specifically designed to maximize the stable time step size for RKDG methods of a given order in one space dimension. These new methods represent the best available RKDG methods in terms of computational efficiency, with significant improvements over methods using existing SSPRK time steppers that have been optimized with respect to SSP coefficients. Second-, third-, and fourth-order methods with up to eight stages are presented, and their stability properties are verified through application to numerical test cases.
Computational Procedures for a Class of GI/D/k Systems in Discrete Time
Md. Mostafizur Rahman
2009-01-01
Full Text Available A class of discrete time GI/D/k systems is considered for which the interarrival times have finite support and customers are served in first-in first-out (FIFO order. The system is formulated as a single server queue with new general independent interarrival times and constant service duration by assuming cyclic assignment of customers to the identical servers. Then the queue length is set up as a quasi-birth-death (QBD type Markov chain. It is shown that this transformed GI/D/1 system has special structures which make the computation of the matrix R simple and efficient, thereby reducing the number of multiplications in each iteration significantly. As a result we were able to keep the computation time very low. Moreover, use of the resulting structural properties makes the computation of the distribution of queue length of the transformed system efficient. The computation of the distribution of waiting time is also shown to be simple by exploiting the special structures.
Discrete step model of helix-coil kinetics: Distribution of fluctuation times
Poland, Douglas
1996-07-01
A method is outlined for the computer simulation of the cooperative kinetics required to construct the distribution function for time intervals between fluctuations in conformational states in macromolecules. Using the helix-coil transition in polyamino acids as an example, we develop a Monte Carlo cellular automata approximation of the kinetics of this system in discrete time. This approximation is tested against a number of exact solutions for homopolymers and is then used to calculate moments of the distribution function for the time intervals between switches in conformational state at a given site (e.g., given a switch from coil to helix at zero time, how long will it take before the state switches back). The maximum-entropy method is used to construct the very broad distribution function from the moments. In heteropolymers the diffusion of helix-coil boundaries is reduced, helix being more localized on strong helix-forming residues. We investigate the effect of a specific sequence of amino acid residues on conformational fluctuations by using the known σ and s values for the naturally occurring amino acids to simulate the kinetics of helix formation (limiting the range of cooperativity to the α-helix) in sperm whale myoglobin, giving the time evolution to the equilibrium probability profile in this system.
Robust Stability Analysis and Synthesis for Switched Discrete-Time Systems with Time Delay
Liguo Zhang
2010-01-01
Full Text Available The problems of robust stability analysis and synthesis for a class of uncertain switched time-delay systems with polytopic type uncertainties are addressed. Based on the constructive use of an appropriate switched Lyapunov function, sufficient linear matrix inequalities (LMIs conditions are investigated to make such systems a uniform quadratic stability with an L2-gain smaller than a given constant level. System synthesis is to design switched feedback schemes, whether based on state, output measurements, or by using dynamic output feedback, to guarantee that the corresponding closed-loop system satisfies the LMIs conditions. Two numerical examples are provided that demonstrate the efficiency of this approach.