Directory of Open Access Journals (Sweden)
Cheng-yi Zhang
2016-06-01
Full Text Available Abstract Some convergence conditions on successive over-relaxed (SOR iterative method and symmetric SOR (SSOR iterative method are proposed for non-Hermitian positive definite linear systems. Some examples are given to demonstrate the results obtained.
Convergence of TTS Iterative Method for Non-Hermitian Positive Definite Linear Systems
Directory of Open Access Journals (Sweden)
Cheng-Yi Zhang
2014-01-01
Full Text Available The TTS iterative method is proposed to solve non-Hermitian positive definite linear systems and some convergence conditions are presented. Subsequently, these convergence conditions are applied to the ALUS method proposed by Xiang et al. in 2012 and comparison of some convergence theorems is made. Furthermore, an example is given to demonstrate the results obtained in this paper.
A REGULARIZED CONJUGATE GRADIENT METHOD FOR SYMMETRIC POSITIVE DEFINITE SYSTEM OF LINEAR EQUATIONS
Institute of Scientific and Technical Information of China (English)
Zhong-zhi Bai; Shao-liang Zhang
2002-01-01
A class of regularized conjugate gradient methods is presented for solving the large sparse system of linear equations of which the coefficient matrix is an ill-conditioned symmetric positive definite matrix. The convergence properties of these methods are discussed in depth, and the best possible choices of the parameters involved in the new methods are investigated in detail. Numerical computations show that the new methods are more efficient and robust than both classical relaxation methods and classical conjugate direction methods.
Institute of Scientific and Technical Information of China (English)
Ichitaro Yamazaki; Zhaojun Bai; Wenbin Chen; Richard Scalettar
2009-01-01
We study preconditioning techniques used in conjunction with the conjugate gradient method for solving multi-length-scale symmetric positive definite linear systems originating from the quantum Monte Carlo simulation of electron interaction of correlated materials. Existing preconditioning techniques are not designed to be adaptive to varying numerical properties of the multi-length-scale systems. In this paper, we propose a hybrid incomplete Cholesky (HIC) preconditioner and demonstrate its adaptivity to the multi-length-scale systems. In addition, we propose an extension of the compressed sparse column with row access (CSCR) sparse matrix storage format to efficiently accommodate the data access pattern to compute the HIC preconditioner. We show that for moderately correlated materials, the HIC preconditioner achieves the optimal linear scaling of the simulation. The development of a linear-scaling preconditioner for strongly correlated materials remains an open topic.
Directory of Open Access Journals (Sweden)
Pedro Mayorga
2016-11-01
Full Text Available Linear systems with tridiagonal structures are very common in problems related not only to engineering, but chem-istry, biomedical or finance, for example, real time cubic B-Spline interpolation of ND-images, real time processing of Electrocardio-graphy (ECG and hand drawing recognition. In those problems which the matrix is positive definite, it is possible to optimize the solution in O(n?? time. This paper describes such systems whose size grows over time and proposes an approximation in ???????? time of such systems based on a series of previous approximations. In addition, it is described the development of the method and is proved that the proposed solution converges linearly to the optimal. A real-time cubic B-Spline interpolation of an ECG is computed with this proposal, for this application the proposed method shows a global relative error near to ????-6 and its computation is faster than traditional methods, as shown in the experiments.
The development of an algebraic multigrid algorithm for symmetric positive definite linear systems
Energy Technology Data Exchange (ETDEWEB)
Vanek, P.; Mandel, J.; Brezina, M. [Univ. of Colorado, Denver, CO (United States)
1996-12-31
An algebraic multigrid algorithm for symmetric, positive definite linear systems is developed based on the concept of prolongation by smoothed aggregation. Coarse levels are generated automatically. We present a set of requirements motivated heuristically by a convergence theory. The algorithm then attempts to satisfy the requirements. Input to the method are the coefficient matrix and zero energy modes, which are determined from nodal coordinates and knowledge of the differential equation. Efficiency of the resulting algorithm is demonstrated by computational results on real world problems from solid elasticity, plate blending, and shells.
The report documents a series of seminars at Rome Air Development Center with the content equivalent to an intense course in Linear Systems . Material...is slanted toward the practicing engineer and introduces some of the fundamental concepts and techniques for analyzing linear systems . Techniques for
Linear systems theory revisited
Willigenburg, van L.G.; Koning, de W.L.
2008-01-01
This paper investigates and clarifies how different definitions of reachability, observability, controllability, reconstructability and minimality that appear in the control literature, may be equivalent or different, depending on the type of linear system. The differences are caused by (1) whether
Bourlès, Henri
2013-01-01
Linear systems have all the necessary elements (modeling, identification, analysis and control), from an educational point of view, to help us understand the discipline of automation and apply it efficiently. This book is progressive and organized in such a way that different levels of readership are possible. It is addressed both to beginners and those with a good understanding of automation wishing to enhance their knowledge on the subject. The theory is rigorously developed and illustrated by numerous examples which can be reproduced with the help of appropriate computation software. 60 exe
LINEAR SYSTEMS AND LINEAR INTERPOLATION I
Institute of Scientific and Technical Information of China (English)
丁立峰
2001-01-01
he linear interpolation of linear system on a family of linear systems is introduced and discussed. Some results and examples on singly generated systems on a finite dimensional vector space are given.
Non linear system become linear system
Directory of Open Access Journals (Sweden)
Petre Bucur
2007-01-01
Full Text Available The present paper refers to the theory and the practice of the systems regarding non-linear systems and their applications. We aimed the integration of these systems to elaborate their response as well as to highlight some outstanding features.
Callier, Frank M.; Desoer, Charles A.
1991-01-01
The aim of this book is to provide a systematic and rigorous access to the main topics of linear state-space system theory in both the continuous-time case and the discrete-time case; and the I/O description of linear systems. The main thrusts of the work are the analysis of system descriptions and derivations of their properties, LQ-optimal control, state feedback and state estimation, and MIMO unity-feedback systems.
Feedback linearization of piecewise linear systems
Camlibel, Kanat; Ustoglu, Ilker
2005-01-01
One of the classical problems of nonlinear systems and control theory is feedback linearization. Its obvious motivation is that one can utilize linear control theory if the nonlinear system at hand is linearizable by feedback. This problem is well-understood for the smooth nonlinear systems. In the
Institute of Scientific and Technical Information of China (English)
Junfeng Yin; Quanyu Dou
2012-01-01
In this paper,a generalized preconditioned Hermitian and skew-Hermitian splitting (GPHSS) iteration method for a non-Hermitian positive-definite matrix is studied,which covers standard Hermitian and skew-Hermitian splitting (HSS) iteration and also many existing variants.Theoretical analysis gives an upper bound for the spectral radius of the iteration matrix.From practical point of view,we have analyzed and implemented inexact generalized preconditioned Hermitian and skew-Hermitian splitting (IGPHSS) iteration,which employs Krylov subspace methods as its inner processes.Numerical experiments from three-dimensional convection-diffusion equation show that the GPHSS and IGPHSS iterations are efficient and competitive with standard HSS iteration and AHSS iteration.
Definitions Are Important: The Case of Linear Algebra
Berman, Abraham; Shvartsman, Ludmila
2016-01-01
In this paper we describe an experiment in a linear algebra course. The aim of the experiment was to promote the students' understanding of the studied concepts focusing on their definitions. It seems to be a given that students should understand concepts' definitions before working substantially with them. Unfortunately, in many cases they do…
Energy Technology Data Exchange (ETDEWEB)
Concus, P.; Golub, G.H.; O' Leary, D.P.
1976-01-01
A generalized conjugate gradient method is considered for solving sparse, symmetric, positive-definite systems of linear equations, principally those arising from the discretization of boundary value problems for elliptic partial differential equations. The method is based on splitting off from the original coefficient matrix a symmetric, positive-definite one which corresponds to a more easily solvable system of equations, and then accelerating the associated iteration by using conjugate gradients. Optimality and convergence properties are presented, and the relation to other methods is discussed. Several splittings for which the method seems particularly effective are also discussed; and for some, numerical examples are given. 1 figure, 1 table. (auth)
Linear programming with positive semi-definite matrices
Directory of Open Access Journals (Sweden)
Lasserre J. B.
1996-01-01
Full Text Available We consider the general linear programming problem over the cone of positive semi-definite matrices. We first provide a simple sufficient condition for existence of optimal solutions and absence of a duality gap without requiring existence of a strictly feasible solution. We then simply characterize the analogues of the standard concepts of linear programming, i.e., extreme points, basis, reduced cost, degeneracy, pivoting step as well as a Simplex-like algorithm.
Observability conditions of switched linear singular systems
Institute of Scientific and Technical Information of China (English)
Bin MENG; Jifeng ZHANG
2007-01-01
The observability problem of switched linear singular(SLS) systems is studied in this paper. Based on the observability definition, the unobservable subspaces of given switching laws are investigated under the condition that all subsystems are regular. A necessary condition and a sufficient condition for observability of SLS systems are given. It is shown that the observability and controllability are dual for some special SLS systems with circulatory switching laws. The method developed here is applicable to the observability analysis of normal switched linear systems.
Properties of blocked linear systems.
Chen, Weitian; Anderson, Brian D O; Deistler, Manfred; Filler, Alexander
2012-10-01
This paper presents a systematic study on the properties of blocked linear systems that have resulted from blocking discrete-time linear time invariant systems. The main idea is to explore the relationship between the blocked and the unblocked systems. Existing results are reviewed and a number of important new results are derived. Focus is given particularly on the zero properties of the blocked system as no such study has been found in the literature.
Formal modeling and verification of fractional order linear systems.
Zhao, Chunna; Shi, Likun; Guan, Yong; Li, Xiaojuan; Shi, Zhiping
2016-05-01
This paper presents a formalization of a fractional order linear system in a higher-order logic (HOL) theorem proving system. Based on the formalization of the Grünwald-Letnikov (GL) definition, we formally specify and verify the linear and superposition properties of fractional order systems. The proof provides a rigor and solid underpinnings for verifying concrete fractional order linear control systems. Our implementation in HOL demonstrates the effectiveness of our approach in practical applications.
Feedback systems for linear colliders
Hendrickson, L; Himel, Thomas M; Minty, Michiko G; Phinney, N; Raimondi, Pantaleo; Raubenheimer, T O; Shoaee, H; Tenenbaum, P G
1999-01-01
Feedback systems are essential for stable operation of a linear collider, providing a cost-effective method for relaxing tight tolerances. In the Stanford Linear Collider (SLC), feedback controls beam parameters such as trajectory, energy, and intensity throughout the accelerator. A novel dithering optimization system which adjusts final focus parameters to maximize luminosity contributed to achieving record performance in the 1997-98 run. Performance limitations of the steering feedback have been investigated, and improvements have been made. For the Next Linear Collider (NLC), extensive feedback systems are planned as an intregal part of the design. Feedback requiremetns for JLC (the Japanese Linear Collider) are essentially identical to NLC; some of the TESLA requirements are similar but there are significant differences. For NLC, algorithms which incorporate improvements upon the SLC implementation are being prototyped. Specialized systems for the damping rings, rf and interaction point will operate at hi...
Iterative solution of linear systems
Freund, Roland W.; Golub, Gene H.; Nachtigal, Noel M.
1992-01-01
Recent advances in the field of iterative methods for solving large linear systems are reviewed. The main focus is on developments in the area of conjugate gradient-type algorithms and Krylov subspace methods for nonHermitian matrices.
Window observers for linear systems
Directory of Open Access Journals (Sweden)
Utkin Vadim
2000-01-01
Full Text Available Given a linear system x ˙ = A x + B u with output y = C x and a window function ω ( t , i.e., ∀ t , ω ( t ∈ {0,1 }, and assuming that the window function is Lebesgue measurable, we refer to the following observer, x ˆ = A x + B u + ω ( t L C ( x − x ˆ as a window observer. The stability issue is treated in this paper. It is proven that for linear time-invariant systems, the window observer can be stabilized by an appropriate design under a very mild condition on the window functions, albeit for linear time-varying system, some regularity of the window functions is required to achieve observer designs with the asymptotic stability. The corresponding design methods are developed. An example is included to illustrate the possible applications
Preconditioned quantum linear system algorithm.
Clader, B D; Jacobs, B C; Sprouse, C R
2013-06-21
We describe a quantum algorithm that generalizes the quantum linear system algorithm [Harrow et al., Phys. Rev. Lett. 103, 150502 (2009)] to arbitrary problem specifications. We develop a state preparation routine that can initialize generic states, show how simple ancilla measurements can be used to calculate many quantities of interest, and integrate a quantum-compatible preconditioner that greatly expands the number of problems that can achieve exponential speedup over classical linear systems solvers. To demonstrate the algorithm's applicability, we show how it can be used to compute the electromagnetic scattering cross section of an arbitrary target exponentially faster than the best classical algorithm.
Logistic systems with linear feedback
Son, Leonid; Shulgin, Dmitry; Ogluzdina, Olga
2016-08-01
A wide variety of systems may be described by specific dependence, which is known as logistic curve, or S-curve, between the internal characteristic and the external parameter. Linear feedback between these two values may be suggested for a wide set of systems also. In present paper, we suggest a bifurcation behavior for systems with both features, and discuss it for two cases, which are the Ising magnet in external field, and the development of manufacturing enterprise.
Weak Markov Processes as Linear Systems
Gohm, Rolf
2012-01-01
A noncommutative Fornasini-Marchesini system (a multi-variable version of a linear system) can be realized within a weak Markov process (a model for quantum evolution). For a discrete time parameter this is worked out systematically as a theory of representations of structure maps of a system by a weak process. We introduce subprocesses and quotient processes which can be described naturally by a suitable category of weak processes. A corresponding notion of cascade for processes induces a represented cascade of systems. We study the control theoretic notion of observability which turns out to be particularly interesting in connection with a cascade structure. As an application we gain new insights into stationary Markov chains where observability for the system is closely related to asymptotic completeness in the scattering theory of the chain. This motivates a general definition of asymptotic completeness in the category of weak processes.
Linear Systems on Tropical Curves
Haase, Christian; Yu, Josephine
2009-01-01
A tropical curve \\Gamma is a metric graph with possibly unbounded edges, and tropical rational functions are continuous piecewise linear functions with integer slopes. We define the complete linear system |D| of a divisor D on a tropical curve \\Gamma analogously to the classical counterpart. We investigate the structure of |D| as a cell complex and show that linear systems are quotients of tropical modules, finitely generated by vertices of the cell complex. Using a finite set of generators, |D| defines a map from \\Gamma to a tropical projective space, and the image can be extended to a tropical curve of degree equal to \\deg(D). The tropical convex hull of the image realizes the linear system |D| as a polyhedral complex. We show that curves for which the canonical divisor is not very ample are hyperelliptic. We also show that the Picard group of a \\Q-tropical curve is a direct limit of critical groups of finite graphs converging to the curve.
Characterization of well-posedness of piecewise linear systems
Imura, J.-I.; Schaft, van der A.J.
1998-01-01
One of the basic issues in the study of hybrid systems is the well-posedness (existence and uniqueness of solutions) problem of discontinuous dynamical systems. This paper addresses this problem for a class of piecewise-linear discontinuous systems under the definition of solutions of Carath\\'eodory
Characterization of well-posedness of piecewise linear systems
Imura, Jun-ichi; Schaft, van der Arjan
2000-01-01
One of the basic issues in the study of hybrid systems is the well-posedness (existence and uniqueness of solutions) problem of discontinuous dynamical systems. The paper addresses this problem for a class of piecewise-linear discontinuous systems under the definition of solutions of Caratheodory. T
Characterization of Well-Posedness of Piecewise-Linear Systems
Imura, Jun-ichi; Schaft, Arjan van der
2000-01-01
One of the basic issues in the study of hybrid systems is the well-posedness (existence and uniqueness of solutions) problem of discontinuous dynamical systems. The paper addresses this problem for a class of piecewise-linear discontinuous systems under the definition of solutions of Carathéodory. T
Dual, use-based definition of "system"
CSIR Research Space (South Africa)
Gonçalves, DP
2015-09-01
Full Text Available The standard definition (ISO 15288, 2008) of the concept of a system is not complete and is the definition of a closed system. Such a definition is inadequate for systems engineering. A use-based definition is proposed which spans the open...
Several splittings for non-Hermitian linear systems
Institute of Scientific and Technical Information of China (English)
2008-01-01
For large sparse non-Hermitian positive definite system of linear equations,we present several variants of the Hermitian and skew-Hermitian splitting(HSS)about the coefficient matrix and establish correspondingly several HSS-based iterative schemes.Theoretical analyses show that these methods are convergent unconditionally to the exact solution of the referred system of linear equations,and they may show advantages on problems that the HSS method is ineffiective.
Several splittings for non-Hermitian linear systems
Institute of Scientific and Technical Information of China (English)
BAI Zhong-Zhi
2008-01-01
For large sparse non-Hermitian positive definite system of linear equations, we present several variants of the Hermitian and skew-Hermitian splitting (HSS) about the coefficient matrix and establish correspondingly several HSS-based iterative schemes. Theoretical analyses show that these methods are convergent unconditionally to the exact solution of the referred system of linear equations,and they may show advantages on problems that the HSS method is ineffective.
Linear operator inequalities for strongly stable weakly regular linear systems
Curtain, RF
2001-01-01
We consider the question of the existence of solutions to certain linear operator inequalities (Lur'e equations) for strongly stable, weakly regular linear systems with generating operators A, B, C, 0. These operator inequalities are related to the spectral factorization of an associated Popov funct
Linearization of Systems of Nonlinear Diffusion Equations
Institute of Scientific and Technical Information of China (English)
KANG Jing; QU Chang-Zheng
2007-01-01
We investigate the linearization of systems of n-component nonlinear diffusion equations; such systems have physical applications in soil science, mathematical biology and invariant curve flows. Equivalence transformations of their auxiliary systems are used to identify the systems that can be linearized. We also provide several examples of systems with two-component equations, and show how to linearize them by nonlocal mappings.
Linear control design for guaranteed stability of uncertain linear systems
Yedavalli, R. K.
1986-01-01
In this paper, a linear control design algorithm based on the elemental perturbation bounds developed recently is presented for a simple second order linear uncertain system satisfying matching conditions. The proposed method is compared with Guaranteed Cost Control (GCC), Multistep Guaranteed Cost Control (MGCC) and the Matching Condition (MC) methods and is shown to give guaranteed stability with lesser values for the control gains than some of the existing methods for the example considered.
Linear and Nonlinear Systems Analysis of the Visual System: Why does it seem so linear?
Shapley, Robert
2009-01-01
Linear and nonlinear systems analysis are tools that can be used to study communication systems like the visual system. The first step of systems analysis often is to test whether or not the system is linear. Retinal pathways are surprisingly linear, and some neurons in the visual cortex also emulate linear sensory transducers. We conclude that the retinal linearity depends on specialized ribbon synapses while cortical linearity is the result of balanced excitatory and inhibitory synaptic interactions. PMID:18940193
A linear quadratic regulator approach to the stabilization of uncertain linear systems
Shieh, L. S.; Sunkel, J. W.; Wang, Y. J.
1990-01-01
This paper presents a linear quadratic regulator approach to the stabilization of uncertain linear systems. The uncertain systems under consideration are described by state equations with the presence of time-varying unknown-but-bounded uncertainty matrices. The method is based on linear quadratic regulator (LQR) theory and Liapunov stability theory. The robust stabilizing control law for a given uncertain system can be easily constructed from the symmetric positive-definite solution of the associated augmented Riccati equation. The proposed approach can be applied to matched and/or mismatched systems with uncertainty matrices in which only their matrix norms are bounded by some prescribed values and/or their entries are bounded by some prescribed constraint sets. Several numerical examples are presented to illustrate the results.
On Mario Bunge's Definition of System and System Boundary
Cavallo, Andrew M.
2012-01-01
In this short paper we discuss Mario Bunge's definition of system boundary. It is quickly discovered that Bunge's definition of system and system boundary are both deficient. We thus propose new definitions, which (hopefully) improve the situation. Our definition of system boundary works off the same intuition behind Bunge's.
LDRD final report on a unified linear reference system
Energy Technology Data Exchange (ETDEWEB)
Espinoza, J. Jr.; Mackoy, R.D. [Sandia National Labs., Albuquerque, NM (United States). Decision Support Systems Software Engineering Dept.; Fletcher, D.R. [Univ. of New Mexico, Albuquerque, NM (United States). Alliance for Transportation Research
1997-06-01
The purpose of the project was to describe existing deficiencies in Geographic Information Systems for transportation (GIS-T) applications and prescribe solutions that would benefit the transportation community in general. After an in-depth literature search and much consultation with noted transportation experts, the need for a common linear reference system that integrated and supported the planning and operational needs of the transportation community became very apparent. The focus of the project was set on a unified linear reference system and how to go about its requirements definition, design, implementation, and promulgation to the transportation community.
Construction and minimality of coordinated linear systems
Kempker, P.L.; Ran, A.C.M.; Schuppen, J.H. van
2014-01-01
Coordinated linear systems are a particular class of hierarchical systems with a top-to-bottom information structure, consisting of a coordinator system and two or more subsystems. This paper deals with the construction and minimality of coordinated linear systems. Construction procedures are given
Dynamic stabilization of regular linear systems
Weiss, G; Curtain, RF
We consider a general class of infinite-dimensional linear systems, called regular linear systems, for which convenient representations are known to exist both in time and in frequency domain, For this class of systems, we investigate the concepts of stabilizability and detectability, in particular,
Linear systems and operators in Hilbert space
Fuhrmann, Paul A
2014-01-01
A treatment of system theory within the context of finite dimensional spaces, this text is appropriate for students with no previous experience of operator theory. The three-part approach, with notes and references for each section, covers linear algebra and finite dimensional systems, operators in Hilbert space, and linear systems in Hilbert space. 1981 edition.
Dynamic stabilization of regular linear systems
Weiss, G; Curtain, RF
1997-01-01
We consider a general class of infinite-dimensional linear systems, called regular linear systems, for which convenient representations are known to exist both in time and in frequency domain, For this class of systems, we investigate the concepts of stabilizability and detectability, in particular,
De la Sen, M.
2009-01-01
The causality properties of linear time-varing systems under constant time lags are investigated based on the definition and use of the definitions of appropriate Hankel and Toeplitz causal and anticausal operators.
RELATIVE PARAMETRIZATION OF LINEAR MULTIDIMENSIONAL SYSTEMS
Pommaret, Jean-François
2012-01-01
Presented for publication in the Springer journal MSSP:Multidimensional Systems and Signal Processing; In the last chapter of his book "The Algebraic Theory of Modular Systems " published in 1916, F. S. Macaulay developped specific techniques for dealing with " unmixed polynomial ideals " by introducing what he called " inverse systems ". The purpose of this paper is to extend such a point of view to differential modules defined by linear multidimensional systems, that is by linear systems of...
The mathematics of networks of linear systems
Fuhrmann, Paul A
2015-01-01
This book provides the mathematical foundations of networks of linear control systems, developed from an algebraic systems theory perspective. This includes a thorough treatment of questions of controllability, observability, realization theory, as well as feedback control and observer theory. The potential of networks for linear systems in controlling large-scale networks of interconnected dynamical systems could provide insight into a diversity of scientific and technological disciplines. The scope of the book is quite extensive, ranging from introductory material to advanced topics of current research, making it a suitable reference for graduate students and researchers in the field of networks of linear systems. Part I can be used as the basis for a first course in algebraic system theory, while Part II serves for a second, advanced, course on linear systems. Finally, Part III, which is largely independent of the previous parts, is ideally suited for advanced research seminars aimed at preparing graduate ...
Compositional analysis for linear systems
Kerber, Florian; Schaft, Arjan van der
2010-01-01
Compositional analysis techniques such as assume-guarantee reasoning are frequently used in computer science to validate the design of complex process models. Since many engineering systems are built modularly from interconnections of components, the resulting mathematical models can be arbitrarily
Rapisarda, P; Willems, JC
1997-01-01
Modeling of physical systems consists of writing the equations describing a phenomenon and yields as a result a set of differential-algebraic equations. As such, state-space models are not a natural starting point for modeling, while they have utmost importance in the simulation and control phase. T
STABILITY OF N-DIMENSIONAL LINEAR SYSTEMS WITH MULTIPLE DELAYS AND APPLICATION TO SYNCHRONIZATION
Institute of Scientific and Technical Information of China (English)
Weihua DENG; Jinhu L(U); Changpin LI
2006-01-01
This paper further investigates the stability of the n-dimensional linear systems with multiple delays. Using Laplace transform, we introduce a definition of characteristic equation for the n-dimensional linear systems with multiple delays. Moreover, one sufficient condition is attained for the Lyapunov globally asymptotical stability of the general multi-delay linear systems. In particular, our result shows that some uncommensurate linear delays systems have the similar stability criterion as that of the commensurate linear delays systems. This result also generalizes that of Chen and Moore (2002). Finally, this theorem is applied to chaos synchronization of the multi-delay coupled Chua's systems.
Stochastic stability properties of jump linear systems
Feng, Xiangbo; Loparo, Kenneth A.; Ji, Yuandong; Chizeck, Howard J.
1992-01-01
Jump linear systems are defined as a family of linear systems with randomly jumping parameters (usually governed by a Markov jump process) and are used to model systems subject to failures or changes in structure. The authors study stochastic stability properties in jump linear systems and the relationship among various moment and sample path stability properties. It is shown that all second moment stability properties are equivalent and are sufficient for almost sure sample path stability, and a testable necessary and sufficient condition for second moment stability is derived. The Lyapunov exponent method for the study of almost sure sample stability is discussed, and a theorem which characterizes the Lyapunov exponents of jump linear systems is presented.
Model reduction of linear conservative mechanical systems
Schaft, van der A.J.; Oeloff, J.E.
1990-01-01
An approach for model reduction of linear conservative or weakly damped mechanical systems is proposed. It is based on the balancing of an associated gradient system. It uses the joint knowledge of the system matrix and the input and output matrices of the Hamiltonian system. The key idea is to asso
Linear systems a measurement based approach
Bhattacharyya, S P; Mohsenizadeh, D N
2014-01-01
This brief presents recent results obtained on the analysis, synthesis and design of systems described by linear equations. It is well known that linear equations arise in most branches of science and engineering as well as social, biological and economic systems. The novelty of this approach is that no models of the system are assumed to be available, nor are they required. Instead, a few measurements made on the system can be processed strategically to directly extract design values that meet specifications without constructing a model of the system, implicitly or explicitly. These new concepts are illustrated by applying them to linear DC and AC circuits, mechanical, civil and hydraulic systems, signal flow block diagrams and control systems. These applications are preliminary and suggest many open problems. The results presented in this brief are the latest effort in this direction and the authors hope these will lead to attractive alternatives to model-based design of engineering and other systems.
Linear System Identification via Atomic Norm Regularization
Shah, Parikshit; Tang, Gongguo; Recht, Benjamin
2012-01-01
This paper proposes a new algorithm for linear system identification from noisy measurements. The proposed algorithm balances a data fidelity term with a norm induced by the set of single pole filters. We pose a convex optimization problem that approximately solves the atomic norm minimization problem and identifies the unknown system from noisy linear measurements. This problem can be solved efficiently with standard, freely available software. We provide rigorous statistical guarantees that explicitly bound the estimation error (in the H_2-norm) in terms of the stability radius, the Hankel singular values of the true system and the number of measurements. These results in turn yield complexity bounds and asymptotic consistency. We provide numerical experiments demonstrating the efficacy of our method for estimating linear systems from a variety of linear measurements.
Final focus systems for linear colliders
Energy Technology Data Exchange (ETDEWEB)
Erickson, R.A.
1987-11-01
The final focus system of a linear collider must perform two primary functions, it must focus the two opposing beams so that their transverse dimensions at the interaction point are small enough to yield acceptable luminosity, and it must steer the beams together to maintain collisions. In addition, the final focus system must transport the outgoing beams to a location where they can be recycled or safely dumped. Elementary optical considerations for linear collider final focus systems are discussed, followed by chromatic aberrations. The design of the final focus system of the SLAC Linear Collider (SLC) is described. Tuning and diagnostics and steering to collision are discussed. Most of the examples illustrating the concepts covered are drawn from the SLC, but the principles and conclusions are said to be generally applicable to other linear collider designs as well. 26 refs., 17 figs. (LEW)
Robust control of linear descriptor systems
Feng, Yu
2017-01-01
This book develops original results regarding singular dynamic systems following two different paths. The first consists of generalizing results from classical state-space cases to linear descriptor systems, such as dilated linear matrix inequality (LMI) characterizations for descriptor systems and performance control under regulation constraints. The second is a new path, which considers descriptor systems as a powerful tool for conceiving new control laws, understanding and deciphering some controller’s architecture and even homogenizing different—existing—ways of obtaining some new and/or known results for state-space systems. The book also highlights the comprehensive control problem for descriptor systems as an example of using the descriptor framework in order to transform a non-standard control problem into a classic stabilization control problem. In another section, an accurate solution is derived for the sensitivity constrained linear optimal control also using the descriptor framework. The boo...
Dynamical systems generated by linear maps
Dolićanin, Ćemal B
2014-01-01
The book deals with dynamical systems, generated by linear mappings of finite dimensional spaces and their applications. These systems have a relatively simple structure from the point of view of the modern dynamical systems theory. However, for the dynamical systems of this sort, it is possible to obtain explicit answers to specific questions being useful in applications. The considered problems are natural and look rather simple, but in reality in the course of investigation, they confront users with plenty of subtle questions, and their detailed analysis needs a substantial effort. The problems arising are related to linear algebra and dynamical systems theory, and therefore, the book can be considered as a natural amplification, refinement and supplement to linear algebra and dynamical systems theory textbooks.
Signals and transforms in linear systems analysis
Wasylkiwskyj, Wasyl
2013-01-01
Signals and Transforms in Linear Systems Analysis covers the subject of signals and transforms, particularly in the context of linear systems theory. Chapter 2 provides the theoretical background for the remainder of the text. Chapter 3 treats Fourier series and integrals. Particular attention is paid to convergence properties at step discontinuities. This includes the Gibbs phenomenon and its amelioration via the Fejer summation techniques. Special topics include modulation and analytic signal representation, Fourier transforms and analytic function theory, time-frequency analysis and frequency dispersion. Fundamentals of linear system theory for LTI analogue systems, with a brief account of time-varying systems, are covered in Chapter 4 . Discrete systems are covered in Chapters 6 and 7. The Laplace transform treatment in Chapter 5 relies heavily on analytic function theory as does Chapter 8 on Z -transforms. The necessary background on complex variables is provided in Appendix A. This book is intended to...
Structural Stability of Planar Bimodal Linear Systems
Directory of Open Access Journals (Sweden)
Josep Ferrer
2014-01-01
Full Text Available Structural stability ensures that the qualitative behavior of a system is preserved under small perturbations. We study it for planar bimodal linear dynamical systems, that is, systems consisting of two linear dynamics acting on each side of a given hyperplane and assuming continuity along the separating hyperplane. We describe which one of these systems is structurally stable when (real spiral does not appear and when it does we give necessary and sufficient conditions concerning finite periodic orbits and saddle connections. In particular, we study the finite periodic orbits and the homoclinic orbits in the saddle/spiral case.
Identification and Modelling of Linear Dynamic Systems
Directory of Open Access Journals (Sweden)
Stanislav Kocur
2006-01-01
Full Text Available System identification and modelling are very important parts of system control theory. System control is only as good as good is created model of system. So this article deals with identification and modelling problems. There are simple classification and evolution of identification methods, and then the modelling problem is described. Rest of paper is devoted to two most known and used models of linear dynamic systems.
Stabilization of Slowly Varying Switched Linear Systems
Institute of Scientific and Technical Information of China (English)
ZHANG Bing; LIANG Tong
2012-01-01
The stabilization problem of systems that switch among a finite set of slowly varying linear systems with arbitrary switching frequency is discussed.It is shown that if the entries of the pointwise stabilizing feedback gain matrix are continuously differentiable functions of the entries of the system coefficient matrices,then the closed-loop system is uniformly asymptotically stable if the rate of time variation of the system coefficient matrices is sufficiently small.
Hannah, John; Stewart, Sepideh; Thomas, Michael
2016-01-01
Linear algebra is one of the first abstract mathematics courses that students encounter at university. Research shows that many students find the dense presentation of definitions, theorems and proofs difficult to comprehend. Using a case study approach, we report on a teaching intervention based on Tall's three worlds (embodied, symbolic and…
Superconducting linear accelerator system for NSC
Indian Academy of Sciences (India)
P N Prakash; T S Datta; B P Ajith Kumar; J Antony; P Barua; J Chacko; A Choudhury; G K Chadhari; S Ghosh; S Kar; S A Krishnan; Manoj Kumar; Rajesh Kumar; A Mandal; D S Mathuria; R S Meena; R Mehta; K K Mistri; A Pandey; M V Suresh Babu; B K Sahu; A Sarkar; S S K Sonti; A Rai; S Venkatramanan; J Zacharias; R K Bhowmik; A Roy
2002-11-01
This paper reports the construction of a superconducting linear accelerator as a booster to the 15 UD Pelletron accelerator at Nuclear Science Centre, New Delhi. The LINAC will use superconducting niobium quarter wave resonators as the accelerating element. Construction of the linear accelerator has progressed sufﬁciently. Details of the entire accelerator system including the cryogenics facility, RF electronics development, facilities for fabricating niobium resonators indigenously, and present status of the project are presented.
STABILITY OF A SWITCHED LINEAR SYSTEM
Directory of Open Access Journals (Sweden)
At-Tasneem Mohd Amin
2012-12-01
Full Text Available Hybrid systems are dynamic systems that arise out of the interaction of continuous state dynamics and discrete state dynamics. Switched systems, which are a type of hybrid system, have been given much attention by control systems research over the past decade. Problems with the controllability, observability, converseability and stabilizability of switched systems have always been discussed. In this paper, the trend in research regarding the stability of switched systems will be investigated. Then the variety of methods that have been discovered by researchers for stabilizing switched linear systems with arbitrary switching will be discussed in detail.
Geometric Control of Patterned Linear Systems
Hamilton, Sarah C
2012-01-01
This monograph is aiming at researchers of systems control, especially those interested in multiagent systems, distributed and decentralized control, and structured systems. The book assumes no prior background in geometric control theory; however, a first year graduate course in linear control systems is desirable. Since not all control researchers today are exposed to geometric control theory, the book also adopts a tutorial style by way of examples that illustrate the geometric and abstract algebra concepts used in linear geometric control. In addition, the matrix calculations required for the studied control synthesis problems of linear multivariable control are illustrated via a set of running design examples. As such, some of the design examples are of higher dimension than one may typically see in a text; this is so that all the geometric features of the design problem are illuminated.
Fault tolerant control for switched linear systems
Du, Dongsheng; Shi, Peng
2015-01-01
This book presents up-to-date research and novel methodologies on fault diagnosis and fault tolerant control for switched linear systems. It provides a unified yet neat framework of filtering, fault detection, fault diagnosis and fault tolerant control of switched systems. It can therefore serve as a useful textbook for senior and/or graduate students who are interested in knowing the state-of-the-art of filtering, fault detection, fault diagnosis and fault tolerant control areas, as well as recent advances in switched linear systems.
On output regulation for linear systems
Saberi, Ali; Stoorvogel, Anton A.; Sannuti, Peddapullaiah
2001-01-01
For both continuous- and discrete-time systems, we revisit the output regulation problem for linear systems. We generalize the problem formulation in order � to expand the class of reference or disturbance signals, � to utilize the derivative or feedforward information of reference signals wheneve
When to call a linear system nonnegative
Nieuwenhuis, J.W.
1998-01-01
In this paper we will consider discrete time invariant linear systems that allow for an input-state-output representation with a finite dimensional state space, and that have a finite number of inputs and outputs. The basic issue in this paper is when to call these systems nonnegative. An important
Balanced truncation for linear switched systems
DEFF Research Database (Denmark)
Petreczky, Mihaly; Wisniewski, Rafal; Leth, John-Josef
2013-01-01
in this paper, we provide a bound on the approximation error in the L2L2 norm for continuous-time and the l2l2 norm for discrete-time linear switched systems. We provide a system theoretic interpretation of grammians and their singular values. Furthermore, we show that the performance of balanced truncation...
Controller reconfiguration for non-linear systems
Kanev, S.; Verhaegen, M.
2000-01-01
This paper outlines an algorithm for controller reconfiguration for non-linear systems, based on a combination of a multiple model estimator and a generalized predictive controller. A set of models is constructed, each corresponding to a different operating condition of the system. The interacting m
Coprime factorization for regular linear systems
Curtain, R; Weiss, G; Weiss, M
1996-01-01
Mild sufficient conditions are given for the existence of a doubly coprime factorization of the transfer function of a regular linear system, as well as formulae for such a factorization. The results are illustrated by two examples of delay systems, one of which has infinitely many unstable poles. C
Balanced truncation for linear switched systems
DEFF Research Database (Denmark)
Petreczky, Mihaly; Wisniewski, Rafal; Leth, John-Josef
2013-01-01
in this paper, we provide a bound on the approximation error in the L2L2 norm for continuous-time and the l2l2 norm for discrete-time linear switched systems. We provide a system theoretic interpretation of grammians and their singular values. Furthermore, we show that the performance of balanced truncation...
Linear response theory for quantum open systems
Wei, J. H.; Yan, YiJing
2011-01-01
Basing on the theory of Feynman's influence functional and its hierarchical equations of motion, we develop a linear response theory for quantum open systems. Our theory provides an effective way to calculate dynamical observables of a quantum open system at its steady-state, which can be applied to various fields of non-equilibrium condensed matter physics.
Critical dwell time of switched linear systems
Institute of Scientific and Technical Information of China (English)
Lijun ZHANG; Chunwen LI
2006-01-01
In this paper, we consider the relation between the switching dwell time and the stabilization of switched linear control systems. First of all, a concept of critical dwell time is given for switched linear systems without control inputs, and the critical dwell time is taken as an arbitrary given positive constant for a switched linear control systems with controllable switching models. Secondly, when a switched linear system has many stabilizable switching models, the problem of stabilization of the overall system is considered. An on-line feedback control is designed such that the overall system is asymptotically stabilizable under switching laws which depend only on those of uncontrollable subsystems of the switching models. Finally, when a switched system is partially controllable (While some switching models are probably unstabilizable), an on-line feedback control and a cyclic switching strategy are designed such that the overall system is asymptotically stabilizable if all switching models of this uncontrollable subsystems are asymptotically stable. In addition,algorithms for designing switching laws and controls are presented.
LISA: a linear structured system analysis program
Martinez-Martinez, Sinuhé; Mader, Theodor; Boukhobza, Taha; Hamelin, Frédéric
2007-01-01
International audience; In this paper the program LISA is presented. LISA is a flexible and portable program which has been developed to analyse structural properties of large scale linear and bilinear structured systems. More precisely, the program LISA contains programmed algorithms which allow us to apply recent results in the analysis of structured systems to some particular cases.
Sequent calculus proof systems for inductive definitions
Brotherston, James
2006-01-01
Inductive definitions are the most natural means by which to represent many families of structures occurring in mathematics and computer science, and their corresponding induction / recursion principles provide the fundamental proof techniques by which to reason about such families. This thesis studies formal proof systems for inductive definitions, as needed, e.g., for inductive proof support in automated theorem proving tools. The systems are formulated as sequent calculi for...
Generalized Cross-Gramian for Linear Systems
DEFF Research Database (Denmark)
Shaker, Hamid Reza
2012-01-01
The cross-gramian is a well-known matrix with embedded controllability and observability information. The cross-gramian is related to the Hankel operator and the Hankel singular values of a linear square system and it has several interesting properties. These properties make the cross-gramian...... popular in several applications including model reduction, control configuration selection and sensitivity analysis. The ordinary cross-gramian which has been defined in the literature is the solution of a Sylvester equation. This Sylvester equation is not always solvable and therefore for some linear...... square symmetric systems, the ordinary cross-gramian does not exist. To cope with this problem, a new generalized cross-gramian is introduced in this paper. In contrast to the ordinary cross-gramian, the generalized cross-gramian can be easily obtained for general linear systems and therefore can be used...
Fractional linear systems and electrical circuits
Kaczorek, Tadeusz
2015-01-01
This monograph covers some selected problems of positive and fractional electrical circuits composed of resistors, coils, capacitors and voltage (current) sources. The book consists of 8 chapters, 4 appendices and a list of references. Chapter 1 is devoted to fractional standard and positive continuous-time and discrete-time linear systems without and with delays. In chapter 2 the standard and positive fractional electrical circuits are considered and the fractional electrical circuits in transient states are analyzed. Descriptor linear electrical circuits and their properties are investigated in chapter 3, while chapter 4 is devoted to the stability of fractional standard and positive linear electrical circuits. The reachability, observability and reconstructability of fractional positive electrical circuits and their decoupling zeros are analyzed in chapter 5. The fractional linear electrical circuits with feedbacks are considered in chapter 6. In chapter 7 solutions of minimum energy control for standa...
Researted FOM for Multiple Shifted Linear Systems
Institute of Scientific and Technical Information of China (English)
李占稳; 汪勇; 顾桂定
2005-01-01
The seed method is used for solving multiple linear systems A(i) x(i) = b(i) for l≤ i≤ s , where the coefficient matrix A(i) and the right-hand side b(i) are different in general. It is known that the CG method is an effective method for symmetric coefficient matrices A(i) . In this paper, the FOM method is employed to solve multiple linear systems when coefficient matrices are non-symmetric matrices. One of the systems is selected as the seed system which generates a Krylov subspace, then the residuals of other systems are projected onto the generated Krylov subspace to get the approximate solutions for the unsolved ones. The whole process is repeated until all the systems are solved.
Reset stabilisation of positive linear systems
Zhao, Xudong; Yin, Yunfei; Shen, Jun
2016-09-01
In this paper, the problems of reset stabilisation for positive linear systems (PLSs) are investigated. Some properties relating to reset control of PLSs are first revealed. It is shown that these properties are different from the corresponding ones of general linear systems. Second, a class of periodic reset scheme is designed to exponentially stabilise an unstable PLS with a prescribed decay rate. Then, for a given PLS with reset control, some discussions on the upper bound of its decay rate are presented. Meanwhile, the reset stabilisation for PLSs in a special case is probed as well. Finally, two numerical examples are used to demonstrate the correctness and effectiveness of the obtained theoretical results.
A decoupled system of hyperbolic equations for linearized cosmological perturbations
Ramírez, J
2002-01-01
A decoupled system of hyperbolic partial differential equations for linear perturbations around spatially flat FRW universes is obtained for the first time. The two key ingredients in obtaining this system are i) the explicit decomposition of the perturbing energy momentum tensor into two pieces: intrinsic and free, which have definite and distinct mathematical properties and physical interpretation, and ii) the introduction of a new gauge which plays a similar role as harmonic gauge does for perturbations around Minkowski space-time. The proposed formalism could be highly relevant for physical cosmology, since our universe is most likely flat. We deal with classical perturbations, but our treatment, being covariant, is also very appropriate for the description of linearized quantum gravity around cosmological backgrounds.
On exponential stabilizability of linear neutral systems
Directory of Open Access Journals (Sweden)
Dusser Xavier
2001-01-01
Full Text Available In this paper, we deal with linear neutral functional differential systems. Using an extended state space and an extended control operator, we transform the initial neutral system in an infinite dimensional linear system. We give a sufficient condition for admissibility of the control operator B , conditions under which operator B can be acceptable in order to work with controllability and stabilizability. Necessary and sufficient conditions for exact controllability are provided; in terms of a gramian of controllability N ( μ . Assuming admissibility and exact controllability, a feedback control law is defined from the inverse of the operator N ( μ in order to stabilize exponentially the closed loop system. In this case, the semigroup generated by the closed loop system has an arbitrary decay rate.
Control of stage by stage changing linear dynamic systems
Directory of Open Access Journals (Sweden)
Barseghyan V.R.
2012-01-01
Full Text Available In this paper, the control problems of linear dynamic systems stage by stage changing and the optimal control with the criteria of quality set for the whole range of time intervals are considered. The necessary and sufficient conditions of total controllability are also stated. The constructive solving method of a control problem is offered, as well as the definitions of conditions for the existence of programmed control and motions. The explicit form of control action for a control problem is constructed. The method for solving optimal control problem is offered, and the solution of optimal control of a specific target is brought.
On optimal output regulation for linear systems
Saberi, Ali; Stoorvogel, Anton A.; Sannuti, Peddapullaiah; Shi, Guoyong
2003-01-01
The classical output regulation problem formulation for linear systems has a number of shortcomings; among them a primary one is that it does not take into account the transient response. Although this problem has been studied since the 1970s, a complete picture has not emerged yet. We formulate and
Energy propagation in linear hyperbolic systems
Mainardi, F.; Groesen, van E.
1989-01-01
The concept of energy velocity for linear dispersive waves is usually given for a normal mode solution of the system as the ratio between the mean energy flux and the mean energy density. In the absence of dissipation this velocity is known to coincide with the corresponding group velocity. When dis
Disturbance Decoupling of Switched Linear Systems
Yurtseven, E.; Heemels, W.P.M.H.; Camlibel, M.K.
2010-01-01
In this paper we consider disturbance decoupling problems for switched linear systems. We will provide necessary and sufficient conditions for three different versions of disturbance decoupling, which differ based on which signals are considered to be the disturbance. In the first version the contin
PERIODIC SOLUTIONS OF ASYMPTOTICALLY LINEAR HAMILTONIAN SYSTEMS
Institute of Scientific and Technical Information of China (English)
FEIGUIHUA; QIUQINGJIU
1997-01-01
The authors establish the existence of nontrival periodic solutions of the asymptotically linear Hamiltomian systems in the general case that the asymptotic matrix may be degenerate and time-dependent.This is done by using the critical point theory,Galerkin approximation procedure and the Maslov-type index theory introduced and generalized by Conley,Zehnder and Long.
Weak and strong stabilization of linear systems
Institute of Scientific and Technical Information of China (English)
Mohamed OUZAHRA; Hamid BOURRAY; Asmae KAMAL; Rachid El AYADI
2009-01-01
We study the problem of stabilizing a distributed linear system on a subregion of its geometrical domain. We are concerned with two methods: the first approach enables us to characterize a stabilizing control via the steady state Riccati equation, and the second one is based on decomposing the state space into two suitable subspaces and studying the projections of the initial system onto such subspaces. The obtained results are performed through various examples.
Electronic emulator of linear dynamic systems
Garan, Maryna; Kovalenko, Iaroslav; Moučka, Michal; Vagaská, Alena
2015-01-01
The aim of this article is development and realization of electronic emulator of dynamic systems with setting of parameters from PC. This emulator is the first prototype, which is meant to prove the possibility of emulating the behavior of dynamic systems by microprocessor. The main goal of research is creating of equipment, which can emulate a behavior of pneumatic muscle with sufficient accuracy. Dynamic of pneumatic muscles is significantly non-linear and changeable in the dependence on...
Feedback linearization application for LLRF control system
Energy Technology Data Exchange (ETDEWEB)
Kwon, S.; Regan, A.; Wang, Y.M.; Rohlev, T.
1999-06-01
The Low Energy Demonstration Accelerator (LEDA) being constructed at Los Alamos National Laboratory will serve as the prototype for the low energy section of Acceleration Production of Tritium (APT) accelerator. This paper addresses the problem of the LLRF control system for LEDA. The authors propose a control law which is based on exact feedback linearization coupled with gain scheduling which reduces the effect of the deterministic klystron cathode voltage ripple that is due to harmonics of the high voltage power supply and achieves tracking of desired set points. Also, they propose an estimator of the ripple and its time derivative and the estimates based feedback linearization controller.
Feedback linearization application for LLRF control system
Energy Technology Data Exchange (ETDEWEB)
Kwon, S.; Regan, A.; Wang, Y.M.; Rohlev, T.
1998-12-31
The Low Energy Demonstration Accelerator (LEDA) being constructed at Los Alamos National Laboratory will serve as the prototype for the low energy section of Acceleration Production of Tritium (APT) accelerator. This paper addresses the problem of the LLRF control system for LEDA. The authors propose a control law which is based on exact feedback linearization coupled with gain scheduling which reduces the effect of the deterministic klystron cathode voltage ripple that is due to harmonics of the high voltage power supply and achieves tracking of desired set points. Also, they propose an estimator of the ripple and its time derivative and the estimates based feedback linearization controller.
Parameter identifiability of linear dynamical systems
Glover, K.; Willems, J. C.
1974-01-01
It is assumed that the system matrices of a stationary linear dynamical system were parametrized by a set of unknown parameters. The question considered here is, when can such a set of unknown parameters be identified from the observed data? Conditions for the local identifiability of a parametrization are derived in three situations: (1) when input/output observations are made, (2) when there exists an unknown feedback matrix in the system and (3) when the system is assumed to be driven by white noise and only output observations are made. Also a sufficient condition for global identifiability is derived.
Linear systems optimal and robust control
Sinha, Alok
2007-01-01
Introduction Overview Contents of the Book State Space Description of a Linear System Transfer Function of a Single Input/Single Output (SISO) System State Space Realizations of a SISO System SISO Transfer Function from a State Space Realization Solution of State Space Equations Observability and Controllability of a SISO System Some Important Similarity Transformations Simultaneous Controllability and Observability Multiinput/Multioutput (MIMO) Systems State Space Realizations of a Transfer Function Matrix Controllability and Observability of a MIMO System Matrix-Fraction Description (MFD) MFD of a Transfer Function Matrix for the Minimal Order of a State Space Realization Controller Form Realization from a Right MFD Poles and Zeros of a MIMO Transfer Function Matrix Stability Analysis State Feedback Control and Optimization State Variable Feedback for a Single Input System Computation of State Feedback Gain Matrix for a Multiinput System State Feedback Gain Matrix for a Multi...
Ground states of linearly coupled Schrodinger systems
Directory of Open Access Journals (Sweden)
Haidong Liu
2017-01-01
Full Text Available This article concerns the standing waves of a linearly coupled Schrodinger system which arises from nonlinear optics and condensed matter physics. The coefficients of the system are spatially dependent and have a mixed behavior: they are periodic in some directions and tend to positive constants in other directions. Under suitable assumptions, we prove that the system has a positive ground state. In addition, when the L-infinity-norm of the coupling coefficient tends to zero, the asymptotic behavior of the ground states is also obtained.
Coherent versus Measurement Feedback: Linear Systems Theory for Quantum Information
Yamamoto, Naoki
2014-10-01
To control a quantum system via feedback, we generally have two options in choosing a control scheme. One is the coherent feedback, which feeds the output field of the system, through a fully quantum device, back to manipulate the system without involving any measurement process. The other one is measurement-based feedback, which measures the output field and performs a real-time manipulation on the system based on the measurement results. Both schemes have advantages and disadvantages, depending on the system and the control goal; hence, their comparison in several situations is important. This paper considers a general open linear quantum system with the following specific control goals: backaction evasion, generation of a quantum nondemolished variable, and generation of a decoherence-free subsystem, all of which have important roles in quantum information science. Some no-go theorems are proven, clarifying that those goals cannot be achieved by any measurement-based feedback control. On the other hand, it is shown that, for each control goal there exists a coherent feedback controller accomplishing the task. The key idea to obtain all the results is system theoretic characterizations of the above three notions in terms of controllability and observability properties or transfer functions of linear systems, which are consistent with their standard definitions.
Coherent versus Measurement Feedback: Linear Systems Theory for Quantum Information
Directory of Open Access Journals (Sweden)
Naoki Yamamoto
2014-11-01
Full Text Available To control a quantum system via feedback, we generally have two options in choosing a control scheme. One is the coherent feedback, which feeds the output field of the system, through a fully quantum device, back to manipulate the system without involving any measurement process. The other one is measurement-based feedback, which measures the output field and performs a real-time manipulation on the system based on the measurement results. Both schemes have advantages and disadvantages, depending on the system and the control goal; hence, their comparison in several situations is important. This paper considers a general open linear quantum system with the following specific control goals: backaction evasion, generation of a quantum nondemolished variable, and generation of a decoherence-free subsystem, all of which have important roles in quantum information science. Some no-go theorems are proven, clarifying that those goals cannot be achieved by any measurement-based feedback control. On the other hand, it is shown that, for each control goal there exists a coherent feedback controller accomplishing the task. The key idea to obtain all the results is system theoretic characterizations of the above three notions in terms of controllability and observability properties or transfer functions of linear systems, which are consistent with their standard definitions.
Lectures on algebraic system theory: Linear systems over rings
Kamen, E. W.
1978-01-01
The presentation centers on four classes of systems that can be treated as linear systems over a ring. These are: (1) discrete-time systems over a ring of scalars such as the integers; (2) continuous-time systems containing time delays; (3) large-scale discrete-time systems; and (4) time-varying discrete-time systems.
Minimal solution of singular LR fuzzy linear systems.
Nikuie, M; Ahmad, M Z
2014-01-01
In this paper, the singular LR fuzzy linear system is introduced. Such systems are divided into two parts: singular consistent LR fuzzy linear systems and singular inconsistent LR fuzzy linear systems. The capability of the generalized inverses such as Drazin inverse, pseudoinverse, and {1}-inverse in finding minimal solution of singular consistent LR fuzzy linear systems is investigated.
Nonlinear Energy Collimation System for Linear Colliders
Resta-Lopez, Javier
2011-01-01
The post-linac energy collimation system of multi-TeV linear colliders is designed to fulfil an important function of protection of the Beam Delivery System (BDS) against miss-steered beams likely generated by failure modes in the main linac. For the case of the Compact Linear Collider (CLIC), the energy collimators are required to withstand the impact of a full bunch train in case of failure. This is a very challenging task, assuming the nominal CLIC beam parameters at 1.5 TeV beam energy. The increase of the transverse spot size at the collimators using nonlinear magnets is a potential solution to guarantee the survival of the collimators. In this paper we present an alternative nonlinear optics based on a skew sextupole pair for energy collimation. Performance simulation results are also presented.
Identifiability of linear systems in physical coordinates
Su, Tzu-Jeng; Juang, Jer-Nan
1992-01-01
Identifiability of linear, time-invariant systems in physical coordinates is discussed. It is shown that identification of the system matrix in physical coordinates can be accomplished by determining a transformation matrix that relates the physical locations of actuators and sensors to the test-data-derived input and output matrices. For systems with symmetric matrices, the solution of a constrained optimization problem is used to characterize all the possible solutions of the transformation matrix. Conditions for the existence of a unique transformation matrix are established easily from the explicit form of the solutions. For systems with limited inputs and outputs, the question about which part of the system can be uniquely identified is also answered. A simple mass-spring system is used to verify the conclusions of this study.
Criteria for Stability of Linear Control Systems
Institute of Scientific and Technical Information of China (English)
JING Yan-fei; HUANG Ting-zhu
2007-01-01
As it is well known, it is significant to know whether a matrix is an H-matrix or not in stability analysis of linear control systems. However, to distinguish H-matrices is difficult in real applications. In this paper, a practical extension of the sufficient conditions for H-matrices is investigated under some conditions. A larger scale of H-matrices which can be judged by the proposed method is shown by the numerical examples.
Recursive Inversion Of Externally Defined Linear Systems
Bach, Ralph E., Jr.; Baram, Yoram
1992-01-01
Technical memorandum discusses mathematical technique described in "Recursive Inversion by Finite-Impulse-Response Filters" (ARC-12247). Technique is recursive algorithm yielding finite-impulse-response approximation of unknown single-input/single-output, causal, time-invariant, linear, real system, response of which is sequence of impulses. Useful in such diverse applications as medical diagnoses, identification of military targets, geophysical exploration, and nondestructive testing.
On a conjecture on linear systems
Indian Academy of Sciences (India)
SONICA ANAND
2017-06-01
In a remark to Green’s conjecture, Paranjape and Ramanan analysed the vector bundle $E$ which is the pullback by the canonical map of the universal quotient bundle $T_\\mathbb{P}^{g−1}(−1)$ on $\\mathbb{P}^{g−1}$ and stated a more general conjecture and proved it for the curveswith Clifford Index 1 (trigonal and plane quintics). In this paper, we state the conjecturefor general linear systems and obtain results for the case of hyper-elliptic curves.
Galerkin projection methods for solving multiple related linear systems
Energy Technology Data Exchange (ETDEWEB)
Chan, T.F.; Ng, M.; Wan, W.L.
1996-12-31
We consider using Galerkin projection methods for solving multiple related linear systems A{sup (i)}x{sup (i)} = b{sup (i)} for 1 {le} i {le} s, where A{sup (i)} and b{sup (i)} are different in general. We start with the special case where A{sup (i)} = A and A is symmetric positive definite. The method generates a Krylov subspace from a set of direction vectors obtained by solving one of the systems, called the seed system, by the CG method and then projects the residuals of other systems orthogonally onto the generated Krylov subspace to get the approximate solutions. The whole process is repeated with another unsolved system as a seed until all the systems are solved. We observe in practice a super-convergence behaviour of the CG process of the seed system when compared with the usual CG process. We also observe that only a small number of restarts is required to solve all the systems if the right-hand sides are close to each other. These two features together make the method particularly effective. In this talk, we give theoretical proof to justify these observations. Furthermore, we combine the advantages of this method and the block CG method and propose a block extension of this single seed method. The above procedure can actually be modified for solving multiple linear systems A{sup (i)}x{sup (i)} = b{sup (i)}, where A{sup (i)} are now different. We can also extend the previous analytical results to this more general case. Applications of this method to multiple related linear systems arising from image restoration and recursive least squares computations are considered as examples.
Multiparameter Fractional Difference Linear Control Systems
Directory of Open Access Journals (Sweden)
Dorota Mozyrska
2014-01-01
Full Text Available The Riemann-Liouville-, Caputo-, and Grünwald-Letnikov-type fractional order difference operators are discussed and used to state and solve the controllability and observability problems of linear fractional order discrete-time control systems with multiorder and multistep. It is shown that the obtained results do not depend on the type of fractional operators and steps. The comparison of systems is made under the number of steps needed, firstly to achieve a final point, and secondly to distinguish initial conditions for particular operator.
Operator approach to linear control systems
Cheremensky, A
1996-01-01
Within the framework of the optimization problem for linear control systems with quadratic performance index (LQP), the operator approach allows the construction of a systems theory including a number of particular infinite-dimensional optimization problems with hardly visible concreteness. This approach yields interesting interpretations of these problems and more effective feedback design methods. This book is unique in its emphasis on developing methods for solving a sufficiently general LQP. Although this is complex material, the theory developed here is built on transparent and relatively simple principles, and readers with less experience in the field of operator theory will find enough material to give them a good overview of the current state of LQP theory and its applications. Audience: Graduate students and researchers in the fields of mathematical systems theory, operator theory, cybernetics, and control systems.
The Definition of Novelty in Recommendation System
Directory of Open Access Journals (Sweden)
Liang Zhang
2013-01-01
Full Text Available With the development of information technology and application of the Internet, People gradually entered the time of information overload from information scarcity. User satisfaction with recommender systems is related not only to how accurately the system recommends but also to how much it supports the user’s decision making. Novelty is one of the important metrics of customer satisfaction. There is an increasing realization in the Recommender Systems (RS field that novelty is fundamental qualities of recommendation effectiveness and added-value. This paper combed research results about definition and algorithm of novel recommendation, and starting from the meaning of "novel", defined novelty of item in recommendation system. Experiment proved using the definition of novelty to recommend can effectively recognize the item that the user is familiar with and ensure certain accuracy.
a Continuous-Time Positive Linear System
Directory of Open Access Journals (Sweden)
Kyungsup Kim
2013-01-01
Full Text Available This paper discusses a computational method to construct positive realizations with sparse matrices for continuous-time positive linear systems with multiple complex poles. To construct a positive realization of a continuous-time system, we use a Markov sequence similar to the impulse response sequence that is used in the discrete-time case. The existence of the proposed positive realization can be analyzed with the concept of a polyhedral convex cone. We provide a constructive algorithm to compute positive realizations with sparse matrices of some positive systems under certain conditions. A sufficient condition for the existence of a positive realization, under which the proposed constructive algorithm works well, is analyzed.
ERF Based Precision Linear Drive System
Tönshoff, Hans Kurt; Stegmann, Axel
The design of clutches using electrorheological fluids (ERF) or magnetorheological suspensions (MRS) offers a new approach to precision linear drive systems based on the ‘inch-worm’ principle. This principle needs two clutches or controllable clamps and one (or more) elements to vary the distance between these clamps. To perform a caterpillar-like motion the actuators are controlled in a cyclic mode. This paper presents design elements, system structure and first results of motion performance of a prototype drive system. The presented linear drive combines the high resolution of piezo actuators, the unlimited travel of the ‘inch-worm’ principle and the clutch effect of ERF without a substantial mechanical excitation. The motion of the two clamps is controlled to move a stage in point to point mode or to follow a given velocity profile. Using two piezo actuators the stage can move continuously. Pre-loaded piezo actuators control the distances between the two clamps and the central slide. Each ERF clamp is designed as a set of thin parallel steel plate electrodes which interlock with a set of ground plates. Drive force limits are given by the maximum yield force of the clamps as well as by the relation of the actuator expansion and the ERF/MRS shear stiffness in “solid” mode.
The Optimal Linear Quadratic Feedback State Regulator Problem for Index One Descriptor Systems
Engwerda, J.C.; Salmah, Y.; Wijayanti, I.E.
2008-01-01
In this note we present both necessary and sufficient conditions for the existence of a linear static state feedback controller if the system is described by an index one descriptor system. A priori no definiteness restrictions are made w.r.t. the quadratic performance criterium. It is shown that in
Iterative solution of large linear systems
Young, David M
2003-01-01
This self-contained treatment offers a systematic development of the theory of iterative methods. Its focal point resides in an analysis of the convergence properties of the successive overrelaxation (SOR) method, as applied to a linear system with a consistently ordered matrix. The text explores the convergence properties of the SOR method and related techniques in terms of the spectral radii of the associated matrices as well as in terms of certain matrix norms. Contents include a review of matrix theory and general properties of iterative methods; SOR method and stationary modified SOR meth
Linear Amplifier Model for Optomechanical Systems
Botter, Thierry; Brahms, Nathan; Schreppler, Sydney; Stamper-Kurn, Dan M
2011-01-01
We model optomechanical systems as linear optical amplifiers. This provides a unified treatment of diverse optomechanical phenomena. We emphasize, in particular, the relationship between ponderomotive squeezing and optomechanically induced transparency, two foci of current research. We characterize the amplifier response to quantum and deliberately applied fluctuations, both optical and mechanical. Further, we apply these results to establish quantum limits on external force sensing both on and off cavity resonance. We find that the maximum sensitivity attained on resonance constitutes an absolute upper limit, not surpassed when detuning off cavity resonance. The theory can be extended to a two-sided cavity with losses and limited detection efficiency.
Linear Actuator System for the NASA Docking System
Dick, Brandon N.; Oesch, Christopher; Rupp, Timothy W.
2017-01-01
The Linear Actuator System (LAS) is a major sub-system within the NASA Docking System (NDS). The NDS Block 1 will be used on the Boeing Crew Space Transportation (CST-100) system to achieve docking with the International Space Station. Critical functions in the Soft Capture aspect of docking are performed by the LAS. This paper describes the general function of the LAS, the system's key requirements and technical challenges, and the development and qualification approach for the system.
Control system analysis for the perturbed linear accelerator rf system
Sung Il Kwon
2002-01-01
This paper addresses the modeling problem of the linear accelerator RF system in SNS. Klystrons are modeled as linear parameter varying systems. The effect of the high voltage power supply ripple on the klystron output voltage and the output phase is modeled as an additive disturbance. The cavity is modeled as a linear system and the beam current is modeled as the exogenous disturbance. The output uncertainty of the low level RF system which results from the uncertainties in the RF components and cabling is modeled as multiplicative uncertainty. Also, the feedback loop uncertainty and digital signal processing signal conditioning subsystem uncertainties are lumped together and are modeled as multiplicative uncertainty. Finally, the time delays in the loop are modeled as a lumped time delay. For the perturbed open loop system, the closed loop system performance, and stability are analyzed with the PI feedback controller.
Linear concentration system; Sistema de concentracion lineal
Energy Technology Data Exchange (ETDEWEB)
Gonzalez Lugo, J.I; Leon Rovira, N; Aguayo Tellez, H [Instituto Tecnologico y de Estudios Superiores de Monterrey, Monterrey, Nuevo Leon (Mexico)]. E-mails: a00812662@itesm.mx; noel.leon@itesm.mx; haguayo@itesm.mx
2013-03-15
Solar linear concentration technologies to generate high temperatures are limited to the ranges of 200 to 500 degrees Celsius. While its performance has been tested through prototypes and pilot plants around the world, there are still areas of opportunity that can be exploited to obtain a linear concentration that achieves temperatures above this range in order to have a better use of the available solar energy. Because of this: It is possible to develop a linear concentration system that can track the sun with minimal movement of the absorber-receiver while maintaining temperatures above 850 degrees Celsius sufficient for industrial processes that require that temperature. The methodology consists of a series of stages (conceptual design, simulation, evaluation, development concept, results and validation) through which concepts are generated that allow design and evaluation of solar concentrator configurations with the help of simulation software. We have designed a linear parabolic concentrating system which comprises a set of mirrors segments with different focal lengths that works within the range of 600 degrees Celsius; however, it is advancing in the development of a double concentration to reach 850 degrees Celsius. [Spanish] Las tecnologias de concentracion lineal solar para generar altas temperaturas se ven limitadas a los rangos de 200 a 500 grados centigrados. Si bien su funcionamiento ha sido probado a traves de prototipos y plantas piloto alrededor del mundo, aun existen areas de oportunidad que pueden ser aprovechadas para obtener un sistema de concentracion lineal que permita alcanzar temperaturas mayores a este rango para asi tener un mejor aprovechamiento de la energia solar disponible. Debido a esto: Es posible desarrollar un sistema de concentracion lineal capaz de seguir la trayectoria del Sol con minimo movimiento del absorbedor-recibidor al mismo tiempo que mantiene temperaturas superiores a los 850 grados centigrados suficientes para
Linear optical response of finite systems using multishift linear system solvers.
Hübener, Hannes; Giustino, Feliciano
2014-07-28
We discuss the application of multishift linear system solvers to linear-response time-dependent density functional theory. Using this technique the complete frequency-dependent electronic density response of finite systems to an external perturbation can be calculated at the cost of a single solution of a linear system via conjugate gradients. We show that multishift time-dependent density functional theory yields excitation energies and oscillator strengths in perfect agreement with the standard diagonalization of the response matrix (Casida's method), while being computationally advantageous. We present test calculations for benzene, porphin, and chlorophyll molecules. We argue that multishift solvers may find broad applicability in the context of excited-state calculations within density-functional theory and beyond.
Linear optical response of finite systems using multishift linear system solvers
Energy Technology Data Exchange (ETDEWEB)
Hübener, Hannes; Giustino, Feliciano [Department of Materials, University of Oxford, Oxford OX1 3PH (United Kingdom)
2014-07-28
We discuss the application of multishift linear system solvers to linear-response time-dependent density functional theory. Using this technique the complete frequency-dependent electronic density response of finite systems to an external perturbation can be calculated at the cost of a single solution of a linear system via conjugate gradients. We show that multishift time-dependent density functional theory yields excitation energies and oscillator strengths in perfect agreement with the standard diagonalization of the response matrix (Casida's method), while being computationally advantageous. We present test calculations for benzene, porphin, and chlorophyll molecules. We argue that multishift solvers may find broad applicability in the context of excited-state calculations within density-functional theory and beyond.
A Kalman decomposition to detect temporal linear system srtucture
Willigenburg, Van L.G.; Koning, De W.L.
2015-01-01
Feedback controllers for non-linear systems are often based on a linearized dynamic model. Such a linearized model may be temporarily uncontrollable and/or unreconstructable. This paper introduces the so-called differential Kalman decomposition of time-varying linear systems. It is based on
Control of Linear Systems Over Commutative Normed Algebras with Applications.
1987-02-01
Identify by block number) System Theory, Linear Systems, Control, Systems with Time Delays, Time - Varying Systems, State- Space Models, Pole...modes for the class of linear time -varying systems. These concepts are defined in terms of a noncommutative factorization of opera- tor polynomials...classes of complex linear systems, including systems with time delays, systems with unknown parameters and time -varying systems. In the work on
Dynamics of delayed piecewise linear systems
Directory of Open Access Journals (Sweden)
Laszlo E. Kollar
2003-02-01
Full Text Available In this paper the dynamics of the controlled pendulum is investigated assuming backlash and time delays. The upper equilibrium of the pendulum is stabilized by a piecewise constant control force which is the linear combination of the sampled values of the angle and the angular velocity of the pendulum. The control force is provided by a motor which drives one of the wheels of the cart through an elastic teeth belt. The contact between the teeth of the gear (rigid and the belt (elastic introduces a nonlinearity known as ``backlash" and causes the oscillation of the controlled pendulum around its upper equilibrium. The processing and sampling delays in the determination of the control force tend to destabilize the controlled system as well. We obtain conditions guaranteeing that the pendulum remains in the neighborhood of the upper equilibrium. Experimental findings obtained on a computer controlled inverted pendulum cart structure are also presented showing good agreement with the simulation results.
System theory as applied differential geometry. [linear system
Hermann, R.
1979-01-01
The invariants of input-output systems under the action of the feedback group was examined. The approach used the theory of Lie groups and concepts of modern differential geometry, and illustrated how the latter provides a basis for the discussion of the analytic structure of systems. Finite dimensional linear systems in a single independent variable are considered. Lessons of more general situations (e.g., distributed parameter and multidimensional systems) which are increasingly encountered as technology advances are presented.
Robust Stabilization for Uncertain Linear Delay Markow Jump System
Institute of Scientific and Technical Information of China (English)
钟麦英; 汤兵勇; 黄小原
2001-01-01
Markov jump linear systems are defined as a family of linear systems with randomly Markov jumping parameters and are used to model systems subject to failures or changes in structure. The robust stabilization problem of jump linear delay system with umcerratnty was studied. By using of linear matrix inequalities, the existence conditions of robust stabilizing and the state feedback controller designing methods are also presented and proved. Finally, an illustrated example shows the effectiveness of this approach.
LINEAR SYSTEMS ASSOCIATED WITH NUMERICAL METHODS FOR CONSTRAINED OPITMIZATION
Institute of Scientific and Technical Information of China (English)
Y. Yuan
2003-01-01
Linear systems associated with numerical methods for constrained optimization arediscussed in this paper. It is shown that the corresponding subproblems arise in most well-known methods, no matter line search methods or trust region methods for constrainedoptimization can be expressed as similar systems of linear equations. All these linearsystems can be viewed as some kinds of approximation to the linear system derived by theLagrange-Newton method. Some properties of these linear systems are analyzed.
The nature of solutions to linear passive complementarity systems
Camlibel, Mehmet; Heemels, W.P.M.H.; Schumacher, J.M.
1999-01-01
Linear passive systems with complementarity conditions (as an application, one may consider linear passive networks with ideal diodes) are studied. For these systems contained in the linear complementarity class of hybrid systems, existence and uniqueness of solutions are established. Moreover, the
On Stabilization and Tracking for Switching Linear Systems
Baglietto, Marco; Battistelli, Giorgio; Tesi, Pietro
2012-01-01
This paper describes recent progress in the study of switching linear systems, i.e. linear systems that can be modeled as a family of subsystems connected by switching between a number of discrete modes. We address the problem of stabilization and tracking for switching linear systems in case where
Linear Actuator System for the NASA Docking System
Dick, Brandon; Oesch, Chris
2017-01-01
The Linear Actuator System (LAS) is a major sub-system within the NASA Docking System (NDS). The NDS Block 1 will be used on the Boeing Crew Space Transportation (CST-100) system to achieve docking with the International Space Station. Critical functions in the Soft Capture aspect of docking are performed by the LAS, which implements the Soft Impact Mating and Attenuation Concept (SIMAC). This paper describes the general function of the LAS, the system's key requirements and technical challenges, and the development and qualification approach for the system.
Directory of Open Access Journals (Sweden)
Luca Faes
2012-01-01
Full Text Available This tutorial paper introduces a common framework for the evaluation of widely used frequency-domain measures of coupling (coherence, partial coherence and causality (directed coherence, partial directed coherence from the parametric representation of linear multivariate (MV processes. After providing a comprehensive time-domain definition of the various forms of connectivity observed in MV processes, we particularize them to MV autoregressive (MVAR processes and derive the corresponding frequency-domain measures. Then, we discuss the theoretical interpretation of these MVAR-based connectivity measures, showing that each of them reflects a specific time-domain connectivity definition and how this results in the description of peculiar aspects of the information transfer in MV processes. Furthermore, issues related to the practical utilization of these measures on real-time series are pointed out, including MVAR model estimation and significance assessment. Finally, limitations and pitfalls arising from model mis-specification are discussed, indicating possible solutions and providing practical recommendations for a safe computation of the connectivity measures. An example of estimation of the presented measures from multiple EEG signals recorded during a combined visuomotor task is also reported, showing how evaluation of coupling and causality in the frequency domain may help describing specific neurophysiological mechanisms.
Institute of Scientific and Technical Information of China (English)
Min WU; Yong HE; Jinhua SHE
2004-01-01
Necessary and suffcient conditions for the existence of a Lyapunov function in the Lur'e form to guarantee the absolute stability ofLur' e control systems with multiple non-linearities are discussed in this paper. It simplifies the existence problem to one of solving a set of linear matrix inequalities (LMIs). If those LMIs are feasible, free parameters in the Lyapunov function,such as the positive definite matrix and the coefficients of the integral terms, are given by the solution of the LMIs. Otherwise, this Lyapunov function does not exist. Some sufficient conditions are also obtained for the robust absolute stability of uncertain systems.A numerical example is provided to demonstrate the effectiveness of the proposed method.
Quantum algorithm for linear systems of equations.
Harrow, Aram W; Hassidim, Avinatan; Lloyd, Seth
2009-10-09
Solving linear systems of equations is a common problem that arises both on its own and as a subroutine in more complex problems: given a matrix A and a vector b(-->), find a vector x(-->) such that Ax(-->) = b(-->). We consider the case where one does not need to know the solution x(-->) itself, but rather an approximation of the expectation value of some operator associated with x(-->), e.g., x(-->)(dagger) Mx(-->) for some matrix M. In this case, when A is sparse, N x N and has condition number kappa, the fastest known classical algorithms can find x(-->) and estimate x(-->)(dagger) Mx(-->) in time scaling roughly as N square root(kappa). Here, we exhibit a quantum algorithm for estimating x(-->)(dagger) Mx(-->) whose runtime is a polynomial of log(N) and kappa. Indeed, for small values of kappa [i.e., poly log(N)], we prove (using some common complexity-theoretic assumptions) that any classical algorithm for this problem generically requires exponentially more time than our quantum algorithm.
Symmetric linear systems - An application of algebraic systems theory
Hazewinkel, M.; Martin, C.
1983-01-01
Dynamical systems which contain several identical subsystems occur in a variety of applications ranging from command and control systems and discretization of partial differential equations, to the stability augmentation of pairs of helicopters lifting a large mass. Linear models for such systems display certain obvious symmetries. In this paper, we discuss how these symmetries can be incorporated into a mathematical model that utilizes the modern theory of algebraic systems. Such systems are inherently related to the representation theory of algebras over fields. We will show that any control scheme which respects the dynamical structure either implicitly or explicitly uses the underlying algebra.
Symmetric linear systems - An application of algebraic systems theory
Hazewinkel, M.; Martin, C.
1983-01-01
Dynamical systems which contain several identical subsystems occur in a variety of applications ranging from command and control systems and discretization of partial differential equations, to the stability augmentation of pairs of helicopters lifting a large mass. Linear models for such systems display certain obvious symmetries. In this paper, we discuss how these symmetries can be incorporated into a mathematical model that utilizes the modern theory of algebraic systems. Such systems are inherently related to the representation theory of algebras over fields. We will show that any control scheme which respects the dynamical structure either implicitly or explicitly uses the underlying algebra.
Full-State Linearization and Stabilization of SISO Markovian Jump Nonlinear Systems
Directory of Open Access Journals (Sweden)
Zhongwei Lin
2013-01-01
Full Text Available This paper investigates the linearization and stabilizing control design problems for a class of SISO Markovian jump nonlinear systems. According to the proposed relative degree set definition, the system can be transformed into the canonical form through the appropriate coordinate changes followed with the Markovian switchings; that is, the system can be full-state linearized in every jump mode with respect to the relative degree set n,…,n. Then, a stabilizing control is designed through applying the backstepping technique, which guarantees the asymptotic stability of Markovian jump nonlinear systems. A numerical example is presented to illustrate the effectiveness of our results.
Design of saturated controllers for linear singular systems
Institute of Scientific and Technical Information of China (English)
Wang Ruliang; Liu Yongqing
2005-01-01
A designing method is presented to find stabilizing saturated linear controllers for linear continuous time and discrete time singular systems with control constraints. The idea is as follows: The system is first stabilized by a low-gain linear state feedback control. A general Lyapunov function is found, on the basis of which another linear state feedback control is computed.The second step is very similar to a relay control design. The two controls are added and saturated.
SYSTEM IDENTIFICATION METHOD OF LINEAR AND NON—LINEAR LIQUID PREPARATIVE CHROMATOGRAPHIC SEPARATION
Institute of Scientific and Technical Information of China (English)
ShuWenli; LiZhong; 等
1997-01-01
The paper proposes the identification method of linear and non-linear chromatographic system.Isotherms and lumped mass transfer coefficients of chromatography separating isomer sorbitol and mannitol on D80 adsorbent are determined.The analyses of root mean square error of chromatography elution curves are carried out.The results show that the system studied is non-linear and the theoretical elution curves of the non-linear chromatographic model are more accurate than those of the linear chromatographic model,Results of parameter sensitivity analyses show that elution curves of non-linear chromatopraphic separation aremore sensitive to the variation of parameter “ai” in the adsorption isotherms Qi=Ci*/(ai+biCi*) than to the variation of parameter "bi”as well as lumped mass transfer coefficients.
Fission Surface Power System Initial Concept Definition
2010-01-01
Under the NASA Exploration Technology Development Program (ETDP) and in partnership with the Department of Energy (DOE), NASA has embarked on a project to develop Fission Surface Power (FSP) technology. The primary goals of the project are to 1) develop FSP concepts that meet expected surface power requirements at reasonable cost with added benefits over other options, 2) establish a hardwarebased technical foundation for FSP design concepts and reduce overall development risk, 3) reduce the cost uncertainties for FSP and establish greater credibility for flight system cost estimates, and 4) generate the key products to allow NASA decision-makers to consider FSP as a preferred option for flight development. The FSP project was initiated in 2006 as the Prometheus Program and the Jupiter Icy Moons Orbiter (JIMO) mission were phased-out. As a first step, NASA Headquarters commissioned the Affordable Fission Surface Power System Study to evaluate the potential for an affordable FSP development approach. With a cost-effective FSP strategy identified, the FSP team evaluated design options and selected a Preliminary Reference Concept to guide technology development. Since then, the FSP Preliminary Reference Concept has served as a point-of-departure for several NASA mission architecture studies examining the use of nuclear power and has provided the foundation for a series of "Pathfinder" hardware tests. The long-term technology goal is a Technology Demonstration Unit (TDU) integrated system test using full-scale components and a non-nuclear reactor simulator. The FSP team consists of Glenn Research Center (GRC), Marshall Space Flight Center (MSFC) and the DOE National Laboratories at Los Alamos (LANL), Idaho (INL), Oak Ridge (ORNL), and Sandia (SNL). The project is organized into two main elements: Concept Definition and Risk Reduction. Under Concept Definition, the team performs trade studies, develops analytical tools, and formulates system concepts. Under Risk
Performance Analysis of Thermal Energy System with Linear System Method
Institute of Scientific and Technical Information of China (English)
Liping LI; Chunfa ZHANG
2007-01-01
The paper addresses the system performance of coal-fired power unit with changed auxiliary system or other local heat disturbance. The idea of state space model is imported and the universal formula for the calculation of system performance output is deduced on the system state equation. Two important vector of system are worked out under linear system assumption and transform. The transfer matrix is the characteristics of system itself and is constant for a similar condition, which greatly facilitates the analysis. The concept of thermal disturbance vector is proposed to construct the thermal disturbance input easily. The method can be helpful for analyzing any thermal disturbance input satisfying the assumption and also for supplementing the correction means of performance test. An example of 600MW power unit is presented to demonstrate its availability.
Regular linear systems and their reciprocals : applications to Riccati equations
Curtain, RF
2003-01-01
For a regular linear system with zero in the resolvent set of the generator we introduce its reciprocal system, which has bounded generators. We show that there are close relationships between key system theoretic properties of such regular linear systems and their reciprocals. To illustrate the use
Linear System of Equations, Matrix Inversion, and Linear Programming Using MS Excel
El-Gebeily, M.; Yushau, B.
2008-01-01
In this note, we demonstrate with illustrations two different ways that MS Excel can be used to solve Linear Systems of Equation, Linear Programming Problems, and Matrix Inversion Problems. The advantage of using MS Excel is its availability and transparency (the user is responsible for most of the details of how a problem is solved). Further, we…
Evaluation of Linear and Non-Linear Control Schemes Applied to a Hydraulic Servo System
DEFF Research Database (Denmark)
Andersen, Torben Ole; Hansen, Michael Rygaard; Pedersen, Henrik Clemmensen
2005-01-01
Due to the innovation of low-cost electronics such as sensors, microcontrollers etc., the focus on highperformance motion control is increasing. This work focuses on position control of single-input single-output hydraulic servo-systems in general. A hydraulically actuated robotic manipulator...... is used as test facility acting as load for the hydraulic servo system. An experimentally verified non-linear model of the complete system has been developed and used to design a series of both linear and non-linear control schemes. The controllers from each category are compared with respect to design...
Inexact Krylov subspace methods for linear systems
Eshof, J. van den; Sleijpen, G.L.G.
There is a class of linear problems for which the computation of the matrix-vector product is very expensive since a time consuming approximation method is necessary to compute it with some prescribed relative precision. In this paper we investigate the impact of approximately computed
Inexact Krylov subspace methods for linear systems
Eshof, J. van den; Sleijpen, G.L.G.
2004-01-01
There is a class of linear problems for which the computation of the matrix-vector product is very expensive since a time consuming method is necessary to approximate it with some prescribed relative precision. In this paper we investigate the impact of approximately computed matrix-vector
Energy Technology Data Exchange (ETDEWEB)
Ravi Kanth, A.S.V. [Applied Mathematics Division, School of Science and Humanities, V.I.T. University, Vellore-632 014, Tamil Nadu (India)], E-mail: asvravikanth@yahoo.com; Aruna, K. [Applied Mathematics Division, School of Science and Humanities, V.I.T. University, Vellore-632 014, Tamil Nadu (India)
2008-11-17
In this Letter, we propose a reliable algorithm to develop exact and approximate solutions for the linear and non-linear systems of partial differential equations. The approach rest mainly on two-dimensional differential transform method which is one of the approximate methods. The method can easily be applied to many linear and non-linear problems and is capable of reducing the size of computational work. Exact solutions can also be achieved by the known forms of the series solutions. Several illustrative examples are given to demonstrate the effectiveness of the present method.
Non-linear system identification in flow-induced vibration
Energy Technology Data Exchange (ETDEWEB)
Spanos, P.D.; Zeldin, B.A. [Rice Univ., Houston, TX (United States); Lu, R. [Hudson Engineering Corp., Houston, TX (United States)
1996-12-31
The paper introduces a method of identification of non-linear systems encountered in marine engineering applications. The non-linearity is accounted for by a combination of linear subsystems and known zero-memory non-linear transformations; an equivalent linear multi-input-single-output (MISO) system is developed for the identification problem. The unknown transfer functions of the MISO system are identified by assembling a system of linear equations in the frequency domain. This system is solved by performing the Cholesky decomposition of a related matrix. It is shown that the proposed identification method can be interpreted as a {open_quotes}Gram-Schmidt{close_quotes} type of orthogonal decomposition of the input-output quantities of the equivalent MISO system. A numerical example involving the identification of unknown parameters of flow (ocean wave) induced forces on offshore structures elucidates the applicability of the proposed method.
A SYSTEMIC VISION OF BIOLOGY: OVERCOMING LINEARITY
Directory of Open Access Journals (Sweden)
M. Mayer
2005-07-01
were used to build a hipermedia material. This technology permit overcomes a linear communication, improving the comprehension of the network perspective. The teachers speeches revealed their conceptual con- structions along the course, showed the development of the competences in identify interconnection points in the flow and chemical cycling of energy, compatible with a systemic view of life.
Observer Design for (max,plus) Linear System
Hardouin, L.; Maia,C.A.; Cottenceau, B.; Lhommeau, M.
2013-01-01
This paper deals with the state estimation for max-plus linear systems. This estimation is carried out following the ideas of the observer method for classical linear systems. The system matrices are assumed to be known, and the observation of the input and of the output is used to compute the estimated state. The observer design is based on the residuation theory which is suitable to deal with linear mapping inversion in idempotent semiring.
Harnessing piecewise-linear systems to construct dynamic logic architecture.
Peng, Haipeng; Yang, Yixian; Li, Lixiang; Luo, Hong
2008-09-01
This paper explores piecewise-linear systems to construct dynamic logic architecture. We present three schemes to obtain various basic logic gates, adders, and memory by using piecewise-linear systems. These schemes can switch easily among different operational roles by changing parameters. The proposed schemes are computationally efficient and easy to use. It is convenient for us to study and analyze them with the theory of linear systems.
A New Method for Solving General Dual Fuzzy Linear Systems
Directory of Open Access Journals (Sweden)
M. Otadi
2013-09-01
Full Text Available . According to fuzzy arithmetic, general dual fuzzy linear system (GDFLS cannot be replaced by a fuzzy linear system (FLS. In this paper, we use new notation of fuzzy numbers and convert a GDFLS to two linear systems in crisp case, then we discuss complexity of the proposed method. Conditions for the existence of a unique fuzzy solution to n × n GDFLS are derived
Cotton-Type and Joint Invariants for Linear Elliptic Systems
Directory of Open Access Journals (Sweden)
A. Aslam
2013-01-01
that Cotton-type invariants derived from these two approaches are identical. Furthermore, Cotton-type and joint invariants for a general system of two linear elliptic equations are also obtained from the Laplace-type and joint invariants for a system of two linear hyperbolic equations equivalent to the system of linear elliptic equations by complex changes of the independent variables. Examples are presented to illustrate the results.
Change-Of-Bases Abstractions for Non-Linear Systems
Sankaranarayanan, Sriram
2012-01-01
We present abstraction techniques that transform a given non-linear dynamical system into a linear system or an algebraic system described by polynomials of bounded degree, such that, invariant properties of the resulting abstraction can be used to infer invariants for the original system. The abstraction techniques rely on a change-of-basis transformation that associates each state variable of the abstract system with a function involving the state variables of the original system. We present conditions under which a given change of basis transformation for a non-linear system can define an abstraction. Furthermore, the techniques developed here apply to continuous systems defined by Ordinary Differential Equations (ODEs), discrete systems defined by transition systems and hybrid systems that combine continuous as well as discrete subsystems. The techniques presented here allow us to discover, given a non-linear system, if a change of bases transformation involving degree-bounded polynomials yielding an alge...
A Cognitive Approach to Solving Systems of Linear Equations
Ramirez, Ariel A.
2009-01-01
Systems of linear equations are used in a variety of fields. Exposure to the concept of systems of equations initially occurs at the high school level and continues through college. Attempts to unearth what students understand about the solutions of linear systems have been limited. Gaps exist in our knowledge of how students understand systems…
Satellite Power Systems (SPS) concept definition study. Volume 4: SPS point design definition
Hanley, G.
1978-01-01
The satellite power systems point design concept is described. The concept definition includes satellite, ground and space systems, and their relationships. Emphasis is placed on the definition of the GaAlAs photovoltaic satellite system. The major subsystems of the satellite system including power conversion, power distribution and control, microwave, attitude control and stationkeeping, thermal control, structures, and information management and control are discussed.
Synchronization of chaotic fractional-order systems via linear control
Odibat, Zaid,; Corson, Nathalie; Aziz-Alaoui, Moulay; Bertelle, Cyrille
2010-01-01
International audience; The chaotic dynamics of fractional-order systems has attracted much attention recently. Chaotic synchronization of fractional-order systems is further studied in this paper. We investigate the chaos synchronization of two identical systems via a suitable linear controller applied to the response system. Based on the stability results of linear fractional-order systems, sufficient conditions for chaos synchronization of these systems are given. Control laws are derived ...
Singular linear quadratic control problem for systems with linear and constant delay
Sesekin, A. N.; Andreeva, I. Yu.; Shlyakhov, A. S.
2016-12-01
This article is devoted to the singular linear-quadratic optimization problem on the trajectories of the linear non-autonomous system of differential equations with linear and constant delay. It should be noted that such task does not solve the class of integrable controls, so to ensure the existence of a solution is needed to expand the class of controls to include the control impulse components. For the problem under consideration, we have built program control containing impulse components in the initial and final moments time. This is done under certain assumptions on the functional and the right side of the control system.
Asymptotic Stability of Interconnected Passive Non-Linear Systems
Isidori, A.; Joshi, S. M.; Kelkar, A. G.
1999-01-01
This paper addresses the problem of stabilization of a class of internally passive non-linear time-invariant dynamic systems. A class of non-linear marginally strictly passive (MSP) systems is defined, which is less restrictive than input-strictly passive systems. It is shown that the interconnection of a non-linear passive system and a non-linear MSP system is globally asymptotically stable. The result generalizes and weakens the conditions of the passivity theorem, which requires one of the systems to be input-strictly passive. In the case of linear time-invariant systems, it is shown that the MSP property is equivalent to the marginally strictly positive real (MSPR) property, which is much simpler to check.
Weakly linear systems of fuzzy relation inequalities: The heterogeneous case
Ignjatović, Jelena; Damljanović, Nada; Jančić, Ivana
2011-01-01
New types of systems of fuzzy relation inequalities and equations, called weakly linear, have been recently introduced in [J. Ignjatovi\\'c, M. \\'Ciri\\'c, S. Bogdanovi\\'c, On the greatest solutions to weakly linear systems of fuzzy relation inequalities and equations, Fuzzy Sets and Systems 161 (2010) 3081--3113.]. The mentioned paper dealt with homogeneous weakly linear systems, composed of fuzzy relations on a single set, and a method for computing their greatest solutions has been provided. This method is based on the computing of the greatest post-fixed point, contained in a given fuzzy relation, of an isotone function on the lattice of fuzzy relations. Here we adapt this method for computing the greatest solutions of heterogeneous weakly linear systems, where the unknown fuzzy relation relates two possibly different sets. We also introduce and study quotient fuzzy relational systems and establish relationships between solutions to heterogeneous and homogeneous weakly linear systems. Besides, we point out ...
Self-characterization of linear and nonlinear adaptive optics systems
Hampton, Peter J.; Conan, Rodolphe; Keskin, Onur; Bradley, Colin; Agathoklis, Pan
2008-01-01
We present methods used to determine the linear or nonlinear static response and the linear dynamic response of an adaptive optics (AO) system. This AO system consists of a nonlinear microelectromechanical systems deformable mirror (DM), a linear tip-tilt mirror (TTM), a control computer, and a Shack-Hartmann wavefront sensor. The system is modeled using a single-input-single-output structure to determine the one-dimensional transfer function of the dynamic response of the chain of system hardware. An AO system has been shown to be able to characterize its own response without additional instrumentation. Experimentally determined models are given for a TTM and a DM.
The linear position tracking servo system using a linear voice-coil motor
Institute of Scientific and Technical Information of China (English)
2008-01-01
More and more linear servo systems have been used in servo applications. Direct drive technology can greatly increase the bandwidth and the tracking accuracy. A position servo-system based on linear voice-coil motor was designed for one linear oscillation movement application. Besides the conventional position, speed and current control loops, the speed and acceleration feed-forward control of command position signal were also used. The experimental test proved the correctness of the design, and the system can track the given periodic sinnsoid position command signal of 15Hz with high accuracy. The linear voice-coil motor is very suitable for short stroke position tracking application with high dynamic response.
A proposed method for solving fuzzy system of linear equations.
Kargar, Reza; Allahviranloo, Tofigh; Rostami-Malkhalifeh, Mohsen; Jahanshaloo, Gholam Reza
2014-01-01
This paper proposes a new method for solving fuzzy system of linear equations with crisp coefficients matrix and fuzzy or interval right hand side. Some conditions for the existence of a fuzzy or interval solution of m × n linear system are derived and also a practical algorithm is introduced in detail. The method is based on linear programming problem. Finally the applicability of the proposed method is illustrated by some numerical examples.
Marginal linearization method in modeling on fuzzy control systems
Institute of Scientific and Technical Information of China (English)
无
2003-01-01
Marginal linearization method in modeling on fuzzy control systems is proposed, which is to deal with the nonlinear model with variable coefficients. The method can turn a nonlinear model with variable coefficients into a linear model with variable coefficients in the way that the membership functions of the fuzzy sets in fuzzy partitions of the universes are changed from triangle waves into rectangle waves. However, the linearization models are incomplete in their forms because of their lacking some items. For solving this problem, joint approximation by using linear models is introduced. The simulation results show that marginal linearization models are of higher approximation precision than their original nonlinear models.
Definition study for photovoltaic residential prototype system
Imamura, M. S.; Hulstrom, R. L.; Cookson, C.; Waldman, B. H.; Lane, R. A.
1976-01-01
A parametric sensitivity study and definition of the conceptual design is presented. A computer program containing the solar irradiance, solar array, and energy balance models was developed to determine the sensitivities of solar insolation and the corresponding solar array output at five sites selected for this study as well as the performance of several solar array/battery systems. A baseline electrical configuration was chosen, and three design options were recommended. The study indicates that the most sensitive parameters are the solar insolation and the inverter efficiency. The baseline PST selected is comprised of a 133 sg m solar array, 250 ampere hour battery, one to three inverters, and a full shunt regulator to limit the upper solar array voltage. A minicomputer controlled system is recommended to provide the overall control, display, and data acquisition requirements. Architectural renderings of two photovoltaic residential concepts, one above ground and the other underground, are presented. The institutional problems were defined in the areas of legal liabilities during and after installation of the PST, labor practices, building restrictions and architectural guides, and land use.
Robust integral stabilization of regular linear systems
Institute of Scientific and Technical Information of China (English)
XU Chengzheng; FENG Dexing
2004-01-01
We consider regular systems with control and observation. We prove some necessary and sufficient condition for an exponentially stable regular system to admit an integral stabilizing controller. We propose also some robust integral controllers when they exist.
Modal approximations to damped linear systems
Veseli/'c, K
2009-01-01
We consider a finite dimensional damped second order system and obtain spectral inclusion theorems for the related quadratic eigenvalue problem. The inclusion sets are the 'quasi Cassini ovals' which may greatly outperform standard Gershgorin circles. As the unperturbed system we take a modally damped part of the system; this includes the known proportionally damped models, but may give much sharper estimates. These inclusions are then applied to derive some easily calculable sufficient conditions for the overdampedness of a given damped system.
Processing in (linear) systems with stochastic input
Nutu, Catalin Silviu; Axinte, Tiberiu
2016-12-01
The paper is providing a different approach to real-world systems, such as micro and macro systems of our real life, where the man has little or no influence on the system, either not knowing the rules of the respective system or not knowing the input of the system, being thus mainly only spectator of the system's output. In such a system, the input of the system and the laws ruling the system could be only "guessed", based on intuition or previous knowledge of the analyzer of the respective system. But, as we will see in the paper, it exists also another, more theoretical and hence scientific way to approach the matter of the real-world systems, and this approach is mostly based on the theory related to Schrödinger's equation and the wave function associated with it and quantum mechanics as well. The main results of the paper are regarding the utilization of the Schrödinger's equation and related theory but also of the Quantum mechanics, in modeling real-life and real-world systems.
BLOCK BIDIAGONALIZATION METHODS FOR MULTIPLE NONSYMMETRIC LINEAR SYSTEMS
Institute of Scientific and Technical Information of China (English)
戴华
2001-01-01
The symmetric linear system gives us many simplifications and a possibility to adapt the computations to the computer at hand in order to achieve better performance. The aim of this paper is to consider the block bidiagonalization methods derived from a symmetric augmented multiple linear systems and make a comparison with the block GMRES and block biconjugate gradient methods.
Partial Linearization of Mechanical Systems with Application to Observer Design
Sarras, Ioannis; Venkatraman, Aneesh; Ortega, Romeo; Schaft, Arjan van der
2008-01-01
We consider general mechanical systems and establish a necessary and sufficient condition for the existence of a suitable change in the generalized momentum coordinates such that the new dynamics become linear in the transformed momenta. The class of systems which can be (partially) linearized by th
On the Zeno behavior of linear complementarity systems
Camlibel, MK; Schumacher, JM
2001-01-01
In this paper, the so-called Zeno phenomenon is addressed for linear complementarity systems which are interconnections of linear systems and complementarity conditions. We present some sufficient conditions for absence of Zeno behavior. It is also shown that the zero state, which is the most obviou
Model Reduction by Moment Matching for Linear Switched Systems
DEFF Research Database (Denmark)
Bastug, Mert; Petreczky, Mihaly; Wisniewski, Rafal;
2014-01-01
A moment-matching method for the model reduction of linear switched systems (LSSs) is developed. The method is based based upon a partial realization theory of LSSs and it is similar to the Krylov subspace methods used for moment matching for linear systems. The results are illustrated by numeric...
Developments and trends in the parallel solution of linear systems
Duff, I.S.; Vorst, H.A. van der
2001-01-01
In this review paper, we consider some important developments and trends in algorithm design for the solution of linear systems concentrating on aspects that involve the exploitation of parallelism. We briefly discuss the solution of dense linear systems, before studying the solution of sparse eq
Minimal solution of general dual fuzzy linear systems
Energy Technology Data Exchange (ETDEWEB)
Abbasbandy, S. [Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran 14778 (Iran, Islamic Republic of); Department of Mathematics, Faculty of Science, Imam Khomeini International University, Qazvin 34194-288 (Iran, Islamic Republic of)], E-mail: abbasbandy@yahoo.com; Otadi, M.; Mosleh, M. [Department of Mathematics, Science and Research Branch, Islamic Azad University, Tehran 14778 (Iran, Islamic Republic of); Department of Mathematics, Islamic Azad University, Firuozkooh Branch, Firuozkooh (Iran, Islamic Republic of)
2008-08-15
Fuzzy linear systems of equations, play a major role in several applications in various area such as engineering, physics and economics. In this paper, we investigate the existence of a minimal solution of general dual fuzzy linear equation systems. Two necessary and sufficient conditions for the minimal solution existence are given. Also, some examples in engineering and economic are considered.
Tracking control of chaotic dynamical systems with feedback linearization
Institute of Scientific and Technical Information of China (English)
QI Dong-lian; MA Guo-jin
2005-01-01
A new method was proposed for tracking the desired output of chaotic dynamical system using the feedback linearization and nonlinear extended statement observer method. The feedback linearization was used to convert the nonlinear chaotic system into linear system. The extended Luenberger-like statements observer was designed to reconstructing and observing the unmeasured statements when the tracking controller was designed. By this way, the chaotic system could be forced to track variable desired output, which could be a time variant function or an equilibrium points.Taken the Lorenz chaotic system as example, the simulation results show the validity of the conclusion and effectiveness of the algorithm.
Efficient methodology for multibody simulations with discontinuous changes in system definition
Energy Technology Data Exchange (ETDEWEB)
Mukherjee, Rudranarayan M., E-mail: rudranarayan.m.mukherjee@jpl.nasa.gov; Anderson, Kurt S. [Rensselaer Polytechnic Institute, Department of Mechanical, Aeronautical, and Nuclear Engineering (United States)], E-mail: anderk5@rpi.edu
2007-09-15
A new method is presented for accurately and efficiently simulating multi-scale multibody systems with discontinuous changes in system definitions as encountered in adaptive switching between models with different resolutions as well as models with different system topologies. An example of model resolution change is a transition of a system from a discrete particle model to a reduced order articulated multi-rigid body model. The discontinuous changes in system definition may be viewed as an instantaneous change (release or impulsive application of) the system constraints. The method uses a spatial impulse-momentum formulation in a divide and conquer scheme. The approach utilizes a hierarchic assembly-disassembly process by traversing the system topology in a binary tree map to solve for the jumps in the system generalized speeds and the constraint impulsive loads in linear and logarithmic cost in serial and parallel implementations, respectively. The method is applicable for systems in serial chain as well as kinematical loop topologies. The coupling between the unilateral and bilateral constraints is handled efficiently through the use of kinematic joint definitions. The equations of motion for the system are produced in a hierarchic sub-structured form. This has the advantage that changes in sub-structure definitions/models results in a change to the system equations only within the associated sub-structure. This allows for significant changes in model types and definitions without having to reformulate the equations for the whole system.
[The security system of SIEMENS digital linear accelerator].
Wang, Jianping
2013-03-01
The security system plays an important role to protect the safety of patients and equipment in radiotherapy. The principle and structure of three kinds of security system of the Siemens digital linear accelerator were analyzed with some examples.
Controllability of Linear Systems with inner derivation on Lie Groups
Jouan, Philippe
2011-01-01
A vector field on a connected Lie group is said to be linear if its flow is a one parameter group of automorphisms. A control-affine system is linear if the drift is linear and the controlled vector fields right invariant. The controllability properties of such systems are studied, mainly in the case where the derivation of the group Lie algebra that can be associated to the linear vector field is inner. After some general considerations controllability properties on semi simple, nilpotent an...
Compositional Analysis for Linear Control Systems
Kerber, Florian; Schaft, Arjan van der
2010-01-01
The complexity of physical and engineering systems, both in terms of the governing physical phenomena and the number of subprocesses involved, is mirrored in ever more complex mathematical models. While the demand for precise models is indisputable, the analysis of such system models remains
Dissipative systems synthesis : A linear algebraic approach
Belur, Madhu N.; Pillai, Harish K.; Trentelman, H.L.
2007-01-01
In this paper we consider the problem of synthesis of dissipative systems for the case that first and higher order derivatives of the concerned variables also appear in the weighting function. The problem is formulated and solved using the behavioral approach to systems and control. We relate the pr
Compositional Analysis for Linear Control Systems
Kerber, Florian; Schaft, Arjan van der
2010-01-01
The complexity of physical and engineering systems, both in terms of the governing physical phenomena and the number of subprocesses involved, is mirrored in ever more complex mathematical models. While the demand for precise models is indisputable, the analysis of such system models remains challen
Dissipative systems synthesis : A linear algebraic approach
Belur, Madhu N.; Pillai, Harish K.; Trentelman, H.L.
2007-01-01
In this paper we consider the problem of synthesis of dissipative systems for the case that first and higher order derivatives of the concerned variables also appear in the weighting function. The problem is formulated and solved using the behavioral approach to systems and control. We relate the pr
Dissipative Systems Synthesis : a Linear Algebraic Approach
Belur, Madhu N.; Pillai, Harish K.; Trentelman, H.L.
2005-01-01
In this paper we consider the problem of synthesis of dissipative systems for the case that first and higher order derivatives of the concerned variables also appear in the weighting function. The problem is formulated and solved using the behavioral approach to systems and control. It turns out tha
Sinou, Jean-Jacques; Thouverez, Fabrice; Jezequel, Louis
2006-01-01
International audience; Herein, a novel non-linear procedure for producing non-linear behaviour and stable limit cycle amplitudes of non-linear systems subjected to super-critical Hopf bifurcation point is presented. This approach, called Complex Non-Linear Modal Analysis (CNLMA), makes use of the non-linear unstable mode which governs the non-linear dynamic of structural systems in unstable areas. In this study, the computational methodology of CNLMA is presented for the systematic estimatio...
Output Synchronization of Nonidentical Linear Multiagent Systems.
Wu, Yuanqing; Su, Hongye; Shi, Peng; Lu, Renquan; Wu, Zheng-Guang
2017-01-01
In this paper, the problem of output synchronization is investigated for the heterogeneous network with an uncertain leader. It is assumed that parameter perturbations influence the nonidentical linear agents, whose outputs are controlled to track the output of an uncertain leader. Based on the hierarchical structure of the communication graph, a novel control scheme is proposed to guarantee the output synchronization. As there exist parameter uncertainties in the models of the agents, the internal model principle is used to gain robustness versus plant parameter uncertainties. Furthermore, as the precise model of the leader is also not available, the adaptive control principle is adopted to tune the parameters in the local controllers. The developed new technique is able to simultaneously handle uncertainties in the follower parameters as well as the leader parameters. The agents in the upper layers will be treated as the exosystems of the agents in the lower layers. The local controllers are constructed in a sequential order. It is shown that the output synchronization can be achieved globally asymptotically and locally exponentially. Finally, a simulation example is given to illustrate the effectiveness and potential of the theoretic results obtained.
Virtual estimator for piecewise linear systems based on observability analysis.
Morales-Morales, Cornelio; Adam-Medina, Manuel; Cervantes, Ilse; Vela-Valdés, Luis G; Beltrán, Carlos Daniel García
2013-02-27
This article proposes a virtual sensor for piecewise linear systems based on observability analysis that is in function of a commutation law related with the system's outpu. This virtual sensor is also known as a state estimator. Besides, it presents a detector of active mode when the commutation sequences of each linear subsystem are arbitrary and unknown. For the previous, this article proposes a set of virtual estimators that discern the commutation paths of the system and allow estimating their output. In this work a methodology in order to test the observability for piecewise linear systems with discrete time is proposed. An academic example is presented to show the obtained results.
Virtual Estimator for Piecewise Linear Systems Based on Observability Analysis
Morales-Morales, Cornelio; Adam-Medina, Manuel; Cervantes, Ilse; Vela-Valdés and, Luis G.; García Beltrán, Carlos Daniel
2013-01-01
This article proposes a virtual sensor for piecewise linear systems based on observability analysis that is in function of a commutation law related with the system's outpu. This virtual sensor is also known as a state estimator. Besides, it presents a detector of active mode when the commutation sequences of each linear subsystem are arbitrary and unknown. For the previous, this article proposes a set of virtual estimators that discern the commutation paths of the system and allow estimating their output. In this work a methodology in order to test the observability for piecewise linear systems with discrete time is proposed. An academic example is presented to show the obtained results. PMID:23447007
A new active absorption system and its performance to linear and non-linear waves
DEFF Research Database (Denmark)
Andersen, Thomas Lykke; Clavero, M.; Frigaard, Peter Bak;
2016-01-01
Highlights •An active absorption system for wavemakers has been developed. •The theory for flush mounted gauges has been extended to cover also small gaps. •The new system has been validated in a wave flume with wavemakers in both ends. •A generation and absorption procedure for highly non-linear...
Linear operators and linear systems an analytical approach to control theory
Partington, Jonathan R
2004-01-01
This book presents an introduction to the common ground between operator theory and linear systems theory. Suitable for students of functional analysis, this book also acts as an introduction to a mathematical approach to systems and control for graduate students in departments of applied mathematics or engineering.
A robust test of uncertain linear systems
Institute of Scientific and Technical Information of China (English)
Yogesh V.HOTE; D.Roy CHOUDHURY; J.R.P.GUPTA
2009-01-01
In this paper,it is shown that for low-order uncertain systems,there is no need to calculate all the minimum and maximum values of the coefficients for a perturbed system which is expressed in terms of polynomials and hence no need to formulate and test all the four Kharitonov's polynomials.Furthermore,for higher-order systems such as n ≥ 5,the usual four Kharitonov's polynomials need not be tested initially for sufficient condition of perturbed systems; rather,the necessary condition can be checked before going for sufficient condition.In order to show the effectiveness of the proposed method,numerical examples are shown and computational efficiency is highlighted.
Some Oscillation Results for Linear Hamiltonian Systems
Directory of Open Access Journals (Sweden)
Nan Wang
2012-01-01
oscillation criteria are established for the system. These criteria extend and improve some results that have been required before. An interesting example is included to illustrate the importance of our results.
Some Oscillation Results for Linear Hamiltonian Systems
Nan Wang; Fanwei Meng
2012-01-01
The purpose of this paper is to develop a generalized matrix Riccati technique for the selfadjoint matrix Hamiltonian system ${U}^{\\prime }=A(t)U+B(t)V$ , ${V}^{\\prime }=C(t)U-{A}^{\\ast }(t)V$ . By using the standard integral averaging technique and positive functionals, new oscillation and interval oscillation criteria are established for the system. These criteria extend and improve some results that have been required before. An interesting example is included to illustrate the...
Development and Control of a Non Linear Magnetic Levitation System
Directory of Open Access Journals (Sweden)
A Sanjeevi Gandhi
2013-06-01
Full Text Available Nowadays, studies to develop and control non linear systems is of great significance. Magnetic Levitation System has gained considerable interests due to its great practical importance in different engineering fields In this paper an electromagnetic levitation system was developed and mathematical model for the system was derived. The developed system was controlled manually.
Dynamic compensator design for robust stability of linear uncertain systems
Yedavalli, R. K.
1986-01-01
This paper presents a robust linear dynamic compensator design algorithm for linear uncertain systems whose parameters vary within given bounded sets. The algorithm explicitly incorporates the structure of the uncertainty into the design procedure and utilizes the elemental perturbation bounds developed recently. The special cases of linear state feedback and measurement feedback controllers are considered and the relative trade offs are discussed. The design algorithm is illustrated with the help of a simple example.
COMPUTING A NEAREST P-SYMMETRIC NONNEGATIVE DEFINITE MATRIX UNDER LINEAR RESTRICTION
Institute of Scientific and Technical Information of China (English)
Hua Dai
2004-01-01
Let P be an n × n symmetric orthogonal matrix. A real n × n matrix A is called P-symmetric nonnegative definite if A is symmetric nonnegative definite and (PA)T =PA. This paper is concerned with a kind of inverse problem for P-symmetric nonncgative definite matrices: Given a real n × n matrix A, real n × m matrices X and B, find an n × n P-symmetric nonnegative definite matrix A minimizing ‖A- A‖F subject to AX = B.Necessary and sufficient conditions are presented for the solvability of the problem. The expression of the solution to the problem is given. These results are applied to solve an inverse eigenvalue problem for P-symmetric nonnegative definite matrices.
On Dynamic Systems with Piecewise Linear Feature
Directory of Open Access Journals (Sweden)
Amalia Ţîrdea
2010-10-01
Full Text Available Impact dynamics is considered to be one of the most important problems which arise in vibrating systems. Such impact oscillator occurs in the motion with amplitude constraining stop. In the past years, this simple model has been found rich phenomena and given benefit for understanding of impact systems. Different types of impacting response, such as periodic and non-periodic oscillations, can be predicted by using bifurcation diagrams. Many mechanical systems in engineering applications represent systems which are driven in some way and which undergo intermittent or a continuous sequence of contacts with limiting motion by constraints. For example, the principles of the operation of vibration hammers, impact dampers, inertial shakers, milling and forming machines etc, are based on the impact action for moving bodies. With other equipment, machines with clearances, heat exchangers, steam generator tubes, fuel rods in nuclear power plants, rolling railway wheel sets, piping systems, gear transmissions and so on, impacts also occur, but they are undesirable as they bring about failures, strains, and increased noise levels.
Identifying digital records in business systems: the definition of a ...
African Journals Online (AJOL)
Identifying digital records in business systems: the definition of a problem. ... records are created and stored in systems not designed for records management. ... A possible solution is the identification of records via business process analysis ...
Positive Stabilization of Linear Differential Algebraic Equation System
Directory of Open Access Journals (Sweden)
Muhafzan
2016-01-01
Full Text Available We study in this paper the existence of a feedback for linear differential algebraic equation system such that the closed-loop system is positive and stable. A necessary and sufficient condition for such existence has been established. This result can be used to detect the existence of a state feedback law that makes the linear differential algebraic equation system in closed loop positive and stable.
Random Response of Linear Viscoelastic Systems under Random Excitation
Institute of Scientific and Technical Information of China (English)
张天舒; 方同
2001-01-01
A method of analyzing random response of linear viscoelastic systems under random excitation has been presented. The covariance matrices of random responses of a single-degree-freedom linear viscoelastic system subjected to stationary white noise and filtered white noise excitations have been obtained in closed form. For illustration, a numerical example has been included. It is observed that viscoelasticity has damping effect on the mean square random responses of the system, the higher is viscoelastic behavior, the higher the damping effect.
Numerical methods for control optimization in linear systems
Tyatyushkin, A. I.
2015-05-01
Numerical methods are considered for solving optimal control problems in linear systems, namely, terminal control problems with control and phase constraints and time-optimal control problems. Several algorithms with various computer storage requirements are proposed for solving these problems. The algorithms are intended for finding an optimal control in linear systems having certain features, for example, when the reachable set of a system has flat faces.
Controllability, observability, realizability, and stability of dynamic linear systems
Davis, John M.; Gravagne, Ian A.; Jackson, Billy J.; Marks II, Robert J.
2009-01-01
We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time scales. The approach here is based on generalized Laplace transform methods (e.g. shifts and convolution) from the recent work [13]. We study controllability in terms of the controllability Gramian and various rank conditions (including Kalman's) in both the time invariant and time varying settings...
Ensemble control of linear systems with parameter uncertainties
Kou, Kit Ian; Liu, Yang; Zhang, Dandan; Tu, Yanshuai
2016-07-01
In this paper, we study the optimal control problem for a class of four-dimensional linear systems based on quaternionic and Fourier analysis. When the control is unconstrained, the optimal ensemble controller for this linear ensemble control systems is given in terms of prolate spheroidal wave functions. For the constrained convex optimisation problem of such systems, the quadratic programming is presented to obtain the optimal control laws. Simulations are given to verity the effectiveness of the proposed theory.
Linear generalized synchronization of continuous-time chaotic systems
Energy Technology Data Exchange (ETDEWEB)
Lu Junguo E-mail: jglu@sjtu.edu.cn; Xi Yugeng
2003-08-01
This paper develops a general approach for constructing a response system to implement linear generalized synchronization (GS) with the drive continuous-time chaotic system. Some sufficient conditions of global asymptotic linear GS between the drive and response continuous-time chaotic systems are attained from rigorously modern control theory. Finally, we take Chua's circuit as an example for illustration and verification.
Robust Control for Uncertain Linear System Subject to Input Saturation
Directory of Open Access Journals (Sweden)
Qingyun Yang
2014-01-01
Full Text Available A robust control scheme using composite nonlinear feedback (CNF technology is proposed to improve tracking control performance for the uncertain linear system with input saturation and unknown external disturbances. A disturbance observer is presented to estimate the unknown disturbance generated by a linear exogenous system. The designed gain matrix of the disturbance observer is determined by solving linear matrix inequalities (LMIs. Based on the output of the designed disturbance observer, a robust CNF controller including a linear feedback control item and a nonlinear item is developed to follow the desired tracking signals. The linear feedback controller is designed using LMIs and the stability of the closed-loop system is proved via rigorous Lyapunov analysis. Finally, the extensive simulation results are presented to illustrate the effectiveness of the proposed control scheme.
Linear decentralized systems with special structure. [for twin lift helicopters
Martin, C. F.
1982-01-01
Certain fundamental structures associated with linear systems having internal symmetries are outlined. It is shown that the theory of finite-dimensional algebras and their representations are closely related to such systems. It is also demonstrated that certain problems in the decentralized control of symmetric systems are equivalent to long-standing problems of linear systems theory. Even though the structure imposed arose in considering the problems of twin-lift helicopters, any large system composed of several identical intercoupled control systems can be modeled by a linear system that satisfies the constraints imposed. Internal symmetry can be exploited to yield new system-theoretic invariants and a better understanding of the way in which the underlying structure affects overall system performance.
Absolute stability analysis of linear systems with Duhem hysteresis operator
Ouyang, Ruiyue; Jayawardhana, Bayu
2014-01-01
In this paper, we investigate the stability of positive and negative feedback interconnections of a linear system and a Duhem hysteresis operator. We provide sufficient conditions on the linear plant and on the Duhem operator which are based on the counterclockwise (CCW) or clockwise (CW) input–outp
H2 guaranteed cost control of discrete linear systems
Directory of Open Access Journals (Sweden)
W. Colmenares
2000-01-01
guaranteed cost performance on a discrete linear uncertain system where the uncertainty is of the norm bounded type. The conditions are presented as a collection of linear matrix inequalities.The solution, however requires a search over a scalar parameter space.
On the equivalence classes of linear non-autonomous systems *
Institute of Scientific and Technical Information of China (English)
无
2001-01-01
In this paper, the equivalence classification of the linear non-autonomous dynamic systems near singularities is given. Under some conditions their equivalence classes are the same as the autonomous ones. Using a series of linear and nonlinear transforms, the equivalence classification is proved.
A Novel Weak Fuzzy Solution for Fuzzy Linear System
Directory of Open Access Journals (Sweden)
Soheil Salahshour
2016-03-01
Full Text Available This article proposes a novel weak fuzzy solution for the fuzzy linear system. As a matter of fact, we define the right-hand side column of the fuzzy linear system as a piecewise fuzzy function to overcome the related shortcoming, which exists in the previous findings. The strong point of this proposal is that the weak fuzzy solution is always a fuzzy number vector. Two complex and non-complex linear systems under uncertainty are tested to validate the effectiveness and correctness of the presented method.
Distributed Fusion Receding Horizon Filtering in Linear Stochastic Systems
Directory of Open Access Journals (Sweden)
Il Young Song
2009-01-01
Full Text Available This paper presents a distributed receding horizon filtering algorithm for multisensor continuous-time linear stochastic systems. Distributed fusion with a weighted sum structure is applied to local receding horizon Kalman filters having different horizon lengths. The fusion estimate of the state of a dynamic system represents the optimal linear fusion by weighting matrices under the minimum mean square error criterion. The key contribution of this paper lies in the derivation of the differential equations for determining the error cross-covariances between the local receding horizon Kalman filters. The subsequent application of the proposed distributed filter to a linear dynamic system within a multisensor environment demonstrates its effectiveness.
Output feedback controller design for uncertain piecewise linear systems
Institute of Scientific and Technical Information of China (English)
Jianxiong ZHANG; Wansheng TANG
2007-01-01
This paper proposes output feedback controller design methods for uncertain piecewise linear systems based on piecewise quadratic Lyapunov function. The α-stability of closed-loop systems is also considered. It is shown that the output feedback controller design procedure of uncertain piecewise linear systems with α-stability constraint can be cast as solving a set of bilinear matrix inequalities (BMIs). The BMIs problem in this paper can be solved iteratively as a set of two convex optimization problems involving linear matrix inequalities (LMIs) which can be solved numerically efficiently. A numerical example shows the effectiveness of the proposed methods.
Infinite-Dimensional Linear Dynamical Systems with Chaoticity
Fu Xin Chu; Fu, Xin-Chu; Duan, Jinqiao
1998-01-01
The authors present two results on infinite-dimensional linear dynamical systems with chaoticity. One is about the chaoticity of the backward shift map in the space of infinite sequences on a general Fréchet space. The other is about the chaoticity of a translation map in the space of real continuous functions. The chaos is shown in the senses of both Li-Yorke and Wiggins. Treating dimensions as freedoms, the two results imply that in the case of an infinite number of freedoms, a system may exhibit complexity even when the action is linear. Finally, the authors discuss physical applications of infinite-dimensional linear chaotic dynamical systems.
Stability and Stabilization of Block-cascading Switched Linear Systems
Institute of Scientific and Technical Information of China (English)
Ya-Hong Zhu; Dai-Zhan Cheng
2006-01-01
The main purpose of this paper is to investigate the problem of quadratic stability and stabilization in switched linear systems using reducible Lie algebra. First, we investigate the structure of all real invariant subspaces for a given linear system. The result is then used to provide a comparable cascading form for switching models. Using the commoncascading form, a common quadratic Lyapunov function is (QLFs) is explored by finding common QLFs of diagonal blocks.In addition, a cascading Quaker Lemma is proved. Combining it with stability results, the problem of feedback stabilization for a class of switched linear systems is solved.
Capacities of linear quantum optical systems
Lupo, Cosmo; Giovannetti, Vittorio; Pirandola, Stefano; Mancini, Stefano; Lloyd, Seth
2012-06-01
A wide variety of communication channels employ the quantized electromagnetic field to convey information. Their communication capacity crucially depends on losses associated to spatial characteristics of the channel such as diffraction and antenna design. Here we focus on the communication via a finite pupil, showing that diffraction is formally described as a memory channel. By exploiting this equivalence we then compute the communication capacity of an optical refocusing system, modeled as a converging lens. Even though loss of information originates from the finite pupil of the lens, we show that the presence of the refocusing system can substantially enhance the communication capacity. We mainly concentrate on communication of classical information, the extension to quantum information being straightforward.
Capacities of linear quantum optical systems
Lupo, Cosmo; Pirandola, Stefano; Mancini, Stefano; Lloyd, Seth
2012-01-01
A wide variety of communication channels employ the quantized electromagnetic field to convey information. Their communication capacity crucially depends on losses associated to spatial characteristics of the channel such as diffraction and antenna design. Here we focus on the communication via a finite pupil, showing that diffraction is formally described as a memory channel. By exploiting this equivalence we then compute the communication capacity of an optical refocusing system, modeled as a converging lens. Even though loss of information originates from the finite pupil of the lens, we show that the presence of the refocusing system can substantially enhance the communication capacity. We mainly concentrate on communication of classical information, the extension to quantum information being straightforward.
Analysis of Linear Hybrid Systems in CLP
DEFF Research Database (Denmark)
Banda, Gourinath; Gallagher, John Patrick
2009-01-01
notation for specifying real-time systems. The main contributions are (i) a technique for capturing the reachable states of the continuously changing state variables of the LHA as CLP constraints; (ii) a way of representing events in the LHA as constraints in CLP, along with a product construction...... and argue that we contribute to the general field of using static analysis tools for verification...
Weighted least squares stationary approximations to linear systems.
Bierman, G. J.
1972-01-01
Investigation of the problem of replacing a certain time-varying linear system by a stationary one. Several quadratic criteria are proposed to aid in determining suitable candidate systems. One criterion for choosing the matrix B (in the stationary system) is initial-condition dependent, and another bounds the 'worst case' homogeneous system performance. Both of these criteria produce weighted least square fits.
ON CONVERGENCE OF MULTIGRID METHOD FOR NONNEGATIVE DEFINITE SYSTEMS
Institute of Scientific and Technical Information of China (English)
Qian-shun Chang; Wei-wei Sun
2005-01-01
In this paper, we consider multigrid methods for solving symmetric nonnegative definite matrix equations. We present some interesting features of the multigrid method and prove that the method is convergent in L2 space and the convergent solution is unique for such nonnegative definite system and given initial guess.
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...
Analysis of Nonlinear Missile Guidance Systems Through Linear Adjoint Method
Directory of Open Access Journals (Sweden)
Khaled Gamal Eltohamy
2015-12-01
Full Text Available In this paper, a linear simulation algorithm, the adjoint method, is modified and employed as an efficient tool for analyzing the contributions of system parameters to the miss - distance of a nonlinear time-varying missile guidance system model. As an example for the application of the linear adjoint method, the effect of missile flight time on the miss - distance is studied. Since the missile model is highly nonlinear and a time-varying linearized model is required to apply the adjoint method, a new technique that utilizes the time-reversed linearized coefficients of the missile as a replacement for the time-varying describing functions is applied and proven to be successful. It is found that, when compared with Monte Carlo generated results, simulation results of this linear adjoint technique provide acceptable accuracy and can be produced with much less effort.
VT Linear Referencing System - End-to-End 2014
Vermont Center for Geographic Information — LRS2014 is a Linear Referencing System layer that includes interstate, U.S., state (VT), and other transportation routes logged by the Vermont Agency of...
Perfect commuting-operator strategies for linear system games
Cleve, Richard; Liu, Li; Slofstra, William
2017-01-01
Linear system games are a generalization of Mermin's magic square game introduced by Cleve and Mittal. They show that perfect strategies for linear system games in the tensor-product model of entanglement correspond to finite-dimensional operator solutions of a certain set of non-commutative equations. We investigate linear system games in the commuting-operator model of entanglement, where Alice and Bob's measurement operators act on a joint Hilbert space, and Alice's operators must commute with Bob's operators. We show that perfect strategies in this model correspond to possibly infinite-dimensional operator solutions of the non-commutative equations. The proof is based around a finitely presented group associated with the linear system which arises from the non-commutative equations.
A Graph Approach to Observability in Physical Sparse Linear Systems
Directory of Open Access Journals (Sweden)
Santiago Vazquez-Rodriguez
2012-01-01
Full Text Available A sparse linear system constitutes a valid model for a broad range of physical systems, such as electric power networks, industrial processes, control systems or traffic models. The physical magnitudes in those systems may be directly measured by means of sensor networks that, in conjunction with data obtained from contextual and boundary constraints, allow the estimation of the state of the systems. The term observability refers to the capability of estimating the state variables of a system based on the available information. In the case of linear systems, diffierent graphical approaches were developed to address this issue. In this paper a new unified graph based technique is proposed in order to determine the observability of a sparse linear physical system or, at least, a system that can be linearized after a first order derivative, using a given sensor set. A network associated to a linear equation system is introduced, which allows addressing and solving three related problems: the characterization of those cases for which algebraic and topological observability analysis return contradictory results; the characterization of a necessary and sufficient condition for topological observability; the determination of the maximum observable subsystem in case of unobservability. Two examples illustrate the developed techniques.
Arbitrarily low sensitivity (ALS) in linear distributed systems using pointwise linear feedback
Kelemen, Matei; Kennai, Yakar; Horowitz, Isaac
1990-01-01
The sensitivity problem is defined for feedback systems with plants described by linear partial differential operators having constant coefficients, in a bounded one-dimensional domain. there are also finitely many observation points and finitely many lumped feedback loops, and a finite number of di
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
Arbitrarily low sensitivity (ALS) in linear distributed systems using pointwise linear feedback
Kelemen, Matei; Kennai, Yakar; Horowitz, Isaac
1990-01-01
The sensitivity problem is defined for feedback systems with plants described by linear partial differential operators having constant coefficients, in a bounded one-dimensional domain. there are also finitely many observation points and finitely many lumped feedback loops, and a finite number of
Indirect techniques for adaptive input-output linearization of non-linear systems
Teel, Andrew; Kadiyala, Raja; Kokotovic, Peter; Sastry, Shankar
1991-01-01
A technique of indirect adaptive control based on certainty equivalence for input output linearization of nonlinear systems is proven convergent. It does not suffer from the overparameterization drawbacks of the direct adaptive control techniques on the same plant. This paper also contains a semiindirect adaptive controller which has several attractive features of both the direct and indirect schemes.
Liapunov structure and asymptotic expressions of linear differential systems
Institute of Scientific and Technical Information of China (English)
高维新
1996-01-01
With a view to the researches on asymptotic properties for linear differential systems,the characteristic number is transformed into functional dass which can indicate the change trend of the norm for solution,so the invariant structure is given under Liapunov changes and feasible computational method of asymptotic expressions for linear differential systems with variant coefficients,and various asymptotic conclusions induding the necessary and sufllcient conditions of stability are got.
ON THE STABILIZATION OF THE LINEAR HYBRID SYSTEM STRUCTURE
Directory of Open Access Journals (Sweden)
Kirillov
2014-11-01
Full Text Available The linear control hybrid system, consisting of a fi- nite set of subsystems (modes having different dimensions, is considered. The moments of reset time are determined by some complementary function – evolutionary time. This function satisfies the special complementary ordinary differential equation. The mode stabilization problem is solved for some class of piecewise linear controls. The method of stabilization relies on the set of invariant planes, the existence of which is due to the special form of the hybrid system.
Linear Quantum Systems: Non-Classical States and Robust Stability
2016-06-29
linear models, and (v) physical realizability results for finite level quantum systems. Introduction : Classical linear systems theory has a...PAGE Unclassified REPORT DOCUMENTATION PAGE Form ApprovedOMB No. 0704-0188 The public reporting burden for this collection of information is estimated to...needed, and completing and reviewing the collection of information . Send comments regarding this burden estimate or any other aspect of this
Model Identification of Linear Parameter Varying Aircraft Systems
Fujimore, Atsushi; Ljung, Lennart
2007-01-01
This article presents a parameter estimation of continuous-time polytopic models for a linear parameter varying (LPV) system. The prediction error method of linear time invariant (LTI) models is modified for polytopic models. The modified prediction error method is applied to an LPV aircraft system whose varying parameter is the flight velocity and model parameters are the stability and control derivatives (SCDs). In an identification simulation, the polytopic model is more suitable for expre...
An Efficient Bayesian Iterative Method for Solving Linear Systems
Institute of Scientific and Technical Information of China (English)
Deng DING; Kin Sio FONG; Ka Hou CHAN
2012-01-01
This paper concerns with the statistical methods for solving general linear systems.After a brief review of Bayesian perspective for inverse problems,a new and efficient iterative method for general linear systems from a Bayesian perspective is proposed.The convergence of this iterative method is proved,and the corresponding error analysis is studied.Finally,numerical experiments are given to support the efficiency of this iterative method,and some conclusions are obtained.
Satisfactory control of discrete-time linear periodic systems
Institute of Scientific and Technical Information of China (English)
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.
A Proof System for the Linear Time μ-Calculus
DEFF Research Database (Denmark)
Dax, Christian; Hofmann, Martin; Lange, Martin
2006-01-01
for the latter because of nestings of fixpoint operators and variables with several occurrences. We present a simple sound and complete infinitary proof system for the linear time μ-calculus and then present two decision procedures for provability in the system, hence validity of formulas. One uses......The linear time μ-calculus extends LTL with arbitrary least and greatest fixpoint operators. This gives it the power to express all ω-regular languages, i.e. strictly more than LTL. The validity problem is PSPACE-complete for both LTL and the linear time μ-calculus. In practice it is more difficult...
Solar system tests for linear massive conformal gravity
Faria, F F
2016-01-01
We first find the linearized gravitational field of a static spherically symmetric mass distribution in massive conformal gravity. Then we test this field with two solar system experiments: deflection of light by the sun and radar echo delay. The result is that the linear massive conformal gravity agrees with the linear general relativistic observations in the solar system. However, besides the standard general relativistic deflection of light, the theory gives an extra deflection at galactic scales. It is likely that this additional deflection replaces the effects of dark matter in general relativity.
Existence of homoclinic connections in continuous piecewise linear systems.
Carmona, Victoriano; Fernández-Sánchez, Fernando; García-Medina, Elisabeth; Teruel, Antonio E
2010-03-01
Numerical methods are often used to put in evidence the existence of global connections in differential systems. The principal reason is that the corresponding analytical proofs are usually very complicated. In this work we give an analytical proof of the existence of a pair of homoclinic connections in a continuous piecewise linear system, which can be considered to be a version of the widely studied Michelson system. Although the computations developed in this proof are specific to the system, the techniques can be extended to other piecewise linear systems.
Economic MPC for a linear stochastic system of energy units
DEFF Research Database (Denmark)
Jørgensen, John Bagterp; Sokoler, Leo Emil; Standardi, Laura
2016-01-01
in addition to stochastic power producers such as wind turbines and solar power plants. Control of such large scale systems requires new control algorithms. In this paper, we formulate the control of such a system as an Economic Model Predictive Control (MPC) problem. When the power producers and controllable......This paper summarizes comprehensively the work in four recent PhD theses from the Technical University of Denmark related to Economic MPC of future power systems. Future power systems will consist of a large number of decentralized power producers and a large number of controllable power consumers...... power consumers have linear dynamics, the Economic MPC may be expressed as a linear program. We provide linear models for a number of energy units in an energy system, formulate an Economic MPC for coordination of such a system. We indicate how advances in computational MPC makes the solutions...
Design and Simulation of PMSM Feedback Linearization Control System
Directory of Open Access Journals (Sweden)
SONG Xiao-jing
2013-01-01
Full Text Available With the theory of AC adjustable speed as well as a new control theory research is unceasingly thorough, the permanent magnet synchronous motor control system requires high precision of control and high reliability of the occasion, access to a wide range of applications, in the modern AC motor has play a decisive role position. Based on the deep research on the feedback linearization technique based on, by choosing appropriate state transformation and control transform, PMSM model input output linearization, and the design of the feedback linearization controller, realized PMSM decoupling control based on Matlab, and PMSM feedback linearization control system simulation. The simulation results show that, the system in a certain range of speed than the traditional PI controller has better control performance, but to the parameter variation has strong sensitivity. It also determines the direction for future research.
Stability Problems for Chua System with One Linear Control
Directory of Open Access Journals (Sweden)
Camelia Pop Arieşanu
2013-01-01
Full Text Available A Hamilton-Poisson realization and some stability problems for a dynamical system arisen from Chua system are presented. The stability and dynamics of a linearized smooth version of the Chua system are analyzed using the Hamilton-Poisson formalism. This geometrical approach allows to deduce the nonlinear stabilization near different equilibria.
Reachability analysis of switched linear discrete singular systems
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
This paper studies the reachability problem of the switched linear discrete singular (SLDS) systems. Under the condition that all subsystems are regular, the reachability of the SLDS systems is characterized based on a peculiar repeatedly introduced switching sequence. The necessary and sufficient conditions are obtained for the reachability of the SLDS systems.
CONTROLLING L(U)-SYSTEM USING PARTIAL LINEARIZATION
Institute of Scientific and Technical Information of China (English)
于永光; 张锁春
2004-01-01
Partial linearization method is proposed for controlling Lu-system. Through partially cancelling the nonlinear cross-coupling terms the stabilization of the resulting system was realized. This method can be easily realized. The robust behavior was proved with respect to an uncertain system. Numerical simulation are provided to show the effectiveness and feasibility of the method.
Model Reduction of Linear Switched Systems by Restricting Discrete Dynamics
DEFF Research Database (Denmark)
Bastug, Mert; Petreczky, Mihaly; Wisniewski, Rafal
2014-01-01
We present a procedure for reducing the number of continuous states of discrete-time linear switched systems, such that the reduced system has the same behavior as the original system for a subset of switching sequences. The proposed method is expected to be useful for abstraction based control s...
Recursive inversion of externally defined linear systems by FIR filters
Bach, Ralph E., Jr.; Baram, Yoram
1989-01-01
The approximate inversion of an internally unknown linear system, given by its impulse response sequence, by an inverse system having a finite impulse response, is considered. The recursive least-squares procedure is shown to have an exact initialization, based on the triangular Toeplitz structure of the matrix involved. The proposed approach also suggests solutions to the problem of system identification and compensation.
Observability and controllability for linear neutral type systems
Rabah, Rabah; Sklyar, Grigory,
2014-01-01
International audience; For a large class of linear neutral type systems which include distributed delays we give the duality relation between exact controllability and exact observability. This duality is based on the representation of the abstract adjoint system as a special neutral type system. As a consequence of this duality relation, a characterization of exact observability is obtained. The time of observability is precised.
Incremental Closed-loop Identification of Linear Parameter Varying Systems
DEFF Research Database (Denmark)
Bendtsen, Jan Dimon; Trangbæk, Klaus
2011-01-01
This paper deals with system identification for control of linear parameter varying systems. In practical applications, it is often important to be able to identify small plant changes in an incremental manner without shutting down the system and/or disconnecting the controller; unfortunately, cl...
Stability and response bounds of non-conservative linear systems
DEFF Research Database (Denmark)
Pommer, Christian
2003-01-01
For a linear system of second order differential equations the stability is studied by Lyapunov's direct method. The Lyapunov matrix equation is solved and a sufficient condition for stability is expressed by the system matrices. For a system which satisfies the condition for stability the Lyapunov...
Assessment Of Some Acceleration Schemes In The Solution Of Systems Of Linear Equations.
Directory of Open Access Journals (Sweden)
S. Azizu
2015-06-01
Full Text Available Abstract In this paper assessment of acceleration schemes in the solution of systems of linear equations has been studied. The iterative methods Jacobi Gauss-Seidel and SOR methods were incorporated into the acceleration scheme Chebyshev extrapolation Residual smoothing Accelerated gradient and Richardson Extrapolation to speed up their convergence. The Conjugate gradient methods of GMRES BICGSTAB and QMR were also assessed. The research focused on Banded systems Tridiagonal systems and Dense Symmetric positive definite systems of linear equations for numerical experiments. The experiments were based on the following performance criteria convergence number of iterations speed of convergence and relative residual of each method. Matlab version 7.0.1 was used for the computation of the resulting algorithms. Assessment of the numerical results showed that the accelerated schemes improved the performance of Jacobi Gauss-Seidel and SOR methods. The Chebyshev and Richardson acceleration methods converged faster than the conjugate gradient methods of GMRES MINRES QMR and BICGSTAB in general.
THE STABILITY OF LINEAR MULTISTEP METHODS FOR LINEAR SYSTEMS OF NEUTRAL DIFFERENTIAL EQUATIONS
Institute of Scientific and Technical Information of China (English)
Hong-jiong Tian; Jiao-xun Kuang; Lin Qiu
2001-01-01
This paper deals with the numerical solution of initial valueproblems for systems of neutral differential equations where т ＞ 0, f and φ denote given vector-valued functions. The numerical stability of a linear multistep method is investigated by analysing the solution of the test equations y'(t) = Ay(t) + By(t -т ) + Cy'(t -т ), where A, B and C denote constant complex N × N-matrices, and т ＞ 0. We investigate the properties of adaptation of the linear multistep method and the characterization of the stability region. It is proved that the linear multistep method is NGP-stable if and only if it is A-stable for ordinary differential equations.
Exact linearization of the radiation-damped spin system
Rourke; Augustine
2000-02-21
Nonlinear evolution of the Landau-Lifshitz type can be exactly linearized. Special cases include the radiation-damped spin system and the superradiant system in the semiclassical regime, in the presence of time-varying driving fields. For these, the resultant linear system is simply that of a spin 1 / 2 particle, with the radiation damping rate, or superradiant characteristic time, manifested as an imaginary addition to the spin's resonance frequency. Consequently, methods from inverse scattering theory can be used to design driving fields. The behavior of these systems under stochastic excitation can be determined exactly.
Simultaneous quadratic performance stabilization for linear time-delay systems
Institute of Scientific and Technical Information of China (English)
Chen Yuepeng; Zhou Zude; Liu Huanbin; Zhang Qingling
2006-01-01
A newly designed approach of simultaneous stabilization is given for linear discrete time-delay systems. The problem of stabilization for a collection of systems is discussed initially. Adequate condition are obtained in terms of linear matrix inequalities (LMIs) which are independent of time delays such that the resultant collection of discrete time-delay systems are stable with an upper bound of the quadratic performance index. Subsequently, controllers are designed such that the resultant closed-loop discrete time-delay systems are simultaneously stabilized with the upper bound of the quadratic performance index. Finally,a numerical example is given to illustrate the design method.
Modeling and analysis of linear hyperbolic systems of balance laws
Bartecki, Krzysztof
2016-01-01
This monograph focuses on the mathematical modeling of distributed parameter systems in which mass/energy transport or wave propagation phenomena occur and which are described by partial differential equations of hyperbolic type. The case of linear (or linearized) 2 x 2 hyperbolic systems of balance laws is considered, i.e., systems described by two coupled linear partial differential equations with two variables representing physical quantities, depending on both time and one-dimensional spatial variable. Based on practical examples of a double-pipe heat exchanger and a transportation pipeline, two typical configurations of boundary input signals are analyzed: collocated, wherein both signals affect the system at the same spatial point, and anti-collocated, in which the input signals are applied to the two different end points of the system. The results of this book emerge from the practical experience of the author gained during his studies conducted in the experimental installation of a heat exchange cente...
2010-12-09
... Federal Acquisition Regulation Supplement; Business Systems--Definition and Administration (DFARS Case... INFORMATION: I. Background DoD published a proposed rule for Business Systems--Definition and...
H 2 guaranteed cost control of discrete linear systems
Directory of Open Access Journals (Sweden)
Colmenares W.
2000-01-01
Full Text Available This paper presents necessary and sufficient conditions for the existence of a quadratically stabilizing output feedback controller which also assures H 2 guaranteed cost performance on a discrete linear uncertain system where the uncertainty is of the norm bounded type. The conditions are presented as a collection of linear matrix inequalities.The solution, however requires a search over a scalar parameter space.
Correlated L\\'evy noise in linear dynamical systems
Srokowski, Tomasz
2010-01-01
Linear dynamical systems, driven by a non-white noise which has the Levy distribution, are analysed. Noise is modelled by a specific stochastic process which is defined by the Langevin equation with a linear force and the Levy distributed symmetric white noise. Correlation properties of the process are discussed. The Fokker-Planck equation driven by that noise is solved. Distributions have the Levy shape and their width, for a given time, is smaller than for processes in the white noise limit...
Input design for linear dynamic systems using maxmin criteria
DEFF Research Database (Denmark)
Sadegh, Payman; Hansen, Lars H.; Madsen, Henrik
1998-01-01
This paper considers the problem of input design for maximizing the smallest eigenvalue of the information matrix for linear dynamic systems. The optimization of the smallest eigenvalue is of interest in parameter estimation and parameter change detection problems. We describe a simple cutting...... plane algorithm to determine the optimal frequency power weights of the input, using successive solutions to linear programs. We present a case study related to estimation of thermal parameters of a building....
Tape measuring system using linear encoder and digital camera
Eom, Tae Bong; Jeong, Don Young; Kim, Myung Soon; Kim, Jae Wan; Kim, Jong Ahn
2013-04-01
We have designed and constructed the calibration system of line standards such as tape and rule for the secondary calibration laboratories. The system consists of the main body with linear stage and linear encoder, the optical microscope with digital camera, and the computer. The base of the system is a aluminum profile with 2.9 m length, 0.09 m height and 0.18 m width. The linear stage and the linear encoder are fixed on the aluminum profile. The micro-stage driven by micrometer is fixed on the carriage of the long linear stage, and the optical microscope with digital camera and the tablet PC are on the this stage. The linear encoder counts the moving distance of the linear stage with resolution of 1 μm and its counting value is transferred to the tablet PC. The image of the scale mark of the tape is captured by the CCD camera of optical microscope and transferred to the PC through USB interface. The computer automatically determines the center of the scale mark by image processing technique and at the same time reads the moving distance of the linear stage. As a result, the computer can calculate the interval between the scale marks of the tape. In order to achieve the high accuracy, the linear encoder should be calibrated using the laser interferometer or the rigid steel rule. This calibration data of the linear encoder is stored at the computer and the computer corrects the reading value of the linear encoder. In order to determine the center of the scale mark, we use three different algorithms. First, the image profile over specified threshold level is fitted in even order polynomial and the axis of the polynomial is used as the center of the line. Second, the left side and right side areas at the center of the image profile are calculated so that two areas are same. Third, the left and right edges of the image profile are determined at every intensity level of the image and the center of the graduation is calculated as an average of the centers of the left
Control synthesis of linear distributed parameter switched systems
Institute of Scientific and Technical Information of China (English)
Leping Bao; Shumin Fei; Lin Chai
2015-01-01
The control synthesis for switched systems is extended to distributed parameter switched systems in Hilbert space. Based on semigroup and operator theory, by means of multiple Lyapunov method incorporated average dwel time approach, sufficient con-ditions are derived in terms of linear operator inequalities frame-work for distributed parameter switched systems. Being applied to one dimensional heat propagation switched systems, these lin-ear operator inequalities are reduced to linear matrix inequalities subsequently. In particular, the state feedback gain matrices and the switching law are designed, and the state decay estimate is explicitly given whose decay coefficient completely depends on the system’s parameter and the boundary condition. Final y, two numerical examples are given to il ustrate the proposed method.
Duality between noise and spatial resolution in linear systems.
Gureyev, Timur E; Nesterets, Yakov I; de Hoog, Frank; Schmalz, Gerd; Mayo, Sheridan C; Mohammadi, Sara; Tromba, Giuliana
2014-04-21
It is shown that in a broad class of linear systems, including general linear shift-invariant systems, the spatial resolution and the noise satisfy a duality relationship, resembling the uncertainty principle in quantum mechanics. The product of the spatial resolution and the standard deviation of output noise in such systems represents a type of phase-space volume that is invariant with respect to linear scaling of the point-spread function, and it cannot be made smaller than a certain positive absolute lower limit. A corresponding intrinsic "quality" characteristic is introduced and then evaluated for the cases of some popular imaging systems, including computed tomography, generic image convolution and phase-contrast imaging. It is shown that in the latter case the spatial resolution and the noise can sometimes be decoupled, potentially leading to a substantial increase in the imaging quality.
Linearizing Control of Induction Motor Based on Networked Control Systems
Institute of Scientific and Technical Information of China (English)
Jun Ren; Chun-Wen Li; De-Zong Zhao
2009-01-01
A new approach to speed control of induction motors is developed by introducing networked control systems (NCSs) into the induction motor driving system. The control strategy is to stabilize and track the rotor speed of the induction motor when the network time delay occurs in the transport medium of network data. First, a feedback linearization method is used to achieve input-output linearization and decoupling control of the induction motor driving system based on rotor flux model, and then the characteristic of network data is analyzed in terms of the inherent network time delay. A networked control model of an induction motor is established. The sufficient condition of asymptotic stability for the networked induction motor driving system is given, and the state feedback controller is obtained by solving the linear matrix inequalities (LMIs). Simulation results verify the efficiency of the proposed scheme.
Order Reduction of Linear Interval Systems Using Genetic Algorithm
Directory of Open Access Journals (Sweden)
Dr. Rajendra Prasad
2010-10-01
Full Text Available This paper presents an algorithm for order reduction of higher order linear interval system into stable lower order linear interval system by means of Genetic algorithm. In this algorithm the numerator and denominator polynomials are determined by minimizing the Integral square error (ISE using genetic algorithm (GA. The algorithm is simple, rugged and computer oriented. It is shown that the algorithm has several advantages, e.g. the reduced order models retain the steady-state value and stability of the original system. A numerical example illustrates the proposed algorithm.
Analysis of the Structured Perturbation for the BCSCB Linear System
Directory of Open Access Journals (Sweden)
Xia Tang
2015-01-01
Full Text Available Circulant and block circulant type matrices are important tools in solving networked systems. In this paper, based on the style spectral decomposition of the basic circulant matrix and the basic skew circulant matrix, the block style spectral decomposition of the BCSCB matrix is obtained. And then, the structure perturbation is analysed, which includes the condition number and relative error of the BCSCB linear system. Then the optimal backward perturbation bound of the BCSCB linear system is discussed. Simultaneously, the algorithm for the optimal backward perturbation bound is given. Finally, a numerical example is provided to verify the effectiveness of the algorithm.
Linear assignment maps for correlated system-environment states
Energy Technology Data Exchange (ETDEWEB)
Rodriguez-Rosario, Cesar A.; Modi, Kavan; Aspuru-Guzik, Alan
2010-01-20
Assignment maps are mathematical operators that describe initial system-environment states for open quantum systems. We re-examine the notion of assignments that account for correlations between the system and the environment and show that these maps can be made linear at the expense of giving up positivity or consistency of the map. We study the role of positivity and consistency of the map and show the effects of relaxing these. Finally, we establish a connection between the violation of the positivity of linear assignments and the no-broadcasting theorem.
Ferrer, Josep; Pacha, Juan R; Peña, Marta
2012-01-01
We consider the set of bimodal linear systems consisting of two linear dynamics acting on each side of a given hyperplane, assuming continuity along the separating hyperplane. Focusing on the unobservable planar ones, we obtain a simple explicit characterization of controllability. Moreover, we apply the canonical forms of these systems depending on two state variables to obtain explicitly miniversal deformations, to illustrate bifurcation diagrams and to prove that the unobservable controllable systems are stabilizable. Preprint of an article submitted for consideration in IJBC \\copyright 2011 copyright World Scientific Publishing Company http://www.worldscinet.com/ijbc/
Identification of linear stochastic systems through projection filters
Chen, Chung-Wen; Huang, Jen-Kuang; Juang, Jer-Nan
1992-01-01
A novel method is presented for identifying a state-space model and a state estimator for linear stochastic systems from input and output data. The method is primarily based on the relationship between the state-space model and the finite-difference model of linear stochastic systems derived through projection filters. It is proved that least-squares identification of a finite difference model converges to the model derived from the projection filters. System pulse response samples are computed from the coefficients of the finite difference model.
Downlink SINR Distribution of Linearly Precoded Multiuser MIMO Systems
DEFF Research Database (Denmark)
Lin, Zihuai; Sørensen, Troels Bundgaard; Mogensen, Preben
2007-01-01
This paper derives mathematical expressions for the SINR distribution in systems with linearly precoded multiuser MIMO and frequency domain packet scheduling. The packet scheduler is able to exploit the available multiuser diversity in both time, frequency and spatial domains. Our analysis model...... is confined to 3GPP downlink transmission in which we specifically investigate the Single User (SU) and Multi-user (MU) Spatial Divsion Multiplexing (SDM) MIMO schemes. From the analytical results we find that the outage probability for systems using the SU-MIMO scheme is larger than the one for the MU......-MIMO scheme. Also, in comparison to systems without precoding, linear precoding can improve the outage probability....
Space bandwidth-efficient realizations of linear systems.
Kutay, M A; Erden, M F; Ozaktas, H M; Arkan, O; Güleryüz, O; Candan, C A
1998-07-15
One can obtain either exact realizations or useful approximations of linear systems or matrix-vector products that arise in many different applications by implementing them in the form of multistage or multichannel fractional Fourier-domain filters, resulting in space-bandwidth-efficient systems with acceptable decreases in accuracy. Varying the number and the configuration of filters enables one to trade off between accuracy and efficiency in a flexible manner. The proposed scheme constitutes a systematic way of exploiting the regularity or structure of a given linear system or matrix, even when that structure is not readily apparent.
Indirect linear locally distributed damping of coupled systems
Directory of Open Access Journals (Sweden)
Annick BEYRATH
2004-11-01
Full Text Available The aim of this paper is to prove indirect internal stabilization results for diﬀerent coupled systems with linear locally distributed damping (coupled wave equations, wave equations with diﬀerent speeds of propagation. In our case, a linear local damping term appears only in the ﬁrst equation whereas no damping term is applied to the second one (this is indirect stabilization, see [11]. Using thepiecewise multiplier method we prove that the full system is stabilized and that the total energy of the solution of this system decays polynomially.
State Feedback with Memory for Constrained Switched Positive Linear Systems
Directory of Open Access Journals (Sweden)
Jinjin Liu
2015-04-01
Full Text Available In this paper, the stabilization problem in switched linear systems with time-varying delay under constrained state and control is investigated. The synthesis of bounded state-feedback controllers with memory ensures that a closed-loop state is positive and stable. Firstly, synthesis with a sign-restricted (nonnegative and negative control is considered for general switched systems; then, the stabilization issue under bounded controls including the asymmetrically bounded controls and states constraints are addressed. In addition, the results are extended to systems with interval and polytopic uncertainties. All the proposed conditions are solvable in term of linear programming. Numerical examples illustrate the applicability of the results.
Sampling-interval-dependent stability for linear sampled-data systems with non-uniform sampling
Shao, Hanyong; Lam, James; Feng, Zhiguang
2016-09-01
This paper is concerned with the sampling-interval-dependent stability of linear sampled-data systems with non-uniform sampling. A new Lyapunov-like functional is constructed to derive sampling-interval-dependent stability results. The Lyapunov-like functional has three features. First, it depends on time explicitly. Second, it may be discontinuous at the sampling instants. Third, it is not required to be positive definite between sampling instants. Moreover, the new Lyapunov-like functional can make use of the information fully of the sampled-data system, including that of both ends of the sampling interval. By making a new proposition for the Lyapunov-like functional, a sampling-interval-dependent stability criterion with reduced conservatism is derived. The new sampling-interval-dependent stability criterion is further extended to linear sampled-data systems with polytopic uncertainties. Finally, examples are given to illustrate the reduced conservatism of the stability criteria.
State space and input-output linear systems
Delchamps, David F
1988-01-01
It is difficult for me to forget the mild sense of betrayal I felt some ten years ago when I discovered, with considerable dismay, that my two favorite books on linear system theory - Desoer's Notes for a Second Course on Linear Systems and Brockett's Finite Dimensional Linear Systems - were both out of print. Since that time, of course, linear system theory has undergone a transformation of the sort which always attends the maturation of a theory whose range of applicability is expanding in a fashion governed by technological developments and by the rate at which such advances become a part of engineering practice. The growth of the field has inspired the publication of some excellent books; the encyclopedic treatises by Kailath and Chen, in particular, come immediately to mind. Nonetheless, I was inspired to write this book primarily by my practical needs as a teacher and researcher in the field. For the past five years, I have taught a one semester first year gradu ate level linear system theory course i...
Linearly Coupled Synchronization of the New Chaotic Systems
Institute of Scientific and Technical Information of China (English)
LU Jun-an; ZHOU Jin; LI Yi-tian
2005-01-01
This paper investigates synchronization within the new systems, which we denote as Liu system in this paper. New stability criteria for synchronization of linearly coupled Liu systems are attained using the Lyapunov method. Some sufficient conditions for synchronization are concluded through rigorous mathematical theory, which can be further applied to more chaotic systems. Moreover, numerical simulations are given to show the effectiveness of our synchronization criterions.
On the relationship between nonlinear and linear differential systems
Directory of Open Access Journals (Sweden)
ZHOU Zhengxin
2015-06-01
Full Text Available In this article, we establish the relationship between the quadratic time-varying differential systems and the linear systems, giving the sufficient conditions for the quadratic systems to have the reflecting function in the form of fractional function. We use the obtained results to discuss the qualitative behavior of the solutions of the quadratic differential systems and the time-varying Kolmogrov equations.
STRUCTURAL DECOMPOSITION AND ITS PROPERTIES OF LINEAR MULTIVARIABLE SINGULAR SYSTEMS
Institute of Scientific and Technical Information of China (English)
Minghua HE; Ben M. CHEN; Zongli LIN
2007-01-01
We present in this paper a structural decomposition for linear multivariable singular systems.Such a decomposition has a distinct feature of capturing and displaying all the structural properties,such as the finite and infinite zero structures, invertibility structures, and redundant dynamics of the given system. As its counterpart for non-singular systems, we believe that the technique is a powerful tool in solving control problems for singular systems.
INPUT-OUTPUT STRUCTURE OF LINEAR-DIFFERENTIAL ALGEBRAIC SYSTEMS
KUIJPER, M; SCHUMACHER, JM
1993-01-01
Systems of linear differential and algebraic equations occur in various ways, for instance, as a result of automated modeling procedures and in problems involving algebraic constraints, such as zero dynamics and exact model matching. Differential/algebraic systems may represent an input-output relat
INTERCONNECTIONS AND SYMMETRIES OF LINEAR-DIFFERENTIAL SYSTEMS
FAGNANI, F; WILLEMS, JC
1994-01-01
In this paper we study the interplay between control problems and symmetries in the context of linear systems. In particular, we establish sufficient conditions under which it is possible to control a symmetric system in order to make it achieve control objectives, without ''breaking'' its symmetry.
Asymptotic Behavior of Solutions to a Linear Volterra Integrodifferential System
Directory of Open Access Journals (Sweden)
Yue-Wen Cheng
2013-01-01
Full Text Available We investigate the asymptotic behavior of solutions to a linear Volterra integrodifferential system , We show that under some suitable conditions, there exists a solution for the above integrodifferential system, which is asymptotically equivalent to some given functions. Two examples are given to illustrate our theorem.
Energy and linear and angular momenta in simple electromagnetic systems
Mansuripur, Masud
2015-01-01
We present examples of simple electromagnetic systems in which energy, linear momentum, and angular momentum exhibit interesting behavior. The systems are sufficiently simple to allow exact solutions of Maxwell's equations in conjunction with the electrodynamic laws of force, torque, energy, and momentum. In all the cases examined, conservation of energy and momentum is confirmed.
Internal and external stabilisation of linear systems with constraints
Saberi, Ali; Stoorvogel, Anton A.; Sannuti, Peddapullaiah
2012-01-01
Linear systems with constraints on inputs and states are ubiquitous. Control of such systems has been a long-time challenge to control engineers and will continue to remain so. Indeed, the challenge of constraints is intense and dauntingly formidable and familiar. This book focuses on the very funda
Input-output decoupling of Hamiltonian systems : The linear case
Nijmeijer, H.; Schaft, A.J. van der
1985-01-01
In this note we give necessary and sufficient conditions for a linear Hamiltonian system to be input-output decouplable by Hamiltonian feedback, i.e. feedback that preserves the Hamiltonian structure. In a second paper we treat the same problem for nonlinear Hamiltonian systems.
Input-output decoupling of Hamiltonian systems: The linear case
Nijmeijer, H.
1985-01-01
In this note we give necessary and sufficient conditions for a linear Hamiltonian system to be input-output decouplable by Hamiltonian feedback, i.e. feedback that preserves the Hamiltonian structure. In a second paper we treat the same problem for nonlinear Hamiltonian systems.
About one problem of optimal stabilization of linear compound systems
Directory of Open Access Journals (Sweden)
Barseghyan V.R.
2014-12-01
Full Text Available The problem of optimal stabilization of linear compound system is investigated. Based on Lyapunov function method the method of building optimal stabilizing control action is suggested. The solution of the problem of optimal stabilization of a concrete compound system is given.
A parallel linear system solver for circuit simulation problems
Bomhof, W.; Vorst, H.A. van der
2001-01-01
This paper presents a parallel mixed direct/iterative method for solving linear systems Ax = b arising from circuit simulation. The systems are solved by a block LU factorization with an iterative method for the Schur complement. The Schur complement is a small and rather dense matrix. Direct LU
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.
Normalized doubly coprime factorizations for infinite-dimensional linear systems
Curtain, RF; Opmeer, MR
2006-01-01
We obtain explicit formulas for normalized doubly coprime factorizations of the transfer functions of the following class of linear systems: the input and output operators are vector-valued, but bounded, and the system is input and output stabilizable. Moreover, we give explicit formulas for the Bez
Controllability of Linear Systems on Generalized Heisenberg Groups
Dath, Mouhamadou; Jouan, Philippe
2015-01-01
This paper is devoted to the study of controllability of linear systems on generalized Heisenberg groups. Some general necessary controllability conditions and some sufficient ones are provided. We introduce the notion of decoupled systems, and more precise controllability criteria are stated for them.
On the non-linearity of the subsidiary systems
Friedrich, H
2005-01-01
In hyperbolic reductions of the Einstein equations the evolution of gauge conditions or constraint quantities is controlled by subsidiary systems. We point out a class of non-linearities in these systems which may have the potential of generating catastrophic growth of gauge resp. constraint violations in numerical calculations.
Asymptotically optimal feedback control for a system of linear oscillators
Ovseevich, Alexander; Fedorov, Aleksey
2013-12-01
We consider problem of damping of an arbitrary number of linear oscillators under common bounded control. We are looking for a feedback control steering the system to the equilibrium. The obtained control is asymptotically optimal: the ratio of motion time to zero with this control to the minimum one is close to 1, if the initial energy of the system is large.
CPV System with Static Linear Fresnel Lenses in a Greenhouse
Sonneveld, Piet; Zahn, H.; Swinkels, Gert-Jan
2010-01-01
A new CPV system with a static linear Fresnel lens, silicon PV module suitable for concentrated radiation and an innovative tracking system is integrated in a greenhouse covering. The basic idea of this horticultural application is to develop a greenhouse for pot plants (typical shadow plants) which
New approach to solve symmetric fully fuzzy linear systems
Indian Academy of Sciences (India)
P Senthilkumar; G Rajendran
2011-12-01
In this paper, we present a method to solve fully fuzzy linear systems with symmetric coefﬁcient matrix. The symmetric coefﬁcient matrix is decomposed into two systems of equations by using Cholesky method and then a solution can be obtained. Numerical examples are given to illustrate our method.
Shipboard Visibility Measurement System Definition Study.
1982-01-01
an inherent non-linear range resolution due to the compression of the re- turn signal from distant ranges near the image vanishing point. 3.2...anticipated LIDAR backscatter re- turn signal is expected to be substantially smaller in most cases than the return signal at 1.06 um or 1.54 pm (see
Filtering for linear systems with noise correlation and its application to singular systems
Institute of Scientific and Technical Information of China (English)
Wu Jian-Rong; Song Shi-Ji
2004-01-01
In this paper, an optimal filter for a stochastic linear system with previous stage noise correlation is designed.Based on this result, together with the decomposition techniques of the stochastic singular linear system, the design of an optimal filter for a stochastic singular linear system is given.
Dynamic Response of Linear Mechanical Systems Modeling, Analysis and Simulation
Angeles, Jorge
2012-01-01
Dynamic Response of Linear Mechanical Systems: Modeling, Analysis and Simulation can be utilized for a variety of courses, including junior and senior-level vibration and linear mechanical analysis courses. The author connects, by means of a rigorous, yet intuitive approach, the theory of vibration with the more general theory of systems. The book features: A seven-step modeling technique that helps structure the rather unstructured process of mechanical-system modeling A system-theoretic approach to deriving the time response of the linear mathematical models of mechanical systems The modal analysis and the time response of two-degree-of-freedom systems—the first step on the long way to the more elaborate study of multi-degree-of-freedom systems—using the Mohr circle Simple, yet powerful simulation algorithms that exploit the linearity of the system for both single- and multi-degree-of-freedom systems Examples and exercises that rely on modern computational toolboxes for both numerical and symbolic compu...
Damped oscillations of linear systems a mathematical introduction
Veselić, Krešimir
2011-01-01
The theory of linear damped oscillations was originally developed more than hundred years ago and is still of vital research interest to engineers, mathematicians and physicists alike. This theory plays a central role in explaining the stability of mechanical structures in civil engineering, but it also has applications in other fields such as electrical network systems and quantum mechanics. This volume gives an introduction to linear finite dimensional damped systems as they are viewed by an applied mathematician. After a short overview of the physical principles leading to the linear system model, a largely self-contained mathematical theory for this model is presented. This includes the geometry of the underlying indefinite metric space, spectral theory of J-symmetric matrices and the associated quadratic eigenvalue problem. Particular attention is paid to the sensitivity issues which influence numerical computations. Finally, several recent research developments are included, e.g. Lyapunov stability and ...
Optimal second order sliding mode control for linear uncertain systems.
Das, Madhulika; Mahanta, Chitralekha
2014-11-01
In this paper an optimal second order sliding mode controller (OSOSMC) is proposed to track a linear uncertain system. The optimal controller based on the linear quadratic regulator method is designed for the nominal system. An integral sliding mode controller is combined with the optimal controller to ensure robustness of the linear system which is affected by parametric uncertainties and external disturbances. To achieve finite time convergence of the sliding mode, a nonsingular terminal sliding surface is added with the integral sliding surface giving rise to a second order sliding mode controller. The main advantage of the proposed OSOSMC is that the control input is substantially reduced and it becomes chattering free. Simulation results confirm superiority of the proposed OSOSMC over some existing.
Parallel preconditioning for the solution of nonsymmetric banded linear systems
Energy Technology Data Exchange (ETDEWEB)
Amodio, P.; Mazzia, F. [Universita di Bari (Italy)
1994-12-31
Many computational techniques require the solution of banded linear systems. Common examples derive from the solution of partial differential equations and of boundary value problems. In particular the authors are interested in the parallel solution of block Hessemberg linear systems Gx = f, arising from the solution of ordinary differential equations by means of boundary value methods (BVMs), even if the considered preconditioning may be applied to any block banded linear system. BVMs have been extensively investigated in the last few years and their stability properties give promising results. A new class of BVMs called Reverse Adams, which are BV-A-stable for orders up to 6, and BV-A{sub 0}-stable for orders up to 9, have been studied.
Virtual Estimator for Piecewise Linear Systems Based on Observability Analysis
Directory of Open Access Journals (Sweden)
Ilse Cervantes
2013-02-01
Full Text Available This article proposes a virtual sensor for piecewise linear systems based on observability analysis that is in function of a commutation law related with the system’s outpu. This virtual sensor is also known as a state estimator. Besides, it presents a detector of active mode when the commutation sequences of each linear subsystem are arbitrary and unknown. For the previous, this article proposes a set of virtual estimators that discern the commutation paths of the system and allow estimating their output. In this work a methodology in order to test the observability for piecewise linear systems with discrete time is proposed. An academic example is presented to show the obtained results.
Ultra-high Frequency Linear Fiber Optic Systems
Lau, Kam
2011-01-01
This book provides an in-depth treatment of both linear fiber-optic systems and their key enabling devices. It presents a concise but rigorous treatment of the theory and practice of analog (linear) fiber-optics links and systems that constitute the foundation of Hybrid Fiber Coax infrastructure in present-day CATV distribution and cable modem Internet access. Emerging applications in remote fiber-optic feed for free-space millimeter wave enterprise campus networks are also described. Issues such as dispersion and interferometric noise are treated quantitatively, and means for mitigating them are explained. This broad but concise text will thus be invaluable not only to students of fiber-optics communication but also to practicing engineers. To the second edition of this book important new aspects of linear fiber-optic transmission technologies are added, such as high level system architectural issues, algorithms for deriving the optimal frequency assignment, directly modulated or externally modulated laser t...
Institute of Scientific and Technical Information of China (English)
曾庆山; 曹广益; 朱新坚
2004-01-01
The definitions of controllability, observability and stability were presented for fractional-order linear systems. Using the Cayley-Hamilton theorem and Mittag-Leffler function in two parameters, the sufficient and necessary conditions of controllability and observability for such systems were derived. In terms of Lyapunov's stability theory, using the theorems of Mittage-Leffler function in two parameters this paper directly derived the sufficient and necessary condition of stability for such systems. The results obtained are useful for the analysis and synthesis of fractional-order linear control systems.
DEFF Research Database (Denmark)
Bajric, Anela
A single mass Bouc-Wen oscillator with linear static restoring force contribution is approximated by an equivalent linear system. The aim of the linearized model is to emulate the correct force-displacement response of the Bouc-Wenmodel with characteristic hysteretic behaviour. The linearized model...
Linear dynamical quantum systems analysis, synthesis, and control
Nurdin, Hendra I
2017-01-01
This monograph provides an in-depth treatment of the class of linear-dynamical quantum systems. The monograph presents a detailed account of the mathematical modeling of these systems using linear algebra and quantum stochastic calculus as the main tools for a treatment that emphasizes a system-theoretic point of view and the control-theoretic formulations of quantum versions of familiar problems from the classical (non-quantum) setting, including estimation and filtering, realization theory, and feedback control. Both measurement-based feedback control (i.e., feedback control by a classical system involving a continuous-time measurement process) and coherent feedback control (i.e., feedback control by another quantum system without the intervention of any measurements in the feedback loop) are treated. Researchers and graduates studying systems and control theory, quantum probability and stochastics or stochastic control whether from backgrounds in mechanical or electrical engineering or applied mathematics ...
Discrete Time Optimal Adaptive Control for Linear Stochastic Systems
Institute of Scientific and Technical Information of China (English)
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.
Theoretical analysis of balanced truncation for linear switched systems
DEFF Research Database (Denmark)
Petreczky, Mihaly; Wisniewski, Rafal; Leth, John-Josef
2012-01-01
In this paper we present theoretical analysis of model reduction of linear switched systems based on balanced truncation, presented in [1,2]. More precisely, (1) we provide a bound on the estimation error using L2 gain, (2) we provide a system theoretic interpretation of grammians...... for showing this independence is realization theory of linear switched systems. [1] H. R. Shaker and R. Wisniewski, "Generalized gramian framework for model/controller order reduction of switched systems", International Journal of Systems Science, Vol. 42, Issue 8, 2011, 1277-1291. [2] H. R. Shaker and R....... Wisniewski, "Switched Systems Reduction Framework Based on Convex Combination of Generalized Gramians", Journal of Control Science and Engineering, 2009....
Algorithmic Approach to Abstracting Linear Systems by Timed Automata
DEFF Research Database (Denmark)
Sloth, Christoffer; Wisniewski, Rafael
2011-01-01
This paper proposes an LMI-based algorithm for abstracting dynamical systems by timed automata, which enables automatic formal verification of linear systems. The proposed abstraction is based on partitioning the state space of the system using positive invariant sets, generated by Lyapunov...... functions. This partitioning ensures that the vector field of the dynamical system is transversal to all facets of the cells, which induces some desirable properties of the abstraction. The algorithm is based on identifying intersections of level sets of quadratic Lyapunov functions, and determining...... the minimum and maximum time that a trajectory of the system can stay in a set, defined as the set-difference of sub-level sets of Lyapunov functions. The proposed algorithm applies for linear systems and can therefore be efficiently implemented using LMI-based tools....
Linear Control Technique for Anti-Lock Braking System
Directory of Open Access Journals (Sweden)
Chankit Jain
2014-08-01
Full Text Available Antilock braking systems are used in modern cars to prevent the wheels from locking after brakes are applied. The dynamics of the controller needed for antilock braking system depends on various factors. The vehicle model often is in nonlinear form. Controller needs to provide a controlled torque necessary to maintain optimum value of the wheel slip ratio. The slip ratio is represented in terms of vehicle speed and wheel rotation. In present work first of all system dynamic equations are explained and a slip ratio is expressed in terms of system variables namely vehicle linear velocity and angular velocity of the wheel. By applying a bias braking force system, response is obtained using Simulink models. Using the linear control strategies like PI-type the effectiveness of maintaining desired slip ratio is tested. It is always observed that a steady state error of 10% occurring in all the control system models.
Robust output regulation problem for linear time-delay systems
Lu, Maobin; Huang, Jie
2015-06-01
In this paper, we study the robust output regulation problem for linear systems with input time-delay. By extending the internal model design method to linear time-delay systems, we have established solvability conditions for the problem by both dynamic state feedback control and dynamic output feedback control. The advantages of internal model approach over the feedforward design approach are that it can handle perturbations of the uncertain parameters in the plant and the control law, and it does not need to solve the regulator equations.
ON STABILITY BOUNDARY OF LINEAR MULTI-PARAMETER HAMILTONIAN SYSTEMS
Institute of Scientific and Technical Information of China (English)
Qi Zhaohui(齐朝晖); Alexander P.Seyranian
2002-01-01
In this paper an approximate equation is derived to describe smoothparts of the stability boundary for linear Hamiltonian systems, depending on arbitrarynumber of parameters. With this equation, we can obtain parameters correspondingto the stability boundary, as well as to the stability and instability domains, pro-vided that one point on the stability boundary is known. Then differential equationsdescribing the evolution of eigenvalues and eigenvectors along a curve on the sta-bility boundary surface are derived. These equations also allow us to obtain curvesbelonging to the stability boundary. Applications to linear gyroscopic systems areconsidered and studied with examples.
Analysis of Linear Time-varying Systems via Haar Wavelet
Institute of Scientific and Technical Information of China (English)
无
1999-01-01
In this paper Haar wavelet integral operational matrices are introduced and the n applied to analyse linear time-varying systems. The method converts the origi nal problem to solving linear algebraic equations. Hence, computational difficulties are considerably reduced. Based on the property of time-frequency localization of Haar wavelet bases, the solution of a system includes both the frequency information and the time information. Other orthogonal functions do not have this property. An example is given, and the results are shown to be ver y accurate.
On stability of switched linear systems with perturbed switching paths
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
This paper addresses the stability issue of switched linear systems with perturbed switching paths. First,by introducing thenotions of child-path and parent-path, we are able to define the distance between two switching paths by means of their switching matrices chains. Next, we present the nice properties of the defined distance. Then, a stability criterion is presented for a class of switched linear systems with perturbed switching paths. Finally, an illustrative example is presented to verify the effectiveness of the approach.
A NEW APPROACH TO SOLVE SYSTEMS OF LINEAR EQUATIONS
Institute of Scientific and Technical Information of China (English)
Luis Vázquez; José L. Vázquez-Poletti
2001-01-01
We propose a new iterative approach to solve systems of linear equations. The new strategy integrates the algebraic basis of the problem with elements from classical mechanics and the finite difference method. The approach defines two families of convergent iterative methods. Each family is characterized by a linear differential equation, and every method is obtained from a suitable finite difference scheme to integrate the associated differential equation. The methods are general and depend on neither the matrix dimension nor the matrix structure. In this preliminary work, we present the basic features of the method with a simple application to a low dimensional system.
Asymptotical stability analysis of linear fractional differential systems
Institute of Scientific and Technical Information of China (English)
LI Chang-pin; ZHAO Zhen-gang
2009-01-01
It has been recently found that many models were established with the aid of fractional derivatives, such as viscoelastic systems, colored noise, electrode-electrolyte polarization, dielectric polarization, boundary layer effects in ducts,electromagnetic waves, quantitative finance, quantum evolution of complex systems, and fractional kinetics. In this paper, the asymptotical stability of higher-dimensional linear fractional differential systems with the Riemann-Liouville fractional order and Caputo fractional order were studied. The asymptotical stability theorems were also derived.
ON THE OPTIMAL CONTROL COMPUTATION OF LINEAR SYSTEMS
Directory of Open Access Journals (Sweden)
H. Tjahjana
2012-05-01
Full Text Available In this paper, we consider a numerical method for designing optimal controlon Linear Quadratic Regulator (LQR problem. In the optimal control design process through Pontryagin Maximum Principle (PMP, we obtain a system of diferential equations in state and costate variables. This system lacks of initial condition on the adjoint variables, and this situation creates classic dificulty for solving optimal control problems.This paper proposes a constructive method to approximate the initial condition of the adjoint system.
A FLEXIBLE PRECONDITIONED ARNOLDI METHOD FOR SHIFTED LINEAR SYSTEMS'
Institute of Scientific and Technical Information of China (English)
G.-D.Gu; X.-L.Zhou; Lei Lin
2007-01-01
We are interested in the numerical solution of the large nonsymmetric shifted linear system,(A+αI)x=b,for many different values of the shift α in a wide range.We apply the Saad's flexible preconditioning technique[14]to the solution of the shifted systems.Such flexible preconditioning with a few parameters could probably cover all the shifted systems with the shift in a wide range.Numerical experiments report the effectiveness of our approach on some problems.
Control of Non-linear Marine Cooling System
DEFF Research Database (Denmark)
Hansen, Michael; Stoustrup, Jakob; Bendtsen, Jan Dimon
2011-01-01
We consider the problem of designing control laws for a marine cooling system used for cooling the main engine and auxiliary components aboard several classes of container vessels. We focus on achieving simple set point control for the system and do not consider compensation of the non......-linearities, closed circuit flow dynamics or transport delays that are present in the system. Control laws are therefore designed using classical control theory and the performance of the design is illustrated through two simulation examples....
Extension theorems for linear operators on $L_\\infty$ and application to price systems
Bion-Nadal, Jocelyne
2011-01-01
In an $L_\\infty$-framework, we present a few extension theorems for linear operators. We focus the attention on majorant preserving and sandwich preserving types of extensions. These results are then applied to the study of price systems derived by a reasonable restriction of the class of equivalent martingale measures applicable. First we consider equivalent martingale measures with bounds on densities and the corresponding prices bounded by linear minorant and majorant. Then we consider prices bounded by bid-ask dynamics. Finally we study price systems consistent with no-good-deal pricing measures for given bounds on the Sharpe ratio. Within this study we introduce the definition of dynamic no-good-deal pricing measure.
Non-fragile decentralized H∞ controller design for uncertain linear systems
Institute of Scientific and Technical Information of China (English)
Zhao Zhihua; Chen Yuepeng; Zhang Qingling
2008-01-01
Considering the design problem of non-fragile decentralized H∞ controller with gain variations, the dynamic feedback controller by measurement feedback for uncertain linear systems is constructed and studied. The parameter uncertainties are considered to be unknown but norm bounded. The design procedures are investigated in terms of positive definite solutions to modify algebraic Riccati inequalities. Using information exchange among local controllers, the designed non-fragile decentralized H∞ controllers guarantee that the uncertain closed-loop linear systems are stable and with H∞ -norm bound on disturbance attenuation. A sufficient condition that there are such non-fragile H∞ controllers is obtained by algebraic Riccati inequalities. The approaches to solve modified algebraic Riccati inequalities are carried out preliminarily. Finally, a numerical example to show the validity of the proposed approach is given.
On the Transience of Linear Max-Plus Dynamical Systems
Charron-Bost, Bernadette; Nowak, Thomas
2011-01-01
We study the transients of linear max-plus dynamical systems. For that, we consider for each irreducible max-plus matrix A, the weighted graph G(A) such that A is the adjacency matrix of G(A). Based on a novel graph-theoretic counterpart to the number-theoretic Brauer's theorem, we propose two new methods for the construction of arbitrarily long paths in G(A) with maximal weight. That leads to two new upper bounds on the transient of a linear max-plus system which both improve on the bounds previously given by Even and Rajsbaum (STOC 1990, Theory of Computing Systems 1997), by Bouillard and Gaujal (Research Report 2000), and by Soto y Koelemeijer (PhD Thesis 2003), and are, in general, incomparable with Hartmann and Arguelles' bound (Mathematics of Operations Research 1999). With our approach, we also show how to improve the latter bound by a factor of two. A significant benefit of our bounds is that each of them turns out to be linear in the size of the system in various classes of linear max-plus system whe...
SNR Estimation in Linear Systems with Gaussian Matrices
Suliman, Mohamed A.
2017-09-27
This letter proposes a highly accurate algorithm to estimate the signal-to-noise ratio (SNR) for a linear system from a single realization of the received signal. We assume that the linear system has a Gaussian matrix with one sided left correlation. The unknown entries of the signal and the noise are assumed to be independent and identically distributed with zero mean and can be drawn from any distribution. We use the ridge regression function of this linear model in company with tools and techniques adapted from random matrix theory to achieve, in closed form, accurate estimation of the SNR without prior statistical knowledge on the signal or the noise. Simulation results show that the proposed method is very accurate.
Experimental quantum computing to solve systems of linear equations.
Cai, X-D; Weedbrook, C; Su, Z-E; Chen, M-C; Gu, Mile; Zhu, M-J; Li, Li; Liu, Nai-Le; Lu, Chao-Yang; Pan, Jian-Wei
2013-06-07
Solving linear systems of equations is ubiquitous in all areas of science and engineering. With rapidly growing data sets, such a task can be intractable for classical computers, as the best known classical algorithms require a time proportional to the number of variables N. A recently proposed quantum algorithm shows that quantum computers could solve linear systems in a time scale of order log(N), giving an exponential speedup over classical computers. Here we realize the simplest instance of this algorithm, solving 2×2 linear equations for various input vectors on a quantum computer. We use four quantum bits and four controlled logic gates to implement every subroutine required, demonstrating the working principle of this algorithm.
Complex geometric optics for symmetric hyperbolic systems I: linear theory
Maj, Omar
2008-01-01
We obtain an asymptotic solution for $\\ep \\to 0$ of the Cauchy problem for linear first-order symmetric hyperbolic systems with oscillatory initial values written in the eikonal form of geometric optics with frequency $1/\\ep$, but with complex phases. For the most common linear wave propagation models, this kind on Cauchy problems are well-known in the applied literature and their asymptotic theory, referred to as complex geometric optics, is attracting interest for applications. In this work, which is the first of a series of papers dedicated to complex geometric optics for nonlinear symmetric hyperbolic systems, we develop a rigorous linear theory and set the basis for the subsequent nonlinear analysis.
Impact of hierarchical memory systems on linear algebra algorithm design
Energy Technology Data Exchange (ETDEWEB)
Gallivan, K.; Jalby, W.; Meier, U.; Sameh, A.H.
1988-01-01
Linear algebra algorithms based on the BLAS or extended BLAS do not achieve high performance on multivector processors with a hierarchical memory system because of a lack of data locality. For such machines, block linear algebra algorithms must be implemented in terms of matrix-matrix primitives (BLAS3). Designing efficient linear algebra algorithms for these architectures requires analysis of the behavior of the matrix-matrix primitives and the resulting block algorithms as a function of certain system parameters. The analysis must identify the limits of performance improvement possible via blocking and any contradictory trends that require trade-off consideration. The authors propose a methodology that facilitates such an analysis and use it to analyze the performance of the BLAS3 primitives used in block methods. A similar analysis of the block size-performance relationship is also performed at the algorithm level for block versions of the LU decomposition and the Gram-Schmidt orthogonalization procedures.
Stabilising compensators for linear time-varying differential systems
Oberst, Ulrich
2016-04-01
In this paper, we describe a constructive test to decide whether a given linear time-varying (LTV) differential system admits a stabilising compensator for the control tasks of tracking, disturbance rejection or model matching and construct and parametrise all of them if at least one exists. In analogy to the linear time-invariant (LTI) case, the ring of stable rational functions, noncommutative in the LTV situation, and the Kučera-Youla parametrisation play prominent parts in the theory. We transfer Blumthaler's thesis from the LTI to the LTV case and sharpen, complete and simplify the corresponding results in the book 'Linear Time-Varying Systems' by Bourlès and Marinescu.
Definition of the linearity loss of the surface temperature in static tensile tests
Directory of Open Access Journals (Sweden)
A. Risitano
2014-10-01
Full Text Available Static tensile tests on material for mechanical constructions have pointed out the linearity loss of the surface temperature with the application of load. This phenomenon is due to the heat generation caused by the local microplasticizations which carry the material to deviate from its completely thermoelastic behavior,. The identification of the static load which determines the loss of linearity of the temperature under stress, becomes extremely important to define a first dynamic characterization of the material. The temperature variations that can be recorded during the static test are often very limited (a few tenths of degree for every 100 MPa in steels and they require the use of special sensors able to measure very low temperature variations. The experience acquired in such analysis highlighted that, dealing with highly accurate sensors or with particular materials, the identification of the first linearity loss (often by eye in the temperature curves, can be influenced by the sensibility of the investigator himself and can lead to incorrect estimates. The aim of this work is to validate the above mentioned observations on different steels, by applying the autocorrelation function to the data collected during the application of a static load. This, in order to make the results of the thermal analysis free from the sensitivity of the operator and to make the results as objective as possible, for defining the closest time of the linearity loss in the temperature-time function.
Wawro, Megan; Sweeney, George F.; Rabin, Jeffrey M.
2011-01-01
This paper reports on a study investigating students' ways of conceptualizing key ideas in linear algebra, with the particular results presented here focusing on student interactions with the notion of subspace. In interviews conducted with eight undergraduates, we found students' initial descriptions of subspace often varied substantially from…
Design of a dependable Interlock System for linear colliders
Nouvel, Patrice
For high energy accelerators, the interlock system is a key part of the machine protection. The interlock principle is to inhibit the beam either on failure of critical equipment and/or on low beam quality evaluation. The dependability of such a system is the most critical parameter. This thesis presents the design of an dependable interlock system for linear collider with an application to the CLIC (Compact Linear Collider) project. This design process is based on the IEEE 1220 standard and is is divided in four steps. First, the specifications are established, with a focus on the dependability, more precisely the reliability and the availability of the system. The second step is the design proposal based on a functional analysis, the CLIC and interfaced systems architecture. Third, the feasibility study is performed, applying the concepts in an accelerator facility. Finally, the last step is the hardware verification. Its aim is to prove that the proposed design is able to reach the requirements.
On linear degeneracy of integrable quasilinear systems in higher dimensions
Ferapontov, E V; Klein, C
2010-01-01
We investigate $(d+1)$-dimensional quasilinear systems which are integrable by the method of hydrodynamic reductions. In the case $d\\geq 3$ we formulate a conjecture that any such system with an irreducible dispersion relation must be linearly degenerate. We prove this conjecture in the 2-component case, providing a complete classification of multi-dimensional integrable systems in question. In particular, our results imply the non-existence of 2-component integrable systems of hydrodynamic type for $d\\geq 6$. In the second half of the paper we discuss a numerical and analytical evidence for the impossibility of the breakdown of smooth initial data for linearly degenerate systems in 2+1 dimensions.
Optimal control of switched linear systems based on Migrant Particle Swarm Optimization algorithm
Xie, Fuqiang; Wang, Yongji; Zheng, Zongzhun; Li, Chuanfeng
2009-10-01
The optimal control problem for switched linear systems with internally forced switching has more constraints than with externally forced switching. Heavy computations and slow convergence in solving this problem is a major obstacle. In this paper we describe a new approach for solving this problem, which is called Migrant Particle Swarm Optimization (Migrant PSO). Imitating the behavior of a flock of migrant birds, the Migrant PSO applies naturally to both continuous and discrete spaces, in which definitive optimization algorithm and stochastic search method are combined. The efficacy of the proposed algorithm is illustrated via a numerical example.
Bagci, Hakan
2014-11-11
We study sweeping preconditioners for symmetric and positive definite block tridiagonal systems of linear equations. The algorithm provides an approximate inverse that can be used directly or in a preconditioned iterative scheme. These algorithms are based on replacing the Schur complements appearing in a block Gaussian elimination direct solve by hierarchical matrix approximations with reduced off-diagonal ranks. This involves developing low rank hierarchical approximations to inverses. We first provide a convergence analysis for the algorithm for reduced rank hierarchical inverse approximation. These results are then used to prove convergence and preconditioning estimates for the resulting sweeping preconditioner.
Stability and response bounds of non-conservative linear systems
DEFF Research Database (Denmark)
Kliem, Wolfhard; Pommer, Christian
2004-01-01
This paper develops a stability theorem and response bounds for non-conservative systems of the form MX + (D + G)x + (K + N)x = f(t), with hermitian positive-definite matrices M, D and K, and skew-hermitian matrices G and N. To this end, we first find a Lyapunov function by solving the Lyapunov...... matrix equation. Then, if a system satisfies the condition of the stability theorem, the associated Lyapunov function can be used to obtain response bounds for the norms as well as for the individual coordinates of the solution. Examples from rotor dynamics illustrate the results....
Design techniques for large scale linear measurement systems
Energy Technology Data Exchange (ETDEWEB)
Candy, J.V.
1979-03-01
Techniques to design measurement schemes for systems modeled by large scale linear time invariant systems, i.e., physical systems modeled by a large number (> 5) of ordinary differential equations, are described. The techniques are based on transforming the physical system model to a coordinate system facilitating the design and then transforming back to the original coordinates. An example of a three-stage, four-species, extraction column used in the reprocessing of spent nuclear fuel elements is presented. The basic ideas are briefly discussed in the case of noisy measurements. An example using a plutonium nitrate storage vessel (reprocessing) with measurement uncertainty is also presented.
Recent Developments In Theory Of Balanced Linear Systems
Gawronski, Wodek
1994-01-01
Report presents theoretical study of some issues of controllability and observability of system represented by linear, time-invariant mathematical model of the form. x = Ax + Bu, y = Cx + Du, x(0) = xo where x is n-dimensional vector representing state of system; u is p-dimensional vector representing control input to system; y is q-dimensional vector representing output of system; n,p, and q are integers; x(0) is intial (zero-time) state vector; and set of matrices (A,B,C,D) said to constitute state-space representation of system.
Linear optimal control of continuous time chaotic systems.
Merat, Kaveh; Abbaszadeh Chekan, Jafar; Salarieh, Hassan; Alasty, Aria
2014-07-01
In this research study, chaos control of continuous time systems has been performed by using dynamic programming technique. In the first step by crossing the response orbits with a selected Poincare section and subsequently applying linear regression method, the continuous time system is converted to a discrete type. Then, by solving the Riccati equation a sub-optimal algorithm has been devised for the obtained discrete chaotic systems. In the next step, by implementing the acquired algorithm on the quantized continuous time system, the chaos has been suppressed in the Rossler and AFM systems as some case studies.
Linear-constraint wavefront control for exoplanet coronagraphic imaging systems
Sun, He; Eldorado Riggs, A. J.; Kasdin, N. Jeremy; Vanderbei, Robert J.; Groff, Tyler Dean
2017-01-01
A coronagraph is a leading technology for achieving high-contrast imaging of exoplanets in a space telescope. It uses a system of several masks to modify the diffraction and achieve extremely high contrast in the image plane around target stars. However, coronagraphic imaging systems are very sensitive to optical aberrations, so wavefront correction using deformable mirrors (DMs) is necessary to avoid contrast degradation in the image plane. Electric field conjugation (EFC) and Stroke minimization (SM) are two primary high-contrast wavefront controllers explored in the past decade. EFC minimizes the average contrast in the search areas while regularizing the strength of the control inputs. Stroke minimization calculates the minimum DM commands under the constraint that a target average contrast is achieved. Recently in the High Contrast Imaging Lab at Princeton University (HCIL), a new linear-constraint wavefront controller based on stroke minimization was developed and demonstrated using numerical simulation. Instead of only constraining the average contrast over the entire search area, the new controller constrains the electric field of each single pixel using linear programming, which could led to significant increases in speed of the wavefront correction and also create more uniform dark holes. As a follow-up of this work, another linear-constraint controller modified from EFC is demonstrated theoretically and numerically and the lab verification of the linear-constraint controllers is reported. Based on the simulation and lab results, the pros and cons of linear-constraint controllers are carefully compared with EFC and stroke minimization.
A LINEAR-PROGRAMMING ALGORITHM FOR INVARIANT POLYHEDRAL-SETS OF DISCRETE-TIME LINEAR-SYSTEMS
TENDAM, AA; NIEUWENHUIS, JW
1995-01-01
In this paper we formulate necessary and sufficient conditions for an arbitrary polyhedral set to be a positively invariant set of a linear discrete-time system. Polyhedral cones and linear subspaces are included in the analysis. A linear programming algorithm is presented that enables practical
Reducibility and Stability Results for Linear System of Difference Equations
Directory of Open Access Journals (Sweden)
Misir Adil
2008-01-01
Full Text Available We first give a theorem on the reducibility of linear system of difference equations of the form . Next, by the means of Floquet theory, we obtain some stability results. Moreover, some examples are given to illustrate the importance of the results.
Generating Nice Linear Systems for Matrix Gaussian Elimination
Homewood, L. James
2004-01-01
In this article an augmented matrix that represents a system of linear equations is called nice if a sequence of elementary row operations that reduces the matrix to row-echelon form, through matrix Gaussian elimination, does so by restricting all entries to integers in every step. Many instructors wish to use the example of matrix Gaussian…
Output Regulation Problem for Differentiable Families of Linear Systems
Compta, Albert; Ferrer, Josep; Peña, Marta
2009-09-01
Given a family of linear systems depending on a parameter varying in a differentiable manifold, we obtain sufficient conditions for the existence of a (global or local) differentiable family of controllers solving the output regulation problem for the given family. Moreover, we construct it when these conditions hold.
Further results on switched control of linear systems with constraints
Persis, Claudio De; Santis, Raffaella De; Morse, A. Stephen
2002-01-01
In a previous paper we proposed a supervisory control system to globally regulate to zero the state of a very poorly modeled, open-loop unstable but not exponentially unstable, linear process in the presence of input constraints. The process to control was unknown but assumed to belong to a finite f
Competitive forms of symmetry breaking in linear antiferromagnetic systems
Caspers, W.J.; Magnus, W.
1985-01-01
Two different forms of symmetry breaking are considered for linear antiferromagnetic systems (S = 1/2 ). Their relative stability is examined by considering small fluctuations in the harmonic oscillator approximation. Imaginary frequencies correspond with an unstable phase, and the ground state repr
Noether's theory of generalized linear nonholonomic mechanical systems
Institute of Scientific and Technical Information of China (English)
Dong Wen-Shan; Huang Bao-Xin; Fang Jian-Hui
2011-01-01
By introducing the quasi-symmetry of the infinitesimal transformation of the transformation group Gr, the Noether's theorem and the Noether's inverse theorem for generalized linear nonholonomic mechanical systems are obtained in a generalized compound derivative space. An example is given to illustrate the application of the result.
New Riccati equations for well-posed linear systems
Opmeer, MR; Curtain, RF
2004-01-01
We consider the classic problem of minimizing a quadratic cost functional for well-posed linear systems over the class of inputs that are square integrable and that produce a square integrable output. As is well-known, the minimum cost can be expressed in terms of a bounded nonnegative self-adjoint
Robust Solutions for Systems of Uncertain Linear Equations
Zhen, Jianzhe; den Hertog, Dick
2015-01-01
Our contribution is twofold. Firstly, for a system of uncertain linear equations where the uncertainties are column-wise and reside in general convex sets, we show that the intersection of the set of possible solutions and any orthant is convex. We derive a convex representation of this intersection
Observability analysis of nonlinear systems using pseudo-linear transformation
Kawano, Yu; Ohtsuka, Toshiyuki
2013-01-01
In the linear control theory, the observability Popov-Belevitch-Hautus (PBH) test plays an important role in studying observability along with the observability rank condition and observability Gramian. The observability rank condition and observability Gramian have been extended to nonlinear system
The AOR Iterative Method for Preconditioned Linear Systems
Institute of Scientific and Technical Information of China (English)
WANG Zhuan-de; GAO Zhong-xi; HUANG Ting-zhu
2004-01-01
The preconditioned methods for solving linear system are discussed The convergence rate of accelerated overrelaxation (AOR) method can be enlarged by using the preconditioned method when the classical AOR method converges, and the preconditioned method is invalid when the classical iterative method does not converge. The results in corresponding references are improved and perfected.
Non-linear Systems and Educational Development in Europe.
Reilly, David H.
1999-01-01
European educational systems are under immense pressure to change, develop, improve, and satisfy many conflicting demands. Educational development and improvement in these countries is unlikely to progress in a neat, orderly, and linear fashion. Applying nonlinear (chaos) theory to development theory may aid understanding of educational…
Discontinuous Galerkin error estimation for linear symmetric hyperbolic systems
Adjerid, Slimane; Weinhart, Thomas
2009-01-01
In this manuscript we present an error analysis for the discontinuous Galerkin discretization error of multi-dimensional first-order linear symmetric hyperbolic systems of partial differential equations. We perform a local error analysis by writing the local error as a series and showing that its le
Linear energy-preserving integrators for Poisson systems
Cohen, David; Hairer, Ernst
2011-01-01
For Hamiltonian systems with non-canonical structure matrix a new class of numerical integrators is proposed. The methods exactly preserve energy, are invariant with respect to linear transformations, and have arbitrarily high order. Those of optimal order also preserve quadratic Casimir functions. The discussion of the order is based on an interpretation as partitioned Runge-Kutta method with infinitely many stages.
A Robin Problem for Quasi-linear System
Institute of Scientific and Technical Information of China (English)
0UYANGCheng
2004-01-01
In this paper, a Robin problem for quasi-linear system is considered. Under the appropriate assumptions, the existence of solution for the problem is proved and the asymptotic behavior of the solution is studied using the theory of differential inequalities.
Structured Control of Affine Linear Parameter Varying Systems
DEFF Research Database (Denmark)
Adegas, Fabiano Daher; Stoustrup, Jakob
2011-01-01
This paper presents a new procedure to design structured controllers for discrete-time afﬁne linear parametervarying systems (A LPV). The class of control structures includes decentralized of any order, ﬁxed order output feedback, simultaneous plant-control design, among others. A parametervarying...
The IBM RISC System/6000 and linear algebra operations
Energy Technology Data Exchange (ETDEWEB)
Dongarra, J.J. (Tennessee Univ., Knoxville, TN (USA). Dept. of Computer Science Oak Ridge National Lab., TN (USA)); Mays, P. (Numerical Algorithms Group Ltd., Oxford (UK)); Radicati di Brozolo, G. (IBM European Center for Scientific and Engineering Computing, Rome (Italy))
1991-01-01
This paper discusses the IBM RISC System/6000 workstation and a set of experiments with blocked algorithms commonly used in solving problems in numerical linear algebra. We describe the performance of these algorithms and discuss the techniques used in achieving high performance on such an architecture. 10 refs., 11 figs., 6 tabs.
ANALYSIS OF A MECHANICAL SOLVER FOR LINEAR SYSTEMS OF EQUATIONS
Institute of Scientific and Technical Information of China (English)
Luis Vázquez; Salvador Jiménez
2001-01-01
In this contribution we analyse some fundamental features of an iterative method to solve systems of linear equations, following the approach introduced in a previous work[1].Such questions range from optimal parameters and initial conditions to comparison with other methods. An interesting result is that a priori we can give an estimation of the number of iterations to get a given accuracy.
Identifying digital records in business systems: the definition of a ...
African Journals Online (AJOL)
Julia Kastenhofer
This issue certainly needs to be addressed. But the problem of ... the concept and definition of a record in the breadth they deserve. ... for digital records management in fourteen ..... Figure 2: System analysis components. The focus is ... question, though that is a side product, but ... on the system lifecycle as a whole could.
Controllability, observability, realizability, and stability of dynamic linear systems
Directory of Open Access Journals (Sweden)
John M. Davis
2009-03-01
Full Text Available We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time scales. The approach here is based on generalized Laplace transform methods (e.g. shifts and convolution from the recent work [13]. We study controllability in terms of the controllability Gramian and various rank conditions (including Kalman's in both the time invariant and time varying settings and compare the results. We explore observability in terms of both Gramian and rank conditions and establish related realizability results. We conclude by applying this systems theory to connect exponential and BIBO stability problems in this general setting. Numerous examples are included to show the utility of these results.
Controllability, Observability, Reachability, and Stability of Dynamic Linear Systems
Jackson, Billy J; Gravagne, Ian A; Marks, Robert J
2009-01-01
We develop a linear systems theory that coincides with the existing theories for continuous and discrete dynamical systems, but that also extends to linear systems defined on nonuniform time domains. The approach here is based on generalized Laplace transform methods (e.g. shifts and convolution) from our recent work \\cite{DaGrJaMaRa}. We study controllability in terms of the controllability Gramian and various rank conditions (including Kalman's) in both the time invariant and time varying settings and compare the results. We also explore observability in terms of both Gramian and rank conditions as well as realizability results. We conclude by applying this systems theory to connect exponential and BIBO stability problems in this general setting. Numerous examples are included to show the utility of these results.
Comparative index and Sturmian theory for linear Hamiltonian systems
Šepitka, Peter; Šimon Hilscher, Roman
2017-01-01
The comparative index was introduced by J. Elyseeva (2007) as an efficient tool in matrix analysis, which has fundamental applications in the discrete oscillation theory. In this paper we implement the comparative index into the theory of continuous time linear Hamiltonian systems, study its properties, and apply it to obtain new Sturmian separation theorems as well as new and optimal estimates for left and right proper focal points of conjoined bases of these systems on bounded intervals. We derive our results for general possibly abnormal (or uncontrollable) linear Hamiltonian systems. The results turn out to be new even in the case of completely controllable systems. We also provide several examples, which illustrate our new theory.
Toutounji, Mohamad
2004-08-01
Optical linear response function of linearly and quadratically coupled mixed quantum-classical condensed phase systems is derived. The linear response function is derived using Kapral's formalism of statistical mechanics in mixed quantum-classical systems. Our mixed quantum-classical linear dipole moment correlation function J(t) is compared with the full quantum J(t) [Y. J. Yan and S. Mukamel, J. Chem. Phys. 85, 5908 (1986)] in the high temperature limit. Model calculations and discussion of our results are presented. Various formulas of Franck-Condon factors for both linear and quadratic coupling are discussed. (c) 2004 American Institute of Physics.
Solar dynamic power system definition study
Wallin, Wayne E.; Friefeld, Jerry M.
1988-01-01
The solar dynamic power system design and analysis study compared Brayton, alkali-metal Rankine, and free-piston Stirling cycles with silicon planar and GaAs concentrator photovoltaic power systems for application to missions beyond the Phase 2 Space Station level of technology for all power systems. Conceptual designs for Brayton and Stirling power systems were developed for 35 kWe and 7 kWe power levels. All power systems were designed for 7-year end-of-life conditions in low Earth orbit. LiF was selected for thermal energy storage for the solar dynamic systems. Results indicate that the Stirling cycle systems have the highest performance (lowest weight and area) followed by the Brayton cycle, with photovoltaic systems considerably lower in performance. For example, based on the performance assumptions used, the planar silicon power system weight was 55 to 75 percent higher than for the Stirling system. A technology program was developed to address areas wherein significant performance improvements could be realized relative to the current state-of-the-art as represented by Space Station. In addition, a preliminary evaluation of hardenability potential found that solar dynamic systems can be hardened beyond the hardness inherent in the conceptual designs of this study.
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.
Design and performance of the Stanford Linear Collider Control System
Energy Technology Data Exchange (ETDEWEB)
Melen, R.E.
1984-10-01
The success of the Stanford Linear Collider (SLC) will be dependent upon the implementation of a very large advanced computer-based instrumentation and control system. This paper describes the architectural design of this system as well as a critique of its performance. This critique is based on experience obtained from its use in the control and monitoring of 1/3 of the SLAC linac and in support of an expensive experimental machine physics experimental program. 11 references, 3 figures.
A representation theorem for linear discrete-space systems
Directory of Open Access Journals (Sweden)
Irwin W. Sandberg
1998-01-01
Full Text Available The cornerstone of the theory of discrete-time single-input single-output linear systems is the idea that every such system has an input–output map H that can be represented by a convolution or the familiar generalization of a convolution. This thinking involves an oversight which is corrected in this note by adding an additional term to the representation.
Linear Optimization of Frequency Spectrum Assignments Across System
2016-03-01
Instead of separate transmit and receive apertures for each of the multiple radar , communications, and electronic warfare systems, a few pairs of AMRF-C... OPTIMIZATION OF FREQUENCY SPECTRUM ASSIGNMENTS ACROSS SYSTEMS by Steven J. Fischbach March 2016 Thesis Advisor: Jeffrey Hyink Thesis Co-Advisor...March 2016 3. REPORT TYPE AND DATES COVERED Master’s thesis 4. TITLE AND SUBTITLE LINEAR OPTIMIZATION OF FREQUENCY SPECTRUM ASSIGNMENTS ACROSS
H∞ controller synthesis of piecewise discrete time linear systems
Institute of Scientific and Technical Information of China (English)
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.
Stabilization of multiple independent linear systems with control networks
Institute of Scientific and Technical Information of China (English)
Zhenfu BI; Fusheng WANG
2004-01-01
The problem of stabilizing multiple independent linear systems sharing one common network cable is presented and solved.Both the quantization and time sequencing are studied in the field of control over networks by providing the formulated stabilizing sufficient condition which illustrates the relationship between the system instability,quantization and time sequencing,and the data rate is also presented in terms of the quantization and time sequencing. A numerical example is given to illustrate the result.
Geometry of the Limit Sets of Linear Switched Systems
Balde, Moussa; Jouan, Philippe
2011-01-01
International audience; The paper is concerned with asymptotic stability properties of linear switched systems. Under the hypothesis that all the subsystems share a non strict quadratic Lyapunov function, we provide a large class of switching signals for which a large class of switched systems are asymptotically stable. For this purpose we define what we call non chaotic inputs, which generalize the different notions of inputs with dwell time. Next we turn our attention to the behaviour for p...
State Predictive Model Following Control System for Linear Time Delays
Institute of Scientific and Technical Information of China (English)
Da-Zhong Wang; Shu-Jing Wu; Shigenori Okubo
2009-01-01
In this paper, we propose a new state predictive model following control system (MFCS). The considered system has linear time delays. With the MFCS method, we obtain a simple input control law. The bounded property of the internal states for the control is given and the utility of this control design is guaranteed. Finally, an example is given to illustrate the effectiveness of the proposed method.
Gradient estimates for parabolic and elliptic systems from linear laminates
Dong, Hongjie
2012-01-01
We establish several gradient estimates for second-order divergence type parabolic and elliptic systems. The coefficients and data are assumed to be H\\"older or Dini continuous in the time variable and all but one spatial variables. This type of systems arises from the problems of linearly elastic laminates and composite materials. For the proof, we use Campanato's approach in a novel way. Non-divergence type equations under a similar condition are also discussed.
Solving complex-valued linear systems via equivalent real formulations
Energy Technology Data Exchange (ETDEWEB)
DAY,DAVID M.; HEROUX,MICHAEL A.
2000-05-22
Most algorithms used in preconditioned iterative methods are generally applicable to complex valued linear systems, with real valued linear systems simply being a special case. However, most iterative solver packages available today focus exclusively on real valued systems, or deal with complex valued systems as an afterthought. One obvious approach to addressing this problem is to recast the complex problem into one of a several equivalent real forms and then use a real valued solver to solve the related system. However, well-known theoretical results showing unfavorable spectral properties for the equivalent real forms have diminished enthusiasm for this approach. At the same time, experience has shown that there are situations where using an equivalent real form can be very effective. In this paper, the authors explore this approach, giving both theoretical and experimental evidence that an equivalent real form can be useful for a number of practical situations. Furthermore, they show that by making good use of some of the advance features of modem solver packages, they can easily generate equivalent real form preconditioners that are computationally efficient and mathematically identical to their complex counterparts. Using their techniques, they are able to solve very ill-conditioned complex valued linear systems for a variety of large scale applications. However, more importantly, they shed more light on the effectiveness of equivalent real forms and more clearly delineate how and when they should be used.
An Integrated Expert System for Linear Scheduling Heavy Earthmoving Operations
Directory of Open Access Journals (Sweden)
Nizar Markiz
2016-01-01
Full Text Available Heavy earthmoving operations are repetitive in nature and vulnerable to time-related restraints and uncertainties. Therefore, at the conceptual stage, scheduling these operations can take a linear form, known as linear schedule or line of balance (LOB. In such type of work, generating a preliminary line of balance for variable sequencing of activities is crucial. In this paper, an integrated expert system for determining preliminary linear schedules for heavy earthmoving operations at the conceptual stage is presented. The proposed system incorporates numerous factors that influence the analysis of earthmoving operations, which include geological and topographical parameters used to determine productivity rates at the conceptual stage. Also, the proposed system is capable of automatically generating a line of balance based on a stochastic scheduling technique via the metaheuristic simulated annealing intelligent approach to incorporate randomness and uncertainties in performing the associated activities. A parametric analysis is conducted in order to quantify the system’s degree of accuracy. An actual case project is then utilized to illustrate its numerical capabilities. Generating accurate linear schedules for heavy earthmoving operations at the conceptual design stage is anticipated to be of major significance to infrastructure project stakeholders, engineers, and construction managers by detecting schedule’s conflicts early in order to enhance overall operational logistics.
Should Pruning be a Pre-Processor of any Linear System?
Sen, Syamal K.; Ramakrishnan, Suja; Agarwal, Ravi P.; Shaykhian, Gholam Ali
2011-01-01
measure a quantity with an accuracy greater that 0.005% or, equivalently with a relative error less than 0.005%. Hence measurement error is unavoidable in a numerical linear system when the quantities are continuous (or even discrete with extremely large number). Assumptions, though not desirable, are usually made when we find the problem sufficiently difficult to be solved within the available means/tools/resources and hence distort the PP and the corresponding MM. The . error thus introduced in the system could (not always necessarily though) make the system somewhat inconsistent. If the inconsistency (contradiction) is too much then one should definitely not proceed to solve the system in terms of getting a least-squares solution or the minimum-norm least-squares solution. All these solutions will be invariably of no real-world use. If, on the other hand, inconsistency is reasonably low, i.e. the system is near-consistent or, equivalently, has near-linearly-dependent rows, then the foregoing solutions are useful. Pruning in such a near-consistent system should be performed based on the desired accuracy and on the definition of near-linear dependence. In this article, we discuss pruning over various kinds of linear systems and strongly suggest its use as a pre-processor or as a part of an algorithm. Ideally pruning should (i) be a part of the solution process (algorithm) of the system, (ii) reduce both computational error and complexity of the process, and (iii) take into account the numerical zero defined in the context. These are precisely what we achieve through our proposed O(mn2) algorithm presented in Matlab, that uses a subprogram of solving a single linear equation and that has embedded in it the pruning.
Identification and robust control of linear parameter-varying systems
Lee, Lawton Hubert
This dissertation deals with linear parameter-varying (LPV) systems: linear dynamic systems that depend on time-varying parameters. These systems appear in gain scheduling problems, and much recent research has been devoted to their prospective usefulness for systematic gain scheduling. We primarily focus on robust control of uncertain LPV systems and identification of LPV systems that are modelable as linear-fractional transformations (LFTs). Using parameter-dependent quadratic Lyapunov functions, linear matrix inequalities (LMIs), and scaled small-gain arguments, we define notions of stability and induced-{cal L}sb2 performance for uncertain LPV systems whose parameters and rates of parameter variation satisfy given bounds. The performance criterion involves integral quadratic constraints and implies naturally parameter-dependent induced-{cal L}sb2 norm bounds. We formulate and solve an {cal H}sb{infty}-like control problem for an LPV plant with measurable parameters and an "Output/State Feedback" structure: the feedback outputs include some noiselessly measured states. Necessary and sufficient solvability conditions reduce to LMIs that can be solved approximately using finite-dimensional convex programming. Reduced-order LPV controllers are constructed from the LMI solutions. A D-K iteration-like procedure provides robustness to structured, time-varying, parametric uncertainty. The design method is applied to a motivating example: flight control for the F-16 VISTA throughout its subsonic flight envelope. Parameter-dependent weights and {cal H}sb{infty} design principles describe the performance objectives. Closed-loop responses exhibited by nonlinear simulations indicate satisfactory flying qualities. Identification of linear-fractional LPV systems is treated using maximum-likelihood parameter estimation. Computing the gradient and Hessian of a maximum-likelihood cost function reduces to simulating one LPV filter per identified parameter. We use nonlinear
Towards a General Definition of Biometric Systems
Schatten, Markus; Cubrilo, Mirko
2009-01-01
A foundation for closing the gap between biometrics in the narrower and the broader perspective is presented trough a conceptualization of biometric systems in both perspectives. A clear distinction between verification, identification and classification systems is made as well as shown that there are additional classes of biometric systems. In the end a Unified Modeling Language model is developed showing the connections between the two perspectives.
LINEAR-DISPERSION DIVISION MULTIPLE-ACCESS FOR MIMO SYSTEMS
Institute of Scientific and Technical Information of China (English)
Deng Dan; Lv Xingzai; Zhu Jinkang
2008-01-01
Comprehensive study on novel Linear-Dispersion Division Multiple-Access (LDDMA) for multi-user uplink Multiple-Input Multiple-Output (MIMO) systems is proposed. In the new multi- plexing scheme, each user's information symbol is dispersed by a User-Specific Matrix (USM) both in space and time domain and linearly combined at base-station side. And a simple random search al- gorithm, based on capacity maximization criteria, is developed to generate a bank of USMs. Simulation results are presented to demonstrate the advantages of LDDMA. When the Bit Error Rate (BER) reaches 10, the performance gains are 3dB and 5dB, compared with Time-Division Linear Dispersion Codes (TD-LDC) and BLAST, respectively.
Vacuum systems of linear accelerators of the NICA injection complex
Kosachev, V. V.; Bazanov, A. M.; Butenko, A. V.; Galimov, A. R.; Nesterov, A. V.; Pivin, R. V.; Smirnov, A. V.
2016-12-01
The NICA project, which includes several accelerators of charged particles, is under construction in the Laboratory of High Energy Physics, Joint Institute for Nuclear Research (JINR), Dubna. Obtaining the required vacuum conditions is one of the key points in implementing the project, because reaching the required ion lifetime at all stages of particle acceleration is what determines the effective luminosity of the experiments in the long run. Currently, modernization of the vacuum system of the injection complex of the LU-20 linear accelerator of light ions, one of oldest accelerators in the JINR, is being carried out and the new HILAC linear accelerator for the acceleration of gold ions in the collider mode of the NICA complex is being installed. At the end parts of the linear accelerators, the residual gas pressure must be approximately 10-5 Pa, which is determined by the maximum amplitude of the RF electric field used for the acceleration of ions.
Classification system to describe workpieces definitions
Macconnell, W R
2013-01-01
A Classification System to Describe Workpieces provides information pertinent to the fundamental aspects and principles of coding. This book discusses the various applications of the classification system of coding.Organized into three chapters, this book begins with an overview of the requirements of a system of classification pertaining adequately and equally to design, production, and work planning. This text then examines the purpose of the classification system in production to determine the most suitable means of machining a component. Other chapters consider the optimal utilization of m
Non-linear HRV indices under autonomic nervous system blockade.
Bolea, Juan; Pueyo, Esther; Laguna, Pablo; Bailón, Raquel
2014-01-01
Heart rate variability (HRV) has been studied as a non-invasive technique to characterize the autonomic nervous system (ANS) regulation of the heart. Non-linear methods based on chaos theory have been used during the last decades as markers for risk stratification. However, interpretation of these nonlinear methods in terms of sympathetic and parasympathetic activity is not fully established. In this work we study linear and non-linear HRV indices during ANS blockades in order to assess their relation with sympathetic and parasympathetic activities. Power spectral content in low frequency (0.04-0.15 Hz) and high frequency (0.15-0.4 Hz) bands of HRV, as well as correlation dimension, sample and approximate entropies were computed in a database of subjects during single and dual ANS blockade with atropine and/or propranolol. Parasympathetic blockade caused a significant decrease in the low and high frequency power of HRV, as well as in correlation dimension and sample and approximate entropies. Sympathetic blockade caused a significant increase in approximate entropy. Sympathetic activation due to postural change from supine to standing caused a significant decrease in all the investigated non-linear indices and a significant increase in the normalized power in the low frequency band. The other investigated linear indices did not show significant changes. Results suggest that parasympathetic activity has a direct relation with sample and approximate entropies.
Linear Chromosome-generating System of Agrobacterium tumefaciens C58
Huang, Wai Mun; DaGloria, Jeanne; Fox, Heather; Ruan, Qiurong; Tillou, John; Shi, Ke; Aihara, Hideki; Aron, John; Casjens, Sherwood
2012-01-01
Agrobacterium tumefaciens C58, the pathogenic bacteria that causes crown gall disease in plants, harbors one circular and one linear chromosome and two circular plasmids. The telomeres of its unusual linear chromosome are covalently closed hairpins. The circular and linear chromosomes co-segregate and are stably maintained in the organism. We have determined the sequence of the two ends of the linear chromosome thus completing the previously published genome sequence of A. tumefaciens C58. We found that the telomeres carry nearly identical 25-bp sequences at the hairpin ends that are related by dyad symmetry. We further showed that its Atu2523 gene encodes a protelomerase (resolvase) and that the purified enzyme can generate the linear chromosomal closed hairpin ends in a sequence-specific manner. Agrobacterium protelomerase, whose presence is apparently limited to biovar 1 strains, acts via a cleavage-and-religation mechanism by making a pair of transient staggered nicks invariably at 6-bp spacing as the reaction intermediate. The enzyme can be significantly shortened at both the N and C termini and still maintain its enzymatic activity. Although the full-length enzyme can uniquely bind to its product telomeres, the N-terminal truncations cannot. The target site can also be shortened from the native 50-bp inverted repeat to 26 bp; thus, the Agrobacterium hairpin-generating system represents the most compact activity of all hairpin linear chromosome- and plasmid-generating systems to date. The biochemical analyses of the protelomerase reactions further revealed that the tip of the hairpin telomere may be unusually polymorphically capable of accommodating any nucleotide. PMID:22582388
Applications of equivalent linearization approaches to nonlinear piping systems
Energy Technology Data Exchange (ETDEWEB)
Park, Y.; Hofmayer, C. [Brookhaven National Lab., Upton, NY (United States); Chokshi, N. [Nuclear Regulatory Commission, Washington, DC (United States)
1997-04-01
The piping systems in nuclear power plants, even with conventional snubber supports, are highly complex nonlinear structures under severe earthquake loadings mainly due to various mechanical gaps in support structures. Some type of nonlinear analysis is necessary to accurately predict the piping responses under earthquake loadings. The application of equivalent linearization approaches (ELA) to seismic analyses of nonlinear piping systems is presented. Two types of ELA`s are studied; i.e., one based on the response spectrum method and the other based on the linear random vibration theory. The test results of main steam and feedwater piping systems supported by snubbers and energy absorbers are used to evaluate the numerical accuracy and limitations.
Cherniha, Roman
2010-01-01
New definitions of $Q$-conditional symmetry for systems of PDEs are presented, which generalize the standard notation of non-classical (conditional) symmetry. It is shown that different types of $Q$-conditional symmetry of a system generate a hierarchy of conditional symmetry operators. A class of two-component nonlinear RD systems is examined to demonstrate applicability of the definitions proposed and it is shown when different definitions of $Q$-conditional symmetry lead to the same operators.
Linear and nonlinear dynamic systems in financial time series prediction
Directory of Open Access Journals (Sweden)
Salim Lahmiri
2012-10-01
Full Text Available Autoregressive moving average (ARMA process and dynamic neural networks namely the nonlinear autoregressive moving average with exogenous inputs (NARX are compared by evaluating their ability to predict financial time series; for instance the S&P500 returns. Two classes of ARMA are considered. The first one is the standard ARMA model which is a linear static system. The second one uses Kalman filter (KF to estimate and predict ARMA coefficients. This model is a linear dynamic system. The forecasting ability of each system is evaluated by means of mean absolute error (MAE and mean absolute deviation (MAD statistics. Simulation results indicate that the ARMA-KF system performs better than the standard ARMA alone. Thus, introducing dynamics into the ARMA process improves the forecasting accuracy. In addition, the ARMA-KF outperformed the NARX. This result may suggest that the linear component found in the S&P500 return series is more dominant than the nonlinear part. In sum, we conclude that introducing dynamics into the ARMA process provides an effective system for S&P500 time series prediction.
A parallel solver for huge dense linear systems
Badia, J. M.; Movilla, J. L.; Climente, J. I.; Castillo, M.; Marqués, M.; Mayo, R.; Quintana-Ortí, E. S.; Planelles, J.
2011-11-01
HDSS (Huge Dense Linear System Solver) is a Fortran Application Programming Interface (API) to facilitate the parallel solution of very large dense systems to scientists and engineers. The API makes use of parallelism to yield an efficient solution of the systems on a wide range of parallel platforms, from clusters of processors to massively parallel multiprocessors. It exploits out-of-core strategies to leverage the secondary memory in order to solve huge linear systems O(100.000). The API is based on the parallel linear algebra library PLAPACK, and on its Out-Of-Core (OOC) extension POOCLAPACK. Both PLAPACK and POOCLAPACK use the Message Passing Interface (MPI) as the communication layer and BLAS to perform the local matrix operations. The API provides a friendly interface to the users, hiding almost all the technical aspects related to the parallel execution of the code and the use of the secondary memory to solve the systems. In particular, the API can automatically select the best way to store and solve the systems, depending of the dimension of the system, the number of processes and the main memory of the platform. Experimental results on several parallel platforms report high performance, reaching more than 1 TFLOP with 64 cores to solve a system with more than 200 000 equations and more than 10 000 right-hand side vectors. New version program summaryProgram title: Huge Dense System Solver (HDSS) Catalogue identifier: AEHU_v1_1 Program summary URL:http://cpc.cs.qub.ac.uk/summaries/AEHU_v1_1.html Program obtainable from: CPC Program Library, Queen's University, Belfast, N. Ireland Licensing provisions: Standard CPC licence, http://cpc.cs.qub.ac.uk/licence/licence.html No. of lines in distributed program, including test data, etc.: 87 062 No. of bytes in distributed program, including test data, etc.: 1 069 110 Distribution format: tar.gz Programming language: Fortran90, C Computer: Parallel architectures: multiprocessors, computer clusters Operating system
A New Approach for Solving Fully Fuzzy Linear Systems
Directory of Open Access Journals (Sweden)
Amit Kumar
2011-01-01
Full Text Available Several authors have proposed different methods to find the solution of fully fuzzy linear systems (FFLSs that is, fuzzy linear system with fuzzy coefficients involving fuzzy variables. But all the existing methods are based on the assumption that all the fuzzy coefficients and the fuzzy variables are nonnegative fuzzy numbers. In this paper a new method is proposed to solve an FFLS with arbitrary coefficients and arbitrary solution vector, that is, there is no restriction on the elements that have been used in the FFLS. The primary objective of this paper is thus to introduce the concept and a computational method for solving FFLS with no non negative constraint on the parameters. The method incorporates the principles of linear programming in solving an FFLS with arbitrary coefficients and is not only easier to understand but also widens the scope of fuzzy linear equations in scientific applications. To show the advantages of the proposed method over existing methods we solve three FFLSs.
Linear systems analysis of the fMRI signal.
Boynton, Geoffrey M; Engel, Stephen A; Heeger, David J
2012-08-15
In 1995 when we began our investigations of the human visual system using fMRI, little was known about the temporal properties of the fMRI signal. Before we felt comfortable making quantitative estimates of neuronal responses with this new technique, we decided to first conduct a basic study of how the time-course of the fMRI response varied with stimulus timing and strength. The results ended up showing strong evidence that to a first approximation the hemodynamic transformation was linear in time. This was both important and remarkable: important because nearly all fMRI data analysis techniques assume or require linearity, and remarkable because the physiological basis of the hemodynamic transformation is so complex that we still have a far from complete understanding of it. In this paper, we provide highlights of the results of our original paper supporting the linear transform hypothesis. A reanalysis of the original data provides some interesting new insights into the published results. We also provide a detailed appendix describing of the properties and predictions of a linear system in time in the context of the transformation between neuronal responses and the BOLD signal.
Algebraic Theory of Linear Time-Varying Systems and Linear Infinite-Dimensional Systems.
1982-11-01
time-varying analytic systems," IEEE Transactions on Automatic Control , Vol. AC-24, pp. 866-878, December 1979. 6. E. W. Kamen, "A note on the...stability of delay differential equations," IEEE Transactions on Automatic Control , Vol. AC-25, pp. 983-984, October 19=0. 9. W. L. Green and E. W
An extended GS method for dense linear systems
Niki, Hiroshi; Kohno, Toshiyuki; Abe, Kuniyoshi
2009-09-01
Davey and Rosindale [K. Davey, I. Rosindale, An iterative solution scheme for systems of boundary element equations, Internat. J. Numer. Methods Engrg. 37 (1994) 1399-1411] derived the GSOR method, which uses an upper triangular matrix [Omega] in order to solve dense linear systems. By applying functional analysis, the authors presented an expression for the optimum [Omega]. Moreover, Davey and Bounds [K. Davey, S. Bounds, A generalized SOR method for dense linear systems of boundary element equations, SIAM J. Comput. 19 (1998) 953-967] also introduced further interesting results. In this note, we employ a matrix analysis approach to investigate these schemes, and derive theorems that compare these schemes with existing preconditioners for dense linear systems. We show that the convergence rate of the Gauss-Seidel method with preconditioner PG is superior to that of the GSOR method. Moreover, we define some splittings associated with the iterative schemes. Some numerical examples are reported to confirm the theoretical analysis. We show that the EGS method with preconditioner produces an extremely small spectral radius in comparison with the other schemes considered.
Neural Network for Combining Linear and Non-Linear Modelling of Dynamic Systems
DEFF Research Database (Denmark)
Madsen, Per Printz
1994-01-01
The purpose of this paper is to develop a method to combine linear models with MLP networks. In other words to find a method to make a non-linear and multivariable model that performs at least as good as a linear model, when the training data lacks information.......The purpose of this paper is to develop a method to combine linear models with MLP networks. In other words to find a method to make a non-linear and multivariable model that performs at least as good as a linear model, when the training data lacks information....
Non-linear controllers in ship tracking control system
Institute of Scientific and Technical Information of China (English)
LESZEK M
2005-01-01
The cascade systems which stabilize the transverse deviation of the ship in relation to the set path is presented. The ship's path is determined as a broken line with specified coordinates of way points. Three controllers are used in the system. The main primary controller is the trajectory controller. The set value of heading for the course control system or angular velocity for the turning control system is generated. The course control system is used on the straight line of the set trajectory while the turning controller is used during a change of the set trajectory segment. The characteristics of the non-linear controllers are selected in such a way that the properties of the control system with the rate of turn controller are modelled by the first-order inertia, while the system with the course keeping controller is modelled by a second-order linear term. The presented control system is tested in computer simulation. Some results of simulation tests are presented and discussed.
A quasi-linear parabolic system of chemotaxis
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available We consider a quasi-linear parabolic system with respect to unknown functions u and v on a bounded domain of n -dimensional Euclidean space. We assume that the diffusion coefficient of u is a positive smooth function A ( u , and that the diffusion coefficient of v is a positive constant. If A ( u is a positive constant, the system is referred to as so-called Keller-Segel system. In the case where the domain is a bounded domain of two-dimensional Euclidean space, it is shown that some solutions to Keller-Segel system blow up in finite time. In three and more dimensional cases, it is shown that solutions to so-called Nagai system blow up in finite time. Nagai system is introduced by Nagai. The diffusion coefficients of Nagai system are positive constants. In this paper, we describe that solutions to the quasi-linear parabolic system exist globally in time, if the positive function A ( u rapidly increases with respect to u .
Steady-state decoupling and design of linear multivariable systems
Thaler, G. J.
1974-01-01
A constructive criterion for decoupling the steady states of a linear time-invariant multivariable system is presented. This criterion consists of a set of inequalities which, when satisfied, will cause the steady states of a system to be decoupled. Stability analysis and a new design technique for such systems are given. A new and simple connection between single-loop and multivariable cases is found. These results are then applied to the compensation design for NASA STOL C-8A aircraft. Both steady-state decoupling and stability are justified through computer simulations.
Asymptotic control theory for a system of linear oscillators
Fedorov, Aleksey; Ovseevich, Alexander
2013-01-01
We present an asymptotic control theory for a system of an arbitrary number of linear oscillators under a common bounded control. We suggest a design method of a feedback control for this system. By using the DiPerna-Lions theory of singular ODEs, we prove that the suggested control law correctly defines the motion of the system. The obtained control is asymptotically optimal: the ratio of the motion time to zero under this control to the minimum one is close to 1 if the initial energy of the...
Model-Checking Linear-Time Properties of Quantum Systems
Ying, Mingsheng; Yu, Nengkun; Feng, Yuan
2011-01-01
We define a formal framework for reasoning about linear-time properties of quantum systems in which quantum automata are employed in the modeling of systems and certain closed subspaces of state (Hilbert) spaces are used as the atomic propositions about the behavior of systems. We provide an algorithm for verifying invariants of quantum automata. Then automata-based model-checking technique is generalized for the verification of safety properties recognizable by reversible automata and omega-properties recognizable by reversible Buechi automata.
Optimal policies for identification of stochastic linear systems
Lopez-Toledo, A. A.; Athans, M.
1975-01-01
The problem of designing closed-loop policies for identification of multiinput-multioutput linear discrete-time systems with random time-varying parameters is considered in this paper using a Bayesian approach. A sensitivity index gives a measure of performance for the closed-loop laws. The computation of the optimal laws is shown to be nontrivial, an exercise in stochastic control, but open-loop, affine, and open-loop feedback optimal inputs are shown to yield tractable problems. Numerical examples are given. For time-invariant systems, the criterion considered is shown to be related to the trace of the information matrix associated with the system.
Studies for an alternative LHC non-linear collimation system
Lari, L; Boccone, V; Cerutti, F; Versaci, R; Vlachoudis, V; Mereghetti, A; Faus-Golfe, A; Resta-Lopez, J
2012-01-01
A LHC non-linear betatron cleaning collimation system would allow larger gap for the mechanical jaws, reducing as a consequence the collimator-induced impedance, which may limit the LHC beam intensity. In this paper, the performance of the proposed system is analyzed in terms of beam losses distribution around the LHC ring and cleaning efficiency in stable physics condition at 7TeV for Beam1. Moreover, the energy deposition distribution on the machine elements is compared to the present LHC Betatron cleaning collimation system in the Point 7 Insertion Region (IR).
Polynomial system solving for decoding linear codes and algebraic cryptanalysis
2009-01-01
This thesis is devoted to applying symbolic methods to the problems of decoding linear codes and of algebraic cryptanalysis. The paradigm we employ here is as follows. We reformulate the initial problem in terms of systems of polynomial equations over a finite field. The solution(s) of such systems should yield a way to solve the initial problem. Our main tools for handling polynomials and polynomial systems in such a paradigm is the technique of Gröbner bases and normal form reductions. The ...
Geometry of the Limit Sets of Linear Switched Systems
Balde, Moussa
2010-01-01
The paper is concerned with asymptotic stability properties of linear switched systems. Under the hypothesis that all the subsystems share a non strict quadratic Lyapunov function, we provide a large class of switching signals for which a large class of switched systems are asymptotically stable. For this purpose we define what we call non chaotic inputs, which generalize the different notions of inputs with dwell time. Next we turn our attention to the behaviour for possibly chaotic inputs. To finish we give a sufficient condition for a system composed of a pair of Hurwitz matrices to be asymptotically stable for all inputs.
Kalman filtering for time-delayed linear systems
Institute of Scientific and Technical Information of China (English)
LU Xiao; WANG Wei
2006-01-01
This paper is to study the linear minimum variance estimation for discrete- time systems. A simple approach to the problem is presented by developing re-organized innovation analysis for the systems with instantaneous and double time-delayed measurements. It is shown that the derived estimator involves solving three different standard Kalman filtering with the same dimension as the original system. The obtained results form the basis for solving some complicated problems such as H∞ fixed-lag smoothing, preview control, H∞ filtering and control with time delays.
Sandia photovoltaic systems definition and application experiment projects
Energy Technology Data Exchange (ETDEWEB)
Jones, G.
1983-04-01
A compilation is given of the abstracts and visual material used in presentation at the Fourth Photovoltaic Systems Definition and Applications Projects Integration Meeting held at the Marriott Hotel, April 12-14, 1983, in Albuquerque, New Mexico. The meeting provided a forum for detailed analyses on recently completed and current activities. These activities include systems research, balance-of-system technology development, residential experimentation, and evaluation of intermediate-sized applications.
Optimal approximation of linear systems by artificial immune response
Institute of Scientific and Technical Information of China (English)
无
2006-01-01
This paper puts forward a novel artificial immune response algorithm for optimal approximation of linear systems. A quaternion model of artificial immune response is proposed for engineering computing. The model abstracts four elements, namely, antigen, antibody, reaction rules among antibodies, and driving algorithm describing how the rules are applied to antibodies, to simulate the process of immune response. Some reaction rules including clonal selection rules, immunological memory rules and immune regulation rules are introduced. Using the theorem of Markov chain, it is proofed that the new model is convergent. The experimental study on the optimal approximation of a stable linear system and an unstable one show that the approximate models searched by the new model have better performance indices than those obtained by some existing algorithms including the differential evolution algorithm and the multi-agent genetic algorithm.
Nonautonomous linear Hamiltonian systems oscillation, spectral theory and control
Johnson, Russell; Novo, Sylvia; Núñez, Carmen; Fabbri, Roberta
2016-01-01
This monograph contains an in-depth analysis of the dynamics given by a linear Hamiltonian system of general dimension with nonautonomous bounded and uniformly continuous coefficients, without other initial assumptions on time-recurrence. Particular attention is given to the oscillation properties of the solutions as well as to a spectral theory appropriate for such systems. The book contains extensions of results which are well known when the coefficients are autonomous or periodic, as well as in the nonautonomous two-dimensional case. However, a substantial part of the theory presented here is new even in those much simpler situations. The authors make systematic use of basic facts concerning Lagrange planes and symplectic matrices, and apply some fundamental methods of topological dynamics and ergodic theory. Among the tools used in the analysis, which include Lyapunov exponents, Weyl matrices, exponential dichotomy, and weak disconjugacy, a fundamental role is played by the rotation number for linear Hami...
Novel sucker rod pumping system based on linear motor technology
Institute of Scientific and Technical Information of China (English)
李立毅; 李立清; 吴红星; 胡余生; 邹积岩
2004-01-01
Obtaining petroleum at the cost of electrical energy is a common problem in almost all oil fields, and it is mainly caused by low duty radio of induction motor used in beam pumping units. Traditional beam-pumping units have many intrinsic disadvantages such as low efficiency, complex transmission devices, poor flexibility,tremendous volume and weight in long stroke, etc. Therefore, a novel direct driven linear electromagnetic pumping unit (EMPU) has been developed by combining oil extraction technology with linear motor technology. The thrust of EMPU matches the changing of suspension center load to improve the system efficiency and cut down the consumption of energy. Based on previous experience, a small-scale prototype was developed and a simulation was conducted with it. Both theoretical analyses and experimental study showed that the problems exiting in beam pumping units can be solved with EMPU system, and this is a new method which can be used to solve high energy waste in oil fields.
SSNN toolbox for non-linear system identification
Luzar, Marcel; Czajkowski, Andrzej
2015-11-01
The aim of this paper is to develop and design a State Space Neural Network toolbox for a non-linear system identification with an artificial state-space neural networks, which can be used in a model-based robust fault diagnosis and control. Such toolbox is implemented in the MATLAB environment and it uses some of its predefined functions. It is designed in the way that any non-linear multi-input multi-output system is identified and represented in the classical state-space form. The novelty of the proposed approach is that the final result of the identification process is the state, input and output matrices, not only the neural network parameters. Moreover, the toolbox is equipped with the graphical user interface, which makes it useful for the users not familiar with the neural networks theory.
Parametric Analysis of Fiber Non-Linearity in Optical systems
Directory of Open Access Journals (Sweden)
Abhishek Anand
2013-06-01
Full Text Available With the advent of technology Wavelength Division Multiplexing (WDM is always an area of interest in the field of optical communication. When combined with Erbium Doped Fiber Amplifier (EDFA, it provides high data transmission rate and low attenuation. But due to fiber non-linearity such as Self Phase Modulation (SPM and Cross Phase Modulation (XPM the system performance has degraded. This non-linearity depends on different parameters of an optical system such as channel spacing, power of the channel and length of the fiber section. The degradation can be seen in terms of phase deviation and Bit Error Rate (BER performance. Even after dispersion compensation at the fiber end, residual pulse broadening still exists due to cross talk penalty.
Feedback Linearization Controller for a Wind Energy Power System
Directory of Open Access Journals (Sweden)
Muthana Alrifai
2016-09-01
Full Text Available This paper deals with the control of a doubly-fed induction generator (DFIG-based variable speed wind turbine power system. A system of eight ordinary differential equations is used to model the wind energy conversion system. The generator has a wound rotor type with back-to-back three-phase power converter bridges between its rotor and the grid; it is modeled using the direct-quadrature rotating reference frame with aligned stator flux. An input-state feedback linearization controller is proposed for the wind energy power system. The controller guarantees that the states of the system track the desired states. Simulation results are presented to validate the proposed control scheme. Moreover, further simulation results are shown to investigate the robustness of the proposed control scheme to changes in some of the parameters of the system.
A Note on Solutions for Asymptotically Linear Elliptic Systems
Institute of Scientific and Technical Information of China (English)
2008-01-01
In this paper, we axe concerned with the elliptic system of -△u+V(x)u=g(=x,v),x=∈RN,-△v+V(x)v=f(x, u), x∈RN, where V(x) is a continuous potential well, f, g are continuous and asymptotically linear as t→∞. The existence of a positive solution and ground state solution are established via variational methods.
CHEBYSHEV ACCELERATION TECHNIQUE FOR SOLVING FUZZY LINEAR SYSTEM
Directory of Open Access Journals (Sweden)
S.H. Nasseri
2009-10-01
Full Text Available In this paper, Chebyshev acceleration technique is used to solve the fuzzy linear system (FLS. This method is discussed in details and followed by summary of some other acceleration techniques. Moreover, we show that in some situations that the methods such as Jacobi, Gauss-Sidel, SOR and conjugate gradient is divergent, our proposed method is applicable and the acquired results are illustrated by some numerical examples.
Null controllability for linear parabolic cascade systems with interior degeneracy
Directory of Open Access Journals (Sweden)
Idriss Boutaayamou
2016-11-01
Full Text Available We study the null controllability problem for linear degenerate parabolic systems with one control force through Carleman estimates for the associated adjoint problem. The novelty of this article is that for the first time it is considered a problem with an interior degeneracy and a control set that only requires to contain an interval lying on one side of the degeneracy points. The obtained result improves and complements a number of earlier works. As a consequence, observability inequalities are established.
New Interval Oscillation Criteria for Certain Linear Hamiltonian Systems
Directory of Open Access Journals (Sweden)
Jing Shao
2013-01-01
Full Text Available Using a generalized Riccati transformation and the general integral means technique, some new interval oscillation criteria for the linear matrix Hamiltonian system U'=(A(t-λ(tIU+B(tV, V'=C(tU+(μ(tI-A*(tV, t≥t0 are obtained. These results generalize and improve the oscillation criteria due to Zheng (2008. An example is given to dwell upon the importance of our results.
Linear Quantum Systems: Non-Classical States and Robust Stability
2016-06-29
terms of transfer functions which describe the memory behaviour for arbitrary inputs and operating regimes. This allows us to go beyond previous works...characterize the condition required on the pulse shape achieving the perfect state transfer from the light field to the memory subsystem. The key idea to...illustrate the efficacy of this idea . Ian R. Petersen, Notes on coherent feedback control for linear quantum systems. In Australian Control
AZTEC: A parallel iterative package for the solving linear systems
Energy Technology Data Exchange (ETDEWEB)
Hutchinson, S.A.; Shadid, J.N.; Tuminaro, R.S. [Sandia National Labs., Albuquerque, NM (United States)
1996-12-31
We describe a parallel linear system package, AZTEC. The package incorporates a number of parallel iterative methods (e.g. GMRES, biCGSTAB, CGS, TFQMR) and preconditioners (e.g. Jacobi, Gauss-Seidel, polynomial, domain decomposition with LU or ILU within subdomains). Additionally, AZTEC allows for the reuse of previous preconditioning factorizations within Newton schemes for nonlinear methods. Currently, a number of different users are using this package to solve a variety of PDE applications.
Total Dose Effects on Error Rates in Linear Bipolar Systems
Buchner, Stephen; McMorrow, Dale; Bernard, Muriel; Roche, Nicholas; Dusseau, Laurent
2007-01-01
The shapes of single event transients in linear bipolar circuits are distorted by exposure to total ionizing dose radiation. Some transients become broader and others become narrower. Such distortions may affect SET system error rates in a radiation environment. If the transients are broadened by TID, the error rate could increase during the course of a mission, a possibility that has implications for hardness assurance.
Informatics with Systems Science and Cybernetics--Concepts and Definitions.
Samuelson, Kjell
This dictionary defines information science, computer science, systems theory, and cybernetic terms in English and provides the Swedish translation of each term. An index of Swedish terms refers the user to the page where the English equivalent and definition appear. Most of the 38 references listed are in English. (RAA)
A Petri Net Definition of a System Description Language
DEFF Research Database (Denmark)
Jensen, Kurt; Kyng, Morten; Madsen, Ole Lehrmann
1979-01-01
This paper introduces a language for the description of systems with concurrency, and presents a formal definition of its semantics. The language is based on Delta and the semantic model is an extension of Petri nets with a data part and with expressions attached to transitions and to places....
Informatics with Systems Science and Cybernetics--Concepts and Definitions.
Samuelson, Kjell
This dictionary defines information science, computer science, systems theory, and cybernetic terms in English and provides the Swedish translation of each term. An index of Swedish terms refers the user to the page where the English equivalent and definition appear. Most of the 38 references listed are in English. (RAA)
State feedback control of switched linear systems: An LMI approach
Montagner, V. F.; Leite, V. J. S.; Oliveira, R. C. L. F.; Peres, P. L. D.
2006-10-01
This paper addresses the problem of state feedback control of continuous-time switched linear systems with arbitrary switching rules. A quadratic Lyapunov function with a common matrix is used to derive a stabilizing switching control strategy that guarantees: (i) the assignment of all the eigenvalues of each linear subsystem inside a chosen circle in the left-hand half of the complex plane; (ii) a minimum disturbance attenuation level for the closed-loop switched system. The proposed design conditions are given in terms of linear matrix inequalities that encompass previous results based on quadratic stability conditions with fixed control gains. Although the quadratic stability based on a fixed Lyapunov matrix has been widely used in robust control design, the use of this condition to provide a convex design method for switching feedback gains has not been fully investigated. Numerical examples show that the switching control strategy can cope with more stringent design specifications than the fixed gain strategy, being useful to improve the performance of this class of systems.
Method of Conjugate Radii for Solving Linear and Nonlinear Systems
Nachtsheim, Philip R.
1999-01-01
This paper describes a method to solve a system of N linear equations in N steps. A quadratic form is developed involving the sum of the squares of the residuals of the equations. Equating the quadratic form to a constant yields a surface which is an ellipsoid. For different constants, a family of similar ellipsoids can be generated. Starting at an arbitrary point an orthogonal basis is constructed and the center of the family of similar ellipsoids is found in this basis by a sequence of projections. The coordinates of the center in this basis are the solution of linear system of equations. A quadratic form in N variables requires N projections. That is, the current method is an exact method. It is shown that the sequence of projections is equivalent to a special case of the Gram-Schmidt orthogonalization process. The current method enjoys an advantage not shared by the classic Method of Conjugate Gradients. The current method can be extended to nonlinear systems without modification. For nonlinear equations the Method of Conjugate Gradients has to be augmented with a line-search procedure. Results for linear and nonlinear problems are presented.
Some generalisations of linear-graph modelling for dynamic systems
de Silva, Clarence W.; Pourazadi, Shahram
2013-11-01
Proper modelling of a dynamic system can benefit analysis, simulation, design, evaluation and control of the system. The linear-graph (LG) approach is suitable for modelling lumped-parameter dynamic systems. By using the concepts of graph trees, it provides a graphical representation of the system, with a direct correspondence to the physical component topology. This paper systematically extends the application of LGs to multi-domain (mixed-domain or multi-physics) dynamic systems by presenting a unified way to represent different domains - mechanical, electrical, thermal and fluid. Preservation of the structural correspondence across domains is a particular advantage of LGs when modelling mixed-domain systems. The generalisation of Thevenin and Norton equivalent circuits to mixed-domain systems, using LGs, is presented. The structure of an LG model may follow a specific pattern. Vector LGs are introduced to take advantage of such patterns, giving a general LG representation for them. Through these vector LGs, the model representation becomes simpler and rather compact, both topologically and parametrically. A new single LG element is defined to facilitate the modelling of distributed-parameter (DP) systems. Examples are presented using multi-domain systems (a motion-control system and a flow-controlled pump), a multi-body mechanical system (robot manipulator) and DP systems (structural rods) to illustrate the application and advantages of the methodologies developed in the paper.
A survey of packages for large linear systems
Energy Technology Data Exchange (ETDEWEB)
Wu, Kesheng; Milne, Brent
2000-02-11
This paper evaluates portable software packages for the iterative solution of very large sparse linear systems on parallel architectures. While we cannot hope to tell individual users which package will best suit their needs, we do hope that our systematic evaluation provides essential unbiased information about the packages and the evaluation process may serve as an example on how to evaluate these packages. The information contained here include feature comparisons, usability evaluations and performance characterizations. This review is primarily focused on self-contained packages that can be easily integrated into an existing program and are capable of computing solutions to very large sparse linear systems of equations. More specifically, it concentrates on portable parallel linear system solution packages that provide iterative solution schemes and related preconditioning schemes because iterative methods are more frequently used than competing schemes such as direct methods. The eight packages evaluated are: Aztec, BlockSolve,ISIS++, LINSOL, P-SPARSLIB, PARASOL, PETSc, and PINEAPL. Among the eight portable parallel iterative linear system solvers reviewed, we recommend PETSc and Aztec for most application programmers because they have well designed user interface, extensive documentation and very responsive user support. Both PETSc and Aztec are written in the C language and are callable from Fortran. For those users interested in using Fortran 90, PARASOL is a good alternative. ISIS++is a good alternative for those who prefer the C++ language. Both PARASOL and ISIS++ are relatively new and are continuously evolving. Thus their user interface may change. In general, those packages written in Fortran 77 are more cumbersome to use because the user may need to directly deal with a number of arrays of varying sizes. Languages like C++ and Fortran 90 offer more convenient data encapsulation mechanisms which make it easier to implement a clean and intuitive user
Tracking studies of the Compact Linear Collider collimation system
Energy Technology Data Exchange (ETDEWEB)
Agapov, I.; Burkhardt, H.; Schulte, D.; /CERN; Latina, A.; /Fermilab; Blair, G.A.; Malton, S.; /Royal Holloway, U. of London; Resta-Lopez, J.; /Oxford U., JAI
2009-08-01
A collimation system performance study includes several types of computations performed by different codes. Optics calculations are performed with codes such as MADX, tracking studies including additional effects such as wakefields, halo and tail generation, and dynamical machine alignment are done with codes such as PLACET, and energy deposition can be studied with BDSIM. More detailed studies of hadron production in the beam halo interaction with collimators are better performed with GEANT4 and FLUKA. A procedure has been developed that allows one to perform a single tracking study using several codes simultaneously. In this paper we study the performance of the Compact Linear Collider collimation system using such a procedure.
Investigation of $\\eta'N$ system using linear sigma model
Sakai, Shuntaro
2016-01-01
In this paper, we investigate the $\\eta'N$ system using the three-flavor linear sigma model including the effect of the flavor SU(3) symmetry breaking. The $\\eta'N$ bound state is found also in the case including the flavor symmetry braking and the coupling with the $\\eta N$ and $\\pi N$ channels. The $\\eta'N$ interaction becomes more attractive with the inclusion of the flavor symmetry breaking which causes the mixing between the singlet and octet scalar mesons. The existence of such a bound state would have some impact on the $\\eta'$-nucleus system, which is of interest from the theoretical and experimental viewpoint.
Breathing solitary-pulse pairs in a linearly coupled system
Dana, Brenda; Bahabad, Alon
2014-01-01
It is shown that pairs of solitary pulses (SPs) in a linearly-coupled system with opposite group-velocity dispersions form robust breathing bound states. The system can be realized by temporal-modulation coupling of SPs with different carrier frequencies propagating in the same medium, or by coupling of SPs in a dual-core waveguide. Broad SP pairs are produced in a virtually exact form by means of the variational approximation. Strong nonlinearity tends to destroy the periodic evolution of the SP pairs.
A new hyperchaotic system and its linear feedback control
Institute of Scientific and Technical Information of China (English)
Cai Guo-Liang; Zheng-Song; TianLi-Xin
2008-01-01
This paper reports a new hyperchaotic system by adding an additional state variable into a three-dimensional chaotic dynamical system,studies some of its basic dynamical properties,such as the hyperchaotic attractor,Lyapunov exponents,bifurcation diagram and the hyperchaotic attractor evolving into periodic,quasi-periodic dynamical behaviours by varying parameter k.Furthermore,effective linear feedback control method is used to suppress hyperchaes to unstable equilibrium,periodic orbits and quasi-periodic orbits.Numerical simulations are presented to show these results.
Continuity in weak topology: higher order linear systems of ODE
Institute of Scientific and Technical Information of China (English)
ZHANG MeiRong
2008-01-01
We will introduce a type of Fredholm operators which are shown to have a certain continuity in weak topologies. From this, we will prove that the fundamental matrix solutions of k-th,k≥ 2, order linear systems of ordinary differential equations are continuous in coefficient matrixes with weak topologies. Consequently, Floquet multipliers and Lyapunov exponents for periodic systems are continuous in weak topologies. Moreover, for the scalar Hill's equations, Sturm-Liouville eigenvalues,periodic and anti-periodic eigenvalues, and rotation numbers are all continuous in potentials with weak topologies. These results will lead to many interesting variational problems.
Stability Analysis for Multi-Parameter Linear Periodic Systems
DEFF Research Database (Denmark)
Seyranian, A.P.; Solem, Frederik; Pedersen, Pauli
1999-01-01
This paper is devoted to stability analysis of general linear periodic systems depending on real parameters. The Floquet method and perturbation technique are the basis of the development. We start out with the first and higher-order derivatives of the Floquet matrix with respect to problem...... parameters. Then the behaviour of simple and multiple multipliers of the system with a change of parameters is studied. Weak and strong interactions of multipliers in the complex plane are treated separately. The presented theory is exemplified and discussed....
An identification algorithm for linear stochastic systems with time delays
Leondes, C. T.; Wong, E. C.
1982-01-01
Linear discrete stochastic control systems containing unknown multiple time delays, plant parameters and noise variances are considered. An algorithm is established which uses the maximum-likelihood technique to identify the unknown parameters. An estimated likelihood function is evaluated based on the previous parameter estimates, which in turn generates a new descent direction vector to update the unknown parameters. The delays and plant parameters are identified in their respective parameter spaces. An example of a second-order stochastic system has been implemented by digital simulation to demonstrate the applicability of the algorithm.
Linear filtering of systems with memory and application to finance
Directory of Open Access Journals (Sweden)
2006-01-01
Full Text Available We study the linear filtering problem for systems driven by continuous Gaussian processes V ( 1 and V ( 2 with memory described by two parameters. The processes V ( j have the virtue that they possess stationary increments and simple semimartingale representations simultaneously. They allow for straightforward parameter estimations. After giving the semimartingale representations of V ( j by innovation theory, we derive Kalman-Bucy-type filtering equations for the systems. We apply the result to the optimal portfolio problem for an investor with partial observations. We illustrate the tractability of the filtering algorithm by numerical implementations.
Dielectric Collimators for Linear Collider Beam Delivery System
Kanareykin, A; Baturin, S; Tomás, R
2011-01-01
The current status of ILC and CLIC concepts require additional research on wakefield reduction in the collimator sections. New materials and new geometries have been considered recently*. Dielectric collimators for the CLIC Beam Delivery System have been discussed with a view to minimize the BDS collimation wakefields**. Dielectric collimator concepts for the linear collider are presented in this paper; cylindrical and planar collimators for the CLIC parameters have been considered, and simulations to minimize the beam impedance have been performed. The prototype collimator system is planned to be fabricated and experimentally tested at Facilities for Accelerator Science and Experimental Test Beams (FACET) at SLAC.
LMI approach to reliable H∞ control of linear systems
Institute of Scientific and Technical Information of China (English)
Yao Bo; Wang Fuzhong
2006-01-01
The reliable design problem for linear systems is concerned with. A more practical model of actuator faults than outage is considered. An LMI approach of designing reliable controller is presented for the case of actuator faults that can be modeled by a scaling factor. The resulting control systems are reliable in that they provide guaranteed asymptotic stability and H∞ performance when some control component (actuator) faults occur. A numerical example is also given to illustrate the design procedure and their effectiveness. Furthermore, the optimal standard controller and the optimal reliable controller are compared to show the necessity of reliable control.
Linear $r$-matrix algebra for classical separable systems
Eilbeck, J C; Kuznetsov, V B; Tsiganov, A V; Kuznetsov, Vadim B.
1994-01-01
We consider a hierarchy of the natural type Hamiltonian systems of $n$ degrees of freedom with polynomial potentials separable in general ellipsoidal and general paraboloidal coordinates. We give a Lax representation in terms of $2\\times 2$ matrices for the whole hierarchy and construct the associated linear $r$-matrix algebra with the $r$-matrix dependent on the dynamical variables. A Yang-Baxter equation of dynamical type is proposed. Using the method of variable separation we provide the integration of the systems in classical mechanics conctructing the separation equations and, hence, the explicit form of action variables. The quantisation problem is discussed with the help of the separation variables.
Institute of Scientific and Technical Information of China (English)
Yuanyuan ZOU; Shaoyuan LI
2007-01-01
In this paper,a linear programming method is proposed to solve model predictive control for a class of hybrid systems.Firstly,using the(max,+)algebra,a typical subclass of hybrid systems called max-plus-linear(MPL)systems is obtained.And then,model predictive control(MPC)framework is extended to MPL systems.In general,the nonlinear optimization approach or extended linear complementarity problem(ELCP)were applied to solve the MPL-MPC optimization problem.A new optimization method based on canonical forms for max-min-plus-scaling(MMPS)functions (using the operations maximization,minimization,addition and scalar multiplication)with linear constraints on the inputs is presented.The proposed approach consists in solving several linear programming problems and is more efficient than nonlinear optimization.The validity of the algorithm is illustrated by an example.
Directory of Open Access Journals (Sweden)
Sinha Animesh A
2006-08-01
Full Text Available Abstract Background A number of autoimmune diseases have been clinically and pathologically characterized. In contrast, target antigens have been identified only in a few cases and, in these few cases, the knowledge of the exact epitopic antigenic sequence is still lacking. Thus the major objective of current work in the autoimmunity field is the identification of the epitopic sequences that are related to autoimmune reactions. Our labs propose that autoantigen peptide epitopes able to evoke humoral (autoimmune response are defined by the sequence similarity to the host proteome. The underlying scientific rationale is that antigen peptides acquire immunoreactivity in the context of their proteomic similarity level. Sequences uniquely owned by a protein will have high potential to evoke an immune reaction, whereas motifs with high proteomic redundancy should be immunogenically silenced by the tolerance phenomenon. The relationship between sequence redundancy and peptide immunoreactivity has been successfully validated in a number of experimental models. Here the hypothesis has been applied to pemphigus diseases and the corresponding desmoglein autoantigens. Methods Desmoglein 3 sequence similarity analysis to the human proteome followed by dot-blot/NMR immunoassays were carried out to identify and validate possible epitopic sequences. Results Computational analysis led to identifying a linear immunodominant desmoglein-3 epitope highly reactive with the sera from Pemphigus vulgaris as well as Pemphigus foliaceous. The epitopic peptide corresponded to the amino acid REWVKFAKPCRE sequence, was located in the extreme N-terminal region (residues 49 to 60, and had low redundancy to the human proteome. Sequence alignment showed that human desmoglein 1 and 3 share the REW-KFAK–RE sequence as a common motif with 75% residue identity. Conclusion This study 1 validates sequence redundancy to autoproteome as a main factor in shaping desmoglein peptide
Detecting and isolating abrupt changes in linear switching systems
Nazari, Sohail; Zhao, Qing; Huang, Biao
2015-04-01
In this paper, a novel fault detection and isolation (FDI) method for switching linear systems is developed. All input and output signals are assumed to be corrupted with measurement noises. In the proposed method, a 'lifted' linear model named as stochastic hybrid decoupling polynomial (SHDP) is introduced. The SHDP model governs the dynamics of the switching linear system with all different modes, and is independent of the switching sequence. The error-in-variable (EIV) representation of SHDP is derived, and is used for the fault residual generation and isolation following the well-adopted local approach. The proposed FDI method can detect and isolate the fault-induced abrupt changes in switching models' parameters without estimating the switching modes. Furthermore, in this paper, the analytical expressions of the gradient vector and Hessian matrix are obtained based on the EIV SHDP formulation, so that they can be used to implement the online fault detection scheme. The performance of the proposed method is then illustrated by simulation examples.
Distributed control of uncertain systems using superpositions of linear operators.
Sanger, Terence D
2011-08-01
Control in the natural environment is difficult in part because of uncertainty in the effect of actions. Uncertainty can be due to added motor or sensory noise, unmodeled dynamics, or quantization of sensory feedback. Biological systems are faced with further difficulties, since control must be performed by networks of cooperating neurons and neural subsystems. Here, we propose a new mathematical framework for modeling and simulation of distributed control systems operating in an uncertain environment. Stochastic differential operators can be derived from the stochastic differential equation describing a system, and they map the current state density into the differential of the state density. Unlike discrete-time Markov update operators, stochastic differential operators combine linearly for a large class of linear and nonlinear systems, and therefore the combined effects of multiple controllable and uncontrollable subsystems can be predicted. Design using these operators yields systems whose statistical behavior can be specified throughout state-space. The relationship to Bayesian estimation and discrete-time Markov processes is described.
A harmonic linear dynamical system for prominent ECG feature extraction.
Thi, Ngoc Anh Nguyen; Yang, Hyung-Jeong; Kim, SunHee; Do, Luu Ngoc
2014-01-01
Unsupervised mining of electrocardiography (ECG) time series is a crucial task in biomedical applications. To have efficiency of the clustering results, the prominent features extracted from preprocessing analysis on multiple ECG time series need to be investigated. In this paper, a Harmonic Linear Dynamical System is applied to discover vital prominent features via mining the evolving hidden dynamics and correlations in ECG time series. The discovery of the comprehensible and interpretable features of the proposed feature extraction methodology effectively represents the accuracy and the reliability of clustering results. Particularly, the empirical evaluation results of the proposed method demonstrate the improved performance of clustering compared to the previous main stream feature extraction approaches for ECG time series clustering tasks. Furthermore, the experimental results on real-world datasets show scalability with linear computation time to the duration of the time series.
A Harmonic Linear Dynamical System for Prominent ECG Feature Extraction
Directory of Open Access Journals (Sweden)
Ngoc Anh Nguyen Thi
2014-01-01
Full Text Available Unsupervised mining of electrocardiography (ECG time series is a crucial task in biomedical applications. To have efficiency of the clustering results, the prominent features extracted from preprocessing analysis on multiple ECG time series need to be investigated. In this paper, a Harmonic Linear Dynamical System is applied to discover vital prominent features via mining the evolving hidden dynamics and correlations in ECG time series. The discovery of the comprehensible and interpretable features of the proposed feature extraction methodology effectively represents the accuracy and the reliability of clustering results. Particularly, the empirical evaluation results of the proposed method demonstrate the improved performance of clustering compared to the previous main stream feature extraction approaches for ECG time series clustering tasks. Furthermore, the experimental results on real-world datasets show scalability with linear computation time to the duration of the time series.
Development of a linear induction motor based artificial muscle system.
Gruber, A; Arguello, E; Silva, R
2013-01-01
We present the design of a linear induction motor based on electromagnetic interactions. The engine is capable of producing a linear movement from electricity. The design consists of stators arranged in parallel, which produce a magnetic field sufficient to displace a plunger along its axial axis. Furthermore, the winding has a shell and cap of ferromagnetic material that amplifies the magnetic field. This produces a force along the length of the motor that is similar to that of skeletal muscle. In principle, the objective is to use the engine in the development of an artificial muscle system for prosthetic applications, but it could have multiple applications, not only in the medical field, but in other industries.
Synchronization and Control of Linearly Coupled Singular Systems
Directory of Open Access Journals (Sweden)
Fang Qingxiang
2013-01-01
Full Text Available The synchronization and control problem of linearly coupled singular systems is investigated. The uncoupled dynamical behavior at each node is general and can be chaotic or, otherwise the coupling matrix is not assumed to be symmetrical. Some sufficient conditions for globally exponential synchronization are derived based on Lyapunov stability theory. These criteria, which are in terms of linear matrix inequality (LMI, indicate that the left and right eigenvectors corresponding to eigenvalue zero of the coupling matrix play key roles in the stability analysis of the synchronization manifold. The controllers are designed for state feedback control and pinning control, respectively. Finally, a numerical example is provided to illustrate the effectiveness of the proposed conditions.
Born approximation in linear-time invariant system
Gumjudpai, Burin
2015-01-01
Linear-time invariant (LTI) oscillation systems such as forced mechanical vibration, series RLC and parallel RLC circuits can be solved by using simplest initial conditions or employing of Green's function of which knowledge of initial condition of the force term is needed. Here we show a mathematical connection of the LTI system and the Helmholtz equation form of the time-independent Schr\\"{o}dinger equation in quantum mechanical scattering problem. We apply Born approximation in quantum mechanics to obtain LTI general solution in form of infinite Born series which can be expressed as a series of one-dimensional Feynman graphs. Conditions corresponding to the approximation are given for the case of harmonic driving force. The Born series of the harmonic forced oscillation case are derived by directly applying the approximation to the LTI system or by transforming the LTI system to Helmholtz equation prior to doing the approximation.
Control of Linear Parameter Varying Systems with Applications
Mohammadpour, Javad
2012-01-01
Control of Linear Parameter Varying Systems with Applications compiles state-of-the-art contributions on novel analytical and computational methods to address system modeling and identification, complexity reduction, performance analysis and control design for time-varying and nonlinear systems in the LPV framework. The book has an interdisciplinary character by emphasizing techniques that can be commonly applied in various engineering fields. It also includes a rich collection of illustrative applications in diverse domains to substantiate the effectiveness of the design methodologies and provide pointers to open research directions. The book is divided into three parts. The first part collects chapters of a more tutorial character on the background of LPV systems modeling and control. The second part gathers chapters devoted to the theoretical advancement of LPV analysis and synthesis methods to cope with the design constraints such as uncertainties and time delay. The third part of the volume showcases con...
Order reduction of large-scale linear oscillatory system models
Energy Technology Data Exchange (ETDEWEB)
Trudnowksi, D.J. (Pacific Northwest Lab., Richland, WA (United States))
1994-02-01
Eigen analysis and signal analysis techniques of deriving representations of power system oscillatory dynamics result in very high-order linear models. In order to apply many modern control design methods, the models must be reduced to a more manageable order while preserving essential characteristics. Presented in this paper is a model reduction method well suited for large-scale power systems. The method searches for the optimal subset of the high-order model that best represents the system. An Akaike information criterion is used to define the optimal reduced model. The method is first presented, and then examples of applying it to Prony analysis and eigenanalysis models of power systems are given.
Electron cyclotron resonance breakdown studies in a linear plasma system
Indian Academy of Sciences (India)
Vipin K Yadav; K Sathyanarayana; D Bora
2008-03-01
Electron cyclotron resonance (ECR) plasma breakdown is studied in a small linear cylindrical system with four different gases - hydrogen, helium, argon and nitrogen. Microwave power in the experimental system is delivered by a magnetron at 2.45 ± 0.02 GHz in TE10 mode and launched radially to have extra-ordinary (X) wave in plasma. The axial magnetic field required for ECR in the system is such that the fundamental ECR surface ( = 875.0 G) resides at the geometrical centre of the plasma system. ECR breakdown parameters such as plasma delay time and plasma decay time from plasma density measurements are carried out at the centre using a Langmuir probe. The operating parameters such as working gas pressure (1 × 10-5 -1 × 10-2 mbar) and input microwave power (160{800 W) are varied and the corresponding effect on the breakdown parameters is studied. The experimental results obtained are presented in this paper.
Indirect Identification of Linear Stochastic Systems with Known Feedback Dynamics
Huang, Jen-Kuang; Hsiao, Min-Hung; Cox, David E.
1996-01-01
An algorithm is presented for identifying a state-space model of linear stochastic systems operating under known feedback controller. In this algorithm, only the reference input and output of closed-loop data are required. No feedback signal needs to be recorded. The overall closed-loop system dynamics is first identified. Then a recursive formulation is derived to compute the open-loop plant dynamics from the identified closed-loop system dynamics and known feedback controller dynamics. The controller can be a dynamic or constant-gain full-state feedback controller. Numerical simulations and test data of a highly unstable large-gap magnetic suspension system are presented to demonstrate the feasibility of this indirect identification method.
Biometric Authentication System using Non-Linear Chaos
Directory of Open Access Journals (Sweden)
Dr.N.Krishnan
2010-08-01
Full Text Available A major concern nowadays for any Biometric Credential Management System is its potential vulnerability to protect its information sources; i.e. protecting a genuine user’s template from both internal and external threats. These days’ biometric authentication systems face various risks. One of the most serious threats is the ulnerability of the template's database. An attacker with access to a reference template could try to impersonate a legitimate user by reconstructing the biometric sample and by creating a physical spoof.Susceptibility of the database can have a disastrous impact on the whole authentication system. The potential disclosure of digitally stored biometric data raises serious concerns about privacy and data protection. Therefore, we propose a method which would integrate conventional cryptography techniques with biometrics. In this work, we present a biometric crypto system which encrypts the biometric template and the encryption is done by generating pseudo random numbers, based on non-linear dynamics.
Identification of linear systems by an asymptotically stable observer
Phan, Minh Q.; Horta, Lucas G.; Juang, Jer-Nan; Longman, Richard W.
1992-01-01
A formulation is presented for the identification of a linear multivariable system from single or multiple sets of input-output data. The system input-output relationship is expressed in terms of an observer, which is made asymptotically stable by an embedded eigenvalue assignment procedure. The prescribed eigenvalues for the observer may be real, complex, mixed real and complex, or zero. In this formulation, the Markov parameters of the observer are identified from input-output data. The Markov parameters of the actual system are then recovered from those of the observer and used to obtain a state space model of the system by standard realization techniques. The basic mathematical formulation is derived, and extensive numerical examples using simulated noise-free data are presented to illustrate the proposed method.
Generalized PID observer design for descriptor linear systems.
Wu, Ai-Guo; Duan, Guang-Ren; Fu, Yan-Ming
2007-10-01
A type of generalized proportional-integral-derivative observers is proposed for descriptor linear systems. Based on a general parametric solution to a type of generalized Sylvester matrix equations, a parametric design approach for such observers is established. The proposed approach provides parameterizations for all the observer gain matrices, gives the parametric expression for the corresponding left eigenvector matrix of the observer system matrix, realizes the elimination of impulsive behaviors, and guarantees the regularity of the observer system. The design method can offer all the degrees of design freedom, which can be utilized to achieve various desired system specifications and performances. In addition, a numerical example is employed to show the design procedure and illustrate the effect of the presented approach.
Linear systems approach to simulation of optical diffraction.
Lambert, A J; Fraser, D
1998-12-01
The diffractive processes within an optical system can be simulated by computer to compute the diffraction-altered electric-field distribution at the output of the system from the electric-field distribution at the input. In the paraxial approximation the system can be described by an ABCD ray matrix whose elements in turn can be used to simplify the computation such that only a single computational step is required. We describe two rearrangements of such computations that allow the simulation to be expressed in a linear systems formulation, in particular using the fast-Fourier-transform algorithm. We investigate the sampling requirements for the kernel-modifying function or chirp that arises. We also use the special properties of the chirp to determine the spreading imposed by the diffraction. This knowledge can be used to reduce the computation if only a limited region of either the input or the output is of interest.
Frequency weighted system identification and linear quadratic controller design
Horta, Lucas G.; Phan, Minh; Juang, Jer-Nan; Longman, Richard W.; Sulla, Jeffrey L.
1991-01-01
Application of filters for frequency weighting of Markov parameters (pulse response functions) is described in relation to system/observer identification. The time domain identification approach recovers a model which has a pulse response weighted according to frequency. The identified model is composed of the original system and filters. The augmented system is in a form which can be used directly for frequency weighted linear quadratic controller design. Data from either single or multiple experiments can be used to recover the Markov parameters. Measured acceleration signals from a truss structure are used for system identification and the model obtained is used for frequency weighted controller design. The procedure makes the identification and controler design complementary problems.
Controllability and Observability Criteria for Linear Piecewise Constant Impulsive Systems
Directory of Open Access Journals (Sweden)
Hong Shi
2012-01-01
Full Text Available Impulsive differential systems are an important class of mathematical models for many practical systems in physics, chemistry, biology, engineering, and information science that exhibit impulsive dynamical behaviors due to abrupt changes at certain instants during the dynamical processes. This paper studies the controllability and observability of linear piecewise constant impulsive systems. Necessary and sufficient criteria for reachability and controllability are established, respectively. It is proved that the reachability is equivalent to the controllability under some mild conditions. Then, necessary and sufficient criteria for observability and determinability of such systems are established, respectively. It is also proved that the observability is equivalent to the determinability under some mild conditions. Our criteria are of the geometric type, and they can be transformed into algebraic type conveniently. Finally, a numerical example is given to illustrate the utility of our criteria.
Linearization Technologies for Broadband Radio-Over-Fiber Transmission Systems
Directory of Open Access Journals (Sweden)
Xiupu Zhang
2014-11-01
Full Text Available Linearization technologies that can be used for linearizing RoF transmission are reviewed. Three main linearization methods, i.e. electrical analog linearization, optical linearization, and electrical digital linearization are presented and compared. Analog linearization can be achieved using analog predistortion circuits, and can be used for suppression of odd order nonlinear distortion components, such as third and fifth order. Optical linearization includes mixed-polarization, dual-wavelength, optical channelization and the others, implemented in optical domain, to suppress both even and odd order nonlinear distortion components, such as second and third order. Digital predistortion has been a widely used linearization method for RF power amplifiers. However, digital linearization that requires analog to digital converter is severely limited to hundreds of MHz bandwidth. Instead, analog and optical linearization provide broadband linearization with up to tens of GHz. Therefore, for broadband radio over fiber transmission that can be used for future broadband cloud radio access networks, analog and optical linearization are more appropriate than digital linearization. Generally speaking, both analog and optical linearization are able to improve spur-free dynamic range greater than 10 dB over tens of GHz. In order for current digital linearization to be used for broadband radio over fiber transmission, the reduced linearization complexity and increased linearization bandwidth are required. Moreover, some digital linearization methods in which the complexity can be reduced, such as Hammerstein type, may be more promising and require further investigation.
Linear nonequilibrium thermodynamics describes the dynamics of an autocatalytic system.
Cortassa, S; Aon, M A; Westerhoff, H V
1991-01-01
A model simulating oscillations in glycolysis was formulated in terms of nonequilibrium thermodynamics. In the kinetic rate equations every metabolite concentration was replaced with an exponential function of its chemical potential. This led to nonlinear relations between rates and chemical potentials. Each chemical potential was then expanded around its steady-state value as a Taylor series. The linear (first order) term of the Taylor series sufficed to simulate the dynamic behavior of the system, including the damped and even sustained oscillations at low substrate input or high free-energy load. The glycolytic system is autocatalytic in the first half. Because oscillations were obtained only in the presence of that autocatalytic feed-back loop we conclude that this type of kinetic nonlinearity was sufficient to account for the oscillatory behavior. The matrix of phenomenological coefficients of the system is nonsymmetric. Our results indicate that this is the symmetry property and not the linearity of the flow-force relations in the near equilibrium domain that precludes oscillations. Given autocatalytic properties, a system exhibiting liner flow-force relations and being outside the near equilibrium domain may show bifurcations, leading to self-organized behavior. Images FIGURE 5 PMID:1742453
A linear signal transmission system calibration method of wideband GPR
Wu, Bin; Zhao, Kai; Gu, Ling-jia; Cao, Qiong; Li, Xiao-feng; Zheng, Xing-ming
2016-09-01
In VHF pulse Ground Penetrating Radar(GPR) system, the echo pass through the antenna and transmission line circuit, then reach the GPR receiver. Thus the reflection coefficient at the receiver sampling gate interface, which is at the end of the transmission line, is different from the real reflection coefficient of the media at the antenna interface, which could cause the GPR receiving error. The pulse GPR receiver is a wideband system that can't be simply described as traditional narrowband transmission line model. Since the GPR transmission circuit is a linear system, the linear transformation method could be used to analyze the characteristic of the GPR receiving system. A GPR receiver calibration method based on transmission line theory is proposed in this paper, which analyzes the relationship between the reflection coefficients of theory calculation at antenna interface and the measuring data by network analyzer at the sampling gate interface. Then the least square method is introduced to calibrate the transfer function of the GPR receiver transmission circuit. This calibration method can be useful in media quantitative inversion by GPR. When the reflection coefficient at the sampling gate is obtained, the real reflection coefficient of the media at the antenna interface can be easily determined.
Frequency-domain L2-stability conditions for time-varying linear and nonlinear MIMO systems
Institute of Scientific and Technical Information of China (English)
Zhihong HUANG; Y. V. VENKATESH; Cheng XIANG; Tong Heng LEE
2014-01-01
The paper deals with the L2-stability analysis of multi-input-multi-output (MIMO) systems, governed by integral equations, with a matrix of periodic/aperiodic time-varying gains and a vector of monotone, non-monotone and quasi-monotone nonlin-earities. For nonlinear MIMO systems that are described by differential equations, most of the literature on stability is based on an application of quadratic forms as Lyapunov-function candidates. In contrast, a non-Lyapunov framework is employed here to derive new and more general L2-stability conditions in the frequency domain. These conditions have the following features:i) They are expressed in terms of the positive definiteness of the real part of matrices involving the transfer function of the linear time-invariant block and a matrix multiplier function that incorporates the minimax properties of the time-varying linear/nonlinear block. ii) For certain cases of the periodic time-varying gain, they contain, depending on the multiplier function chosen, no restrictions on the normalized rate of variation of the time-varying gain, but, for other periodic/aperiodic time-varying gains, they do. Overall, even when specialized to periodic-coefficient linear and nonlinear MIMO systems, the stability conditions are distinct from and less restrictive than recent results in the literature. No comparable results exist in the literature for aperiodic time-varying gains. Furthermore, some new stability results concerning the dwell-time problem and time-varying gain switching in linear and nonlinear MIMO systems with periodic/aperiodic matrix gains are also presented. Examples are given to illustrate a few of the stability theorems.
Frequency Interval Cross Gramians for Linear and Bilinear Systems
DEFF Research Database (Denmark)
Jazlan, Ahmad; Sreeram, Victor; Shaker, Hamid Reza
2017-01-01
In many control engineering problems, it is desired to analyze the systems at particular frequency intervals of interest. This paper focuses on the development of frequency interval cross gramians for both linear and bilinear systems. New generalized Sylvester equations for calculating...... the frequency interval cross gramians are derived in order to be used to obtain information regarding controllability and observability within a single matrix. The advantage of the proposed method is that it is computationally more efficient compared to existing gramian-based techniques since only half...... of the number of equations need to be solved in order to obtain information regarding the controllability and observability of a system compared to existing techniques. Numerical examples are provided to demonstrate the computational efficiency of the proposed method which uses frequency interval cross gramians...
Frequency Interval Cross Gramians for Linear and Bilinear Systems
DEFF Research Database (Denmark)
Jazlan, Ahmad; Sreeram, Victor; Shaker, Hamid Reza
2016-01-01
In many control engineering problems, it is desired to analyze the systems at particular frequency intervals of interest. This paper focuses on the development of frequency interval cross gramians for both linear and bilinear systems. New generalized Sylvester equations for calculating...... the frequency interval cross gramians are derived in order to be used to obtain information regarding controllability and observability within a single matrix. The advantage of the proposed method is that it is computationally more efficient compared to existing gramian-based techniques since only half...... of the number of equations need to be solved in order to obtain information regarding the controllability and observability of a system compared to existing techniques. Numerical examples are provided to demonstrate the computational efficiency of the proposed method which uses frequency interval cross gramians...
State aggregation and population dynamics in linear systems.
Rowe, Jonathan E; Vose, Michael D; Wright, Alden H
2005-01-01
We consider complex systems that are composed of many interacting elements, evolving under some dynamics. We are interested in characterizing the ways in which these elements may be grouped into higher-level, macroscopic states in a way that is compatible with those dynamics. Such groupings may then be thought of as naturally emergent properties of the system. We formalize this idea and, in the case that the dynamics are linear, prove necessary and sufficient conditions for this to happen. In cases where there is an underlying symmetry among the components of the system, group theory may be used to provide a strong sufficient condition. These observations are illustrated with some artificial life examples.
Novel Approach to Linear Accelerator Superconducting Magnet System
Energy Technology Data Exchange (ETDEWEB)
Kashikhin, Vladimir; /Fermilab
2011-11-28
Superconducting Linear Accelerators include a superconducting magnet system for particle beam transportation that provides the beam focusing and steering. This system consists of a large number of quadrupole magnets and dipole correctors mounted inside or between cryomodules with SCRF cavities. Each magnet has current leads and powered from its own power supply. The paper proposes a novel approach to magnet powering based on using superconducting persistent current switches. A group of magnets is powered from the same power supply through the common, for the group of cryomodules, electrical bus and pair of current leads. Superconducting switches direct the current to the chosen magnet and close the circuit providing the magnet operation in a persistent current mode. Two persistent current switches were fabricated and tested. In the paper also presented the results of magnetic field simulations, decay time constants analysis, and a way of improving quadrupole magnetic center stability. Such approach substantially reduces the magnet system cost and increases the reliability.
Acoustic FMRI noise: linear time-invariant system model.
Rizzo Sierra, Carlos V; Versluis, Maarten J; Hoogduin, Johannes M; Duifhuis, Hendrikus Diek
2008-09-01
Functional magnetic resonance imaging (fMRI) enables sites of brain activation to be localized in human subjects. For auditory system studies, however, the acoustic noise generated by the scanner tends to interfere with the assessments of this activation. Understanding and modeling fMRI acoustic noise is a useful step to its reduction. To study acoustic noise, the MR scanner is modeled as a linear electroacoustical system generating sound pressure signals proportional to the time derivative of the input gradient currents. The transfer function of one MR scanner is determined for two different input specifications: 1) by using the gradient waveform calculated by the scanner software and 2) by using a recording of the gradient current. Up to 4 kHz, the first method is shown as reliable as the second one, and its use is encouraged when direct measurements of gradient currents are not possible. Additionally, the linear order and average damping properties of the gradient coil system are determined by impulse response analysis. Since fMRI is often based on echo planar imaging (EPI) sequences, a useful validation of the transfer function prediction ability can be obtained by calculating the acoustic output for the EPI sequence. We found a predicted sound pressure level (SPL) for the EPI sequence of 104 dB SPL compared to a measured value of 102 dB SPL. As yet, the predicted EPI pressure waveform shows similarity as well as some differences with the directly measured EPI pressure waveform.
Steady state decoupling and design of linear multivariable systems
Huang, J. Y.; Thaler, G. J.
1974-01-01
A constructive criterion for decoupling the steady states of linear multivariable systems is developed. The criterion consists of n(n-1) inequalities with the type numbers of the compensator transfer functions as the unknowns. These unknowns can be chosen to satisfy the inequalities and hence achieve a steady state decoupling scheme. It turns out that pure integrators in the loops play an important role. An extended root locus design method is then developed to take care of the stability and transient response. The overall procedure is applied to the compensation design for STOL C-8A aircraft in the approach mode.
A PRODUCT HYBRID GMRES ALGORITHM FOR NONSYMMETRIC LINEAR SYSTEMS
Institute of Scientific and Technical Information of China (English)
Bao-jiang Zhong
2005-01-01
It has been observed that the residual polynomials resulted from successive restarting cycles of GMRES(m) may differ from one another meaningfully. In this paper, it is further shown that the polynomials can complement one another harmoniously in reducing the iterative residual. This characterization of GMRES(m) is exploited to formulate an efficient hybrid iterative scheme, which can be widely applied to existing hybrid algorithms for solving large nonsymmetric systems of linear equations. In particular, a variant of the hybrid GMRES algorithm of Nachtigal, Reichel and Trefethen (1992) is presented. It is described how the new algorithm may offer significant performance improvements over the original one.
On guaranteed cost control of linear systems with input saturation
Institute of Scientific and Technical Information of China (English)
FU Min-yue
2007-01-01
This work studies the problem of control design for linear systems with input saturation. It is well known that integral quadratic constraints (IQC) can be used to describe input saturation and that the use of IQC in analysis can lead to less conservative performance bound and larger domain of attraction. In this work, it is shown that a class of commonly used IQCs may not help in control synthesis. That is, the use of these IQCs does not enlarge the guaranteed domain of performance for synthesis.
Tuning of the Compact Linear Collider Beam Delivery System
Garcia, H; Inntjore Levinsen, Y; Latina, A; Tomas, R; Snuverink, J
2014-01-01
Tuning the Compact Linear Collider (CLIC) BeamDelivery System (BDS), and in particular the Final Focus (FF), is a challenging task. In simulations without misalignments, the goal is to reach 120%o f the nominal luminosity target, in order to allow for 10% loss due to static imperfections, and another 10% loss from dynamic imperfections. Various approaches have been considered to correct the magnet misalignments, including 1-1 correction, Dispersion Free Steering (DFS), and several minimization methods utilizing multipole movers. In this paper we report on the recent advancements towards a feasible tuning approach that reaches the required luminosity target.
Linear generalized synchronization of chaotic systems with uncertain parameters
Institute of Scientific and Technical Information of China (English)
Jia Zhen
2008-01-01
A more general form of projective synchronization,so called linear generalized synchronization(LGS)is proposed,which includes the generalized projective synchronization(GPS)and the hybrid projective synchronization(HPS)as its special cases.Based on the adaptive technique and Lyapunov stability theory,a general method for achieving the LGS between two chaotic or hyperchaotic systems with uncertain parameters in any scaling matrix is presented.Some numerical simulations are provided to show the effectiveness and feasibility of the proposed synchronization method.
Optimal Robust Fault Detection for Linear Discrete Time Systems
Directory of Open Access Journals (Sweden)
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.
Probing LINEAR Collider Final Focus Systems in SuperKEKB
Thrane, Paul Conrad Vaagen
2017-01-01
A challenge for future linear collider final focus systems is the large chromaticity produced by the final quadrupoles. SuperKEKB will be correcting high levels of chromaticity using the traditional scheme which has been also proposed for the CLIC FFS. We present early simulation results indicating that lowering β*у in the SuperKEKB Low Energy Ring might be possible given on-axis injection and low bunch current, opening the possibility of testing chromaticity correction beyond FFTB level, similar to ILC and approaching that of CLIC. CLIC – Note – 1077
Phase reconstruction from intensity measurements in linear systems.
Bastiaans, Martin J; Wolf, Kurt Bernardo
2003-06-01
The phase of a signal at a plane is reconstructed from the intensity profiles at two close parallel screens connected by a small abcd canonical transform; this applies to propagation along harmonic and repulsive fibers and in free media. We analyze the relationship between the local spatial frequency (the signal phase derivative) and the derivative of the squared modulus of the signal under a one-parameter canonical transform with respect to the parameter. We thus generalize to all linear systems the results that have been obtained separately for Fresnel and fractional Fourier transforms.
Periodic solutions and flip bifurcation in a linear impulsive system
Institute of Scientific and Technical Information of China (English)
Jiang Gui-Rong; Yang Qi-Gui
2008-01-01
In this paper,the dynamical behaviour of a linear impulsive system is discussed both theoretically and numerically.The existence and the stability of period-one solution are discussed by using a discrete map.The conditions of existence for flip bifurcation are derived by using the centre manifold theorem and bifurcation theorem.The bifurcation analysis shows that chaotic solutions appear via a cascade of period-doubling in some interval of parameters.Moreover,the periodic solutions,the bifurcation diagram,and the chaotic attractor,which show their consistence with the theoretical analyses,are given in an example.中图分类:O547
Complete Controllability of Linear Fractional Differential Systems with Singularity
Directory of Open Access Journals (Sweden)
Qun Huang
2015-01-01
Full Text Available This paper is concerned with the controllability of a class of linear fractional differential systems with singularity. The method which is used to deal with the fast subsystem N·cD0,tαx2(t=x2(t+B2u(t and y2(t=C2x2(t is an improvement of the known ones. Based on the movement orbit of the state equation, we obtain several controllability criteria which are sufficient and necessary.
Nonlinear elliptic equations and systems with linear part at resonance
Directory of Open Access Journals (Sweden)
Philip Korman
2016-03-01
Full Text Available The famous result of Landesman and Lazer [10] dealt with resonance at a simple eigenvalue. Soon after publication of [10], Williams [14] gave an extension for repeated eigenvalues. The conditions in Williams [14] are rather restrictive, and no examples were ever given. We show that seemingly different classical result by Lazer and Leach [11], on forced harmonic oscillators at resonance, provides an example for this theorem. The article by Williams [14] also contained a shorter proof. We use a similar approach to study resonance for 2X2 systems. We derive conditions for existence of solutions, which turned out to depend on the spectral properties of the linear part.
Space Telecommunications Radio System (STRS) Definitions and Acronyms
Briones, Janette C.; Handler, Louis M.; Johnson, Sandra K.; Nappier, Jennifer; Gnepp, Steven; Kacpura, Thomas J.; Reinhart, Richard C.; Hall, Charles S.; Mortensen, Dale
2008-01-01
Software-defined radio is a relatively new technology area, and industry consensus on terminology is not always consistent. Confusion exists when the various organizations and standards bodies define different radio terms associated with the actual amount of reconfigurability of the radios. The Space Telecommunications Radio System (STRS) Definitions and Acronyms Document provides the readers of the STRS documents a common understanding of the terminology used and how they will be applied to the STRS architecture.
DEFF Research Database (Denmark)
Ommen, Torben Schmidt; Markussen, Wiebke Brix; Elmegaard, Brian
2014-01-01
differences and differences between the solution found by each optimisation method. One of the investigated approaches utilises LP (linear programming) for optimisation, one uses LP with binary operation constraints, while the third approach uses NLP (non-linear programming). The LP model is used...... of selected units by 23%, while for a non-linear approach the increase can be higher than 39%. The results indicate a higher coherence between the two latter approaches, and that the MLP (mixed integer programming) optimisation is most appropriate from a viewpoint of accuracy and runtime. © 2014 Elsevier Ltd...
A type system for PSPACE derived from light linear logic
Directory of Open Access Journals (Sweden)
Lucien Capedevielle
2012-01-01
Full Text Available We present a polymorphic type system for lambda calculus ensuring that well-typed programs can be executed in polynomial space: dual light affine logic with booleans (DLALB. To build DLALB we start from DLAL (which has a simple type language with a linear and an intuitionistic type arrow, as well as one modality which characterizes FPTIME functions. In order to extend its expressiveness we add two boolean constants and a conditional constructor in the same way as with the system STAB. We show that the value of a well-typed term can be computed by an alternating machine in polynomial time, thus such a term represents a program of PSPACE (given that PSPACE = APTIME. We also prove that all polynomial space decision functions can be represented in DLALB. Therefore DLALB characterizes PSPACE predicates.
Cooperative Output Regulation of Multiagent Linear Parameter-Varying Systems
Directory of Open Access Journals (Sweden)
Afshin Mesbahi
2017-01-01
Full Text Available The output regulation problem is examined in this paper for a class of heterogeneous multiagent systems whose dynamics are governed by polytopic linear parameter-varying (LPV models. The dynamics of the agents are decoupled from each other but the agents’ controllers are assumed to communicate. To design the cooperative LPV controllers, analysis conditions for closed-loop system are first established to ensure stability and reference tracking. Then, the LPV control synthesis problem is addressed, where the offline solution to a time-varying Sylvester equation will be used to determine and update in real time the controller state-space matrices. Two numerical examples will be finally given to demonstrate the efficacy of the proposed cooperative design method.
Linear system identification via backward-time observer models
Juang, Jer-Nan; Phan, Minh
1993-01-01
This paper presents an algorithm to identify a state-space model of a linear system using a backward-time approach. The procedure consists of three basic steps. First, the Markov parameters of a backward-time observer are computed from experimental input-output data. Second, the backward-time observer Markov parameters are decomposed to obtain the backward-time system Markov parameters (backward-time pulse response samples) from which a backward-time state-space model is realized using the Eigensystem Realization Algorithm. Third, the obtained backward-time state space model is converted to the usual forward-time representation. Stochastic properties of this approach will be discussed. Experimental results are given to illustrate when and to what extent this concept works.
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.
Ultra-high Frequency Linear Fiber Optic Systems
Lau, Kam Y
2009-01-01
Designed for a one-semester course on fiber-optics systems and communication links, this book provides a concise but rigorous treatment of the theory and practice of analog (linear) fiber-optics links and systems that constitute the foundation of Hybrid Fiber Coax infrastructure in present-day CATV distribution and cable modem Internet access. Emerging applications in remote fiber-optic feed for free-space millimeter wave enterprise campus networks are also described. Issues such as dispersion and interferometric noise are treated quantitatively, and means for mitigating them are explained. This broad but concise text will thus be invaluable not only to students of fiber-optics communication but also to practicing engineers.
Robust fault detection for switched linear systems with state delays.
Wang, Dong; Wang, Wei; Shi, Peng
2009-06-01
This correspondence deals with the problem of robust fault detection for discrete-time switched systems with state delays under an arbitrary switching signal. The fault detection filter is used as the residual generator, in which the filter parameters are dependent on the system mode. Attention is focused on designing the robust fault detection filter such that, for unknown inputs, control inputs, and model uncertainties, the estimation error between the residuals and faults is minimized. The problem of robust fault detection is converted into an H(infinity)-filtering problem. By a switched Lyapunov functional approach, a sufficient condition for the solvability of this problem is established in terms of linear matrix inequalities. A numerical example is provided to demonstrate the effectiveness of the proposed method.
Linear Volterra Integral Equations as the Limit of Discrete Systems
Institute of Scientific and Technical Information of China (English)
M. Federson; R.Bianconi; L.Barbanti
2004-01-01
We consider the multidimensional abstract linear integral equation of Volterra typex (t)+(*)∫Rt a (s)x (s)ds =f (t),t∈R,as the limit of discrete Stieltjes-type systems and we prove results on the existence of continuous solutions.The functions x,a and f are Banach space-valued de .ned on a compact interval R of R n ,R t is a subinterval of R depending on t∈R and (*)∫denotes either the Bochner-Lebesgue integral or the Henstock integral.The results presented here generalize those in [1]and are in the spirit of [3].As a consequence of our approach,it is possible to study the properties of (1)by transferring the properties of the discrete systems.The Henstock integral setting enables us to consider highly oscillating functions.
Efficient Feedforward Linearization Technique Using Genetic Algorithms for OFDM Systems
Directory of Open Access Journals (Sweden)
García Paloma
2010-01-01
Full Text Available Feedforward is a linearization method that simultaneously offers wide bandwidth and good intermodulation distortion suppression; so it is a good choice for Orthogonal Frequency Division Multiplexing (OFDM systems. Feedforward structure consists of two loops, being necessary an accurate adjustment between them along the time, and when temperature, environmental, or operating changes are produced. Amplitude and phase imbalances of the circuit elements in both loops produce mismatched effects that lead to degrade its performance. A method is proposed to compensate these mismatches, introducing two complex coefficients calculated by means of a genetic algorithm. A full study is carried out to choose the optimal parameters of the genetic algorithm applied to wideband systems based on OFDM technologies, which are very sensitive to nonlinear distortions. The method functionality has been verified by means of simulation.
Energy Technology Data Exchange (ETDEWEB)
1980-12-01
The results of the system definition studies conducted by NASA as a part of the Department of Energy/National Aeronautics and Space Administration SPS Concept Development and Evaluation Program are summarized. The purpose of the system definition efforts was to identify and define candidate SPS concepts and to evaluate the concepts in terms of technical and cost factors. Although the system definition efforts consisted primarily of evaluation and assessment of alternative technical approaches, a reference system was also defined to facilitate economic, environmental, and societal assessments by the Department of Energy. This reference system was designed to deliver 5 GW of electrical power to the utility grid. Topics covered include system definition; energy conversion and power management; power transmission and reception; structures, controls, and materials; construction and operations; and space transportation.
Energy and environmental analysis of a linear concentrating photovoltaic system
Kerzmann, Tony
The world is facing an imminent energy supply crisis. In order to sustain and increase our energy supply in an environmentally-conscious manner, it is necessary to advance renewable technologies. Despite this urgency, however, it is paramount to consider the larger environmental effects associated with using renewable energy resources. This research is meant to better understand linear concentrating photovoltaics (LCPVs) from an engineering and environmental standpoint. In order to analyze the LCPV system, a simulation and life cycle assessment (LCA) were developed. The LCPV system serves two major purposes: it produces electricity, and waste heat is collected for heating use. There are three parts to the LCPV simulation. The first part simulates the multijunction cell output so as to calculate the temperature-dependent electricity generation. The second part simulates the cell cooling and waste heat recovery system using a model consisting of heat transfer and fluid flow equations. The waste heat recovery in the LCPV system was linked to a hot water storage system, which was also modeled. Coupling the waste heat recovery simulation and the hot water storage system gives an overall integrated system that is useful for system design, optimization, and acts as a stepping stone for future multijunction cell Photovoltaic/Thermal (PV/T) systems. Finally, all of the LCPV system components were coded in Engineering Equation Solver (EES) and were used in an energy analysis under actual weather and solar conditions for the Phoenix, AZ, region. The life cycle assessment for the LCPV system allowed for an environmental analysis of the system where areas of the highest environmental impact were pinpointed. While conducting the LCA research, each component of the system was analyzed from a resource extraction, production, and use standpoint. The collective production processes of each LCPV system component were gathered into a single inventory of materials and energy flows
Linear homotopy solution of nonlinear systems of equations in geodesy
Paláncz, Béla; Awange, Joseph L.; Zaletnyik, Piroska; Lewis, Robert H.
2010-01-01
A fundamental task in geodesy is solving systems of equations. Many geodetic problems are represented as systems of multivariate polynomials. A common problem in solving such systems is improper initial starting values for iterative methods, leading to convergence to solutions with no physical meaning, or to convergence that requires global methods. Though symbolic methods such as Groebner bases or resultants have been shown to be very efficient, i.e., providing solutions for determined systems such as 3-point problem of 3D affine transformation, the symbolic algebra can be very time consuming, even with special Computer Algebra Systems (CAS). This study proposes the Linear Homotopy method that can be implemented easily in high-level computer languages like C++ and Fortran that are faster than CAS by at least two orders of magnitude. Using Mathematica, the power of Homotopy is demonstrated in solving three nonlinear geodetic problems: resection, GPS positioning, and affine transformation. The method enlarging the domain of convergence is found to be efficient, less sensitive to rounding of numbers, and has lower complexity compared to other local methods like Newton-Raphson.
2012-02-24
... Defense Federal Acquisition Regulation Supplement; Business Systems--Definition and Administration (DFARS... proposed rule for Business Systems-- Definition and Administration (DFARS Case 2009-D038) in the Federal... contractor business systems, DoD has clarified the definition and administration of contractor...
2010-12-03
... Acquisition Regulation Supplement; Business Systems-- Definition and Administration (DFARS Case 2009-D038...D published a proposed rule for Business Systems--Definition and Administration (DFARS Case 2009... contractor business systems, DoD is considering a rule to clarify the definition and administration...
Predictability of extremes in non-linear hierarchically organized systems
Kossobokov, V. G.; Soloviev, A.
2011-12-01
Understanding the complexity of non-linear dynamics of hierarchically organized systems progresses to new approaches in assessing hazard and risk of the extreme catastrophic events. In particular, a series of interrelated step-by-step studies of seismic process along with its non-stationary though self-organized behaviors, has led already to reproducible intermediate-term middle-range earthquake forecast/prediction technique that has passed control in forward real-time applications during the last two decades. The observed seismic dynamics prior to and after many mega, great, major, and strong earthquakes demonstrate common features of predictability and diverse behavior in course durable phase transitions in complex hierarchical non-linear system of blocks-and-faults of the Earth lithosphere. The confirmed fractal nature of earthquakes and their distribution in space and time implies that many traditional estimations of seismic hazard (from term-less to short-term ones) are usually based on erroneous assumptions of easy tractable analytical models, which leads to widespread practice of their deceptive application. The consequences of underestimation of seismic hazard propagate non-linearly into inflicted underestimation of risk and, eventually, into unexpected societal losses due to earthquakes and associated phenomena (i.e., collapse of buildings, landslides, tsunamis, liquefaction, etc.). The studies aimed at forecast/prediction of extreme events (interpreted as critical transitions) in geophysical and socio-economical systems include: (i) large earthquakes in geophysical systems of the lithosphere blocks-and-faults, (ii) starts and ends of economic recessions, (iii) episodes of a sharp increase in the unemployment rate, (iv) surge of the homicides in socio-economic systems. These studies are based on a heuristic search of phenomena preceding critical transitions and application of methodologies of pattern recognition of infrequent events. Any study of rare
Filtering nonlinear dynamical systems with linear stochastic models
Harlim, J.; Majda, A. J.
2008-06-01
An important emerging scientific issue is the real time filtering through observations of noisy signals for nonlinear dynamical systems as well as the statistical accuracy of spatio-temporal discretizations for filtering such systems. From the practical standpoint, the demand for operationally practical filtering methods escalates as the model resolution is significantly increased. For example, in numerical weather forecasting the current generation of global circulation models with resolution of 35 km has a total of billions of state variables. Numerous ensemble based Kalman filters (Evensen 2003 Ocean Dyn. 53 343-67 Bishop et al 2001 Mon. Weather Rev. 129 420-36 Anderson 2001 Mon. Weather Rev. 129 2884-903 Szunyogh et al 2005 Tellus A 57 528-45 Hunt et al 2007 Physica D 230 112-26) show promising results in addressing this issue; however, all these methods are very sensitive to model resolution, observation frequency, and the nature of the turbulent signals when a practical limited ensemble size (typically less than 100) is used. In this paper, we implement a radical filtering approach to a relatively low (40) dimensional toy model, the L-96 model (Lorenz 1996 Proc. on Predictability (ECMWF, 4-8 September 1995) pp 1-18) in various chaotic regimes in order to address the 'curse of ensemble size' for complex nonlinear systems. Practically, our approach has several desirable features such as extremely high computational efficiency, filter robustness towards variations of ensemble size (we found that the filter is reasonably stable even with a single realization) which makes it feasible for high dimensional problems, and it is independent of any tunable parameters such as the variance inflation coefficient in an ensemble Kalman filter. This radical filtering strategy decouples the problem of filtering a spatially extended nonlinear deterministic system to filtering a Fourier diagonal system of parametrized linear stochastic differential equations (Majda and Grote
Three-dimensional linear system analysis for breast tomosynthesis
Zhao, Bo; Zhao, Wei
2008-01-01
The optimization of digital breast tomosynthesis (DBT) geometry and reconstruction is crucial for the clinical translation of this exciting new imaging technique. In the present work, the authors developed a three-dimensional (3D) cascaded linear system model for DBT to investigate the effects of detector performance, imaging geometry, and image reconstruction algorithm on the reconstructed image quality. The characteristics of a prototype DBT system equipped with an amorphous selenium flat-panel detector and filtered backprojection reconstruction were used as an example in the implementation of the linear system model. The propagation of signal and noise in the frequency domain was divided into six cascaded stages incorporating the detector performance, imaging geometry, and reconstruction filters. The reconstructed tomosynthesis imaging quality was characterized by spatial frequency dependent presampling modulation transfer function (MTF), noise power spectrum (NPS), and detective quantum efficiency (DQE) in 3D. The results showed that both MTF and NPS were affected by the angular range of the tomosynthesis scan and the reconstruction filters. For image planes parallel to the detector (in-plane), MTF at low frequencies was improved with increase in angular range. The shape of the NPS was affected by the reconstruction filters. Noise aliasing in 3D could be introduced by insufficient voxel sampling, especially in the z (slice-thickness) direction where the sampling distance (slice thickness) could be more than ten times that for in-plane images. Aliasing increases the noise at high frequencies, which causes degradation in DQE. Application of a reconstruction filter that limits the frequency components beyond the Nyquist frequency in the z direction, referred to as the slice thickness filter, eliminates noise aliasing and improves 3D DQE. The focal spot blur, which arises from continuous tube travel during tomosynthesis acquisition, could degrade DQE significantly
Falsone, G.; Settineri, D.
2011-06-01
A procedure for evaluating the response cross-correlation of a linear structural system subjected to the action of stationary random multi-correlated processes is presented in this work. It is based on the definition of the fourth-order differential equation governing the modal response cross-correlation and of the corresponding solution. This is expressed in terms of the corresponding fundamental matrix, whose expression is related to the fundamental matrices of the differential equations governing the modal responses. The properties of this matrix allows to define a particular unconditionally stable numerical integration approach, which is composed of two independent step-by-step procedures, a progressive one and a regressive one. The applications have shown a level of accuracy comparable to that corresponding to the numerical solution of the double convolution integral, but the presented approach is characterised by a reduced computational effort.
Energy Technology Data Exchange (ETDEWEB)
Stoddard, Larry [Black & Veatch, Kansas City, MO (United States); Galluzzo, Geoff [Black & Veatch, Kansas City, MO (United States); Andrew, Daniel [Black & Veatch, Kansas City, MO (United States); Adams, Shannon [Black & Veatch, Kansas City, MO (United States)
2016-06-30
generating approximately 10MWe. This report addresses the concept definition of the sCO2 power generation system, a sub-set of items 2 and 3 above. Other reports address the balance of items 1 to 3 above as well as the MS/sCO2 integrated 10MWe facility, Item 2.
Model Based Adaptive Piecewise Linear Controller for Complicated Control Systems
Directory of Open Access Journals (Sweden)
Tain-Sou Tsay
2014-01-01
Full Text Available A model based adaptive piecewise linear control scheme for industry processes with specifications on peak overshoots and rise times is proposed. It is a gain stabilized control technique. Large gain is used for large tracking error to get fast response. Small gain is used between large and small tracking error for good performance. Large gain is used again for small tracking error to cope with large disturbance. Parameters of the three-segment piecewise linear controller are found by an automatic regulating time series which is function of output characteristics of the plant and reference model. The time series will be converged to steady values after the time response of the considered system matching that of the reference model. The proposed control scheme is applied to four numerical examples which have been compensated by PID controllers. Parameters of PID controllers are found by optimization method. It gives an almost command independent response and gives significant improvements for response time and performance.
Institute of Scientific and Technical Information of China (English)
I.Yamazaki; X.S.Li; E.G.Ng
2010-01-01
A parallel hybrid linear solver based on the Schur complement method has the potential to balance the robustness of direct solvers with the efficiency of precon-ditioned iterative solvers. However, when solving large-scale highly-indefinite linear systems, this hybrid solver often suffers from either slow convergence or large memory requirements to solve the Schur complement systems. To overcome this challenge, we in this paper discuss techniques to preprocess the Schur complement systems in paral-lel. Numerical results of solving large-scale highly-indefinite linear systems from various applications demonstrate that these techniques improve the reliability and performance of the hybrid solver and enable efficient solutions of these linear systems on hundreds of processors, which was previously infeasible using existing state-of-the-art solvers.
Parappagoudar, Mahesh B.; Pratihar, Dilip K.; Datta, Gouranga L.
2008-08-01
A cement-bonded moulding sand system takes a fairly long time to attain the required strength. Hence, the moulds prepared with cement as a bonding material will have to wait a long time for the metal to be poured. In this work, an accelerator was used to accelerate the process of developing the bonding strength. Regression analysis was carried out on the experimental data collected as per statistical design of experiments (DOE) to establish input-output relationships of the process. The experiments were conducted to measure compression strength and hardness (output parameters) by varying the input variables, namely amount of cement, amount of accelerator, water in the form of cement-to-water ratio, and testing time. A two-level full-factorial design was used for linear regression model, whereas a three-level central composite design (CCD) had been utilized to develop non-linear regression model. Surface plots and main effects plots were used to study the effects of amount of cement, amount of accelerator, water and testing time on compression strength, and mould hardness. It was observed from both the linear as well as non-linear models that amount of cement, accelerator, and testing time have some positive contributions, whereas cement-to-water ratio has negative contribution to both the above responses. Compression strength was found to have linear relationship with the amount of cement and accelerator, and non-linear relationship with the remaining process parameters. Mould hardness was seen to vary linearly with testing time and non-linearly with the other parameters. Analysis of variance (ANOVA) was performed to test statistical adequacy of the models. Twenty random test cases were considered to test and compare their performances. Non-linear regression models were found to perform better than the linear models for both the responses. An attempt was also made to express compression strength of the moulding sand system as a function of mould hardness.
Linear System Models for Ultrasonic Imaging: Application to Signal Statistics
Zemp, Roger J.; Abbey, Craig K.; Insana, Michael F.
2009-01-01
Linear equations for modeling echo signals from shift-variant systems forming ultrasonic B-mode, Doppler, and strain images are analyzed and extended. The approach is based on a solution to the homogeneous wave equation for random inhomogeneous media. When the system is shift-variant, the spatial sensitivity function—defined as a spatial weighting function that determines the scattering volume for a fixed point of time—has advantages over the point-spread function traditionally used to analyze ultrasound systems. Spatial sensitivity functions are necessary for determining statistical moments in the context of rigorous image quality assessment, and they are time-reversed copies of point-spread functions for shift variant systems. A criterion is proposed to assess the validity of a local shift-invariance assumption. The analysis reveals realistic situations in which in-phase signals are correlated to the corresponding quadrature signals, which has strong implications for assessing lesion detectability. Also revealed is an opportunity to enhance near- and far-field spatial resolution by matched filtering unfocused beams. The analysis connects several well-known approaches to modeling ultrasonic echo signals. PMID:12839176
Numerical Study of Concentration Characteristics of Linear Fresnel Reflector System
Energy Technology Data Exchange (ETDEWEB)
Lee, Hyun Jin [Kookmin Univ., Seoul (Korea, Republic of); Kim, Jong Kyu; Lee, Sang Nam [Korea Institute of Energy Research, Daejeon (Korea, Republic of)
2015-12-15
In this study, we numerically investigated the concentration characteristics of a linear Fresnel reflector system that can drive a solar thermal absorption refrigeration system to be installed in Saudi Arabia. Using an optical modeling program based on the Monte Carlo ray-tracing method, we simulated the concentrated solar flux, concentration efficiency, and concentrated solar energy on four representative days of the year - the vernal equinox, summer solstice, autumnal equinox, and winter solstice. Except the winter solstice, the concentrations were approximately steady from 9 AM to 15 PM, and the concentration efficiencies exceed 70%. Moreover, the maximum solar flux around the solar receiver center changes only within the range of 13.0 - 14.6 kW/m{sup 2}. When we investigated the effects of the receiver installation height, reflector width, and reflector gap, the optimal receiver installation height was found to be 5 m. A smaller reflector width had a greater concentration efficiency. However, the design of the reflector width should be based on the capacity of the refrigeration system because it dominantly affects the concentrated solar energy. The present study was an essential prerequisite for thermal analyses of the solar receiver. Thus, an optical-thermal integration study in the future will assist with the performance prediction and design of the entire system.
Versatile Low Level RF System For Linear Accelerators
Potter, James M.
2011-06-01
The Low Level RF (LLRF) system is the source of all of the rf signals required for an rf linear accelerator. These signals are amplified to drive accelerator and buncher cavities. It can even provide the synchronizing signal for the rf power for a synchrotron. The use of Direct Digital Synthesis (DDS) techniques results in a versatile system that can provide multiple coherent signals at the same or different frequencies with adjustable amplitudes and phase relations. Pulsing the DDS allows rf switching with an essentially infinite on/off ratio. The LLRF system includes a versatile phase detector that allows phase-locking the rf frequency to a cavity at any phase angle over the full 360° range. With the use of stepper motor driven slug tuners multiple cavity resonant frequencies can be phase locked to the rf source frequency. No external phase shifters are required and there is no feedback loop phase setup required. All that is needed is to turn the frequency feedback on. The use of Digital Signal Processing (DSP) allows amplitude and phase control over the entire rf pulse. This paper describes the basic principles of a LLRF system that has been used for both proton accelerators and electron accelerators, including multiple tank accelerators, sub-harmonic and fundamental bunchers, and synchrotrons.
Integrability of Quadratic Non-autonomous Quantum Linear Systems
Lopez, Raquel
The Quantum Harmonic Oscillator is one of the most important models in Quantum Mechanics. Analogous to the classical mass vibrating back and forth on a spring, the quantum oscillator system has attracted substantial attention over the years because of its importance in many advanced and difficult quantum problems. This dissertation deals with solving generalized models of the time-dependent Schrodinger equation which are called generalized quantum harmonic oscillators, and these are characterized by an arbitrary quadratic Hamiltonian of linear momentum and position operators. The primary challenge in this work is that most quantum models with timedependence are not solvable explicitly, yet this challenge became the driving motivation for this work. In this dissertation, the methods used to solve the time-dependent Schrodinger equation are the fundamental singularity (or Green's function) and the Fourier (eigenfunction expansion) methods. Certain Riccati- and Ermakov-type systems arise, and these systems are highlighted and investigated. The overall aims of this dissertation are to show that quadratic Hamiltonian systems are completely integrable systems, and to provide explicit approaches to solving the time-dependent Schr¨odinger equation governed by an arbitrary quadratic Hamiltonian operator. The methods and results established in the dissertation are not yet well recognized in the literature, yet hold for high promise for further future research. Finally, the most recent results in the dissertation correspond to the harmonic oscillator group and its symmetries. A simple derivation of the maximum kinematical invariance groups of the free particle and quantum harmonic oscillator is constructed from the view point of the Riccati- and Ermakov-type systems, which shows an alternative to the traditional Lie Algebra approach. To conclude, a missing class of solutions of the time-dependent Schrodinger equation for the simple harmonic oscillator in one dimension is
Linear Temporal Logic (LTL) Based Monitoring of Smart Manufacturing Systems
Heddy, Gerald; Huzaifa, Umer; Beling, Peter; Haimes, Yacov; Marvel, Jeremy; Weiss, Brian; LaViers, Amy
2017-01-01
The vision of Smart Manufacturing Systems (SMS) includes collaborative robots that can adapt to a range of scenarios. This vision requires a classification of multiple system behaviors, or sequences of movement, that can achieve the same high-level tasks. Likewise, this vision presents unique challenges regarding the management of environmental variables in concert with discrete, logic-based programming. Overcoming these challenges requires targeted performance and health monitoring of both the logical controller and the physical components of the robotic system. Prognostics and health management (PHM) defines a field of techniques and methods that enable condition-monitoring, diagnostics, and prognostics of physical elements, functional processes, overall systems, etc. PHM is warranted in this effort given that the controller is vulnerable to program changes, which propagate in unexpected ways, logical runtime exceptions, sensor failure, and even bit rot. The physical component’s health is affected by the wear and tear experienced by machines constantly in motion. The controller’s source of faults is inherently discrete, while the latter occurs in a manner that builds up continuously over time. Such a disconnect poses unique challenges for PHM. This paper presents a robotic monitoring system that captures and resolves this disconnect. This effort leverages supervisory robotic control and model checking with linear temporal logic (LTL), presenting them as a novel monitoring system for PHM. This methodology has been demonstrated in a MATLAB-based simulator for an industry inspired use-case in the context of PHM. Future work will use the methodology to develop adaptive, intelligent control strategies to evenly distribute wear on the joints of the robotic arms, maximizing the life of the system. PMID:28730154
Modeling and control of switching max-plus-linear systems with random and deterministic switching
Van den Boom, T.J.J.; De Schutter, B.
2012-01-01
Switching max-plus-linear (SMPL) systems are discrete-event systems that can switch between different modes of operation. In each mode the system is described by a max-plus-linear state equation and a max-plus-linear output equation, with different system matrices for each mode. The switching may
Modeling and control of switching max-plus-linear systems with random and deterministic switching
Van den Boom, T.J.J.; De Schutter, B.
2012-01-01
Switching max-plus-linear (SMPL) systems are discrete-event systems that can switch between different modes of operation. In each mode the system is described by a max-plus-linear state equation and a max-plus-linear output equation, with different system matrices for each mode. The switching may de
Evaluation of beach cleanup effects using linear system analysis.
Kataoka, Tomoya; Hinata, Hirofumi
2015-02-15
We established a method for evaluating beach cleanup effects (BCEs) based on a linear system analysis, and investigated factors determining BCEs. Here we focus on two BCEs: decreasing the total mass of toxic metals that could leach into a beach from marine plastics and preventing the fragmentation of marine plastics on the beach. Both BCEs depend strongly on the average residence time of marine plastics on the beach (τ(r)) and the period of temporal variability of the input flux of marine plastics (T). Cleanups on the beach where τ(r) is longer than T are more effective than those where τ(r) is shorter than T. In addition, both BCEs are the highest near the time when the remnants of plastics reach the local maximum (peak time). Therefore, it is crucial to understand the following three factors for effective cleanups: the average residence time, the plastic input period and the peak time.
IS IT PSYCHOLOGY ABOUT LINEAR OR DYNAMIC SYSTEMS?
Directory of Open Access Journals (Sweden)
Dana BALAS-TIMAR
2014-06-01
Full Text Available Advances in Physics and Mathematics have proven that our complex world does not obey anymore the standard linear modelling systems rules. This paradigm seems to take over much of the scientific research in all sciences. Psychologists, no matter what their orientation is, are striving to create global models that can explain and predict human behaviour and emotions. In this quest, there have been elaborated many meta-analyses that gather relevant findings in order to create a conceptual framework of understanding human behaviour and affect. This paper presents arguments for sustaining the curvilinear relationships hypothesis that occur between variables (job satisfaction, job performance, age in an organizational context research. Conclusions set up a new conceptualization of the variable dynamic relationship inferences in Psychology.
Hitting probabilities for non-linear systems of stochastic waves
Dalang, Robert C
2012-01-01
We consider a $d$-dimensional random field $u = \\{u(t,x)\\}$ that solves a non-linear system of stochastic wave equations in spatial dimensions $k \\in \\{1,2,3\\}$, driven by a spatially homogeneous Gaussian noise that is white in time. We mainly consider the case where the spatial covariance is given by a Riesz kernel with exponent $\\beta$. Using Malliavin calculus, we establish upper and lower bounds on the probabilities that the random field visits a deterministic subset of $\\IR^d$, in terms, respectively, of Hausdorff measure and Newtonian capacity of this set. The dimension that appears in the Hausdorff measure is close to optimal, and shows that when $d(2-\\beta) > 2(k+1)$, points are polar for $u$. Conversely, in low dimensions $d$, points are not polar. There is however an interval in which the question of polarity of points remains open.
Method and system for non-linear motion estimation
Lu, Ligang (Inventor)
2011-01-01
A method and system for extrapolating and interpolating a visual signal including determining a first motion vector between a first pixel position in a first image to a second pixel position in a second image, determining a second motion vector between the second pixel position in the second image and a third pixel position in a third image, determining a third motion vector between one of the first pixel position in the first image and the second pixel position in the second image, and the second pixel position in the second image and the third pixel position in the third image using a non-linear model, determining a position of the fourth pixel in a fourth image based upon the third motion vector.
Compressive System Identification in the Linear Time-Invariant framework
Toth, Roland
2011-12-01
Selection of an efficient model parametrization (model order, delay, etc.) has crucial importance in parametric system identification. It navigates a trade-off between representation capabilities of the model (structural bias) and effects of over-parametrization (variance increase of the estimates). There exists many approaches to this widely studied problem in terms of statistical regularization methods and information criteria. In this paper, an alternative ℓ 1 regularization scheme is proposed for estimation of sparse linear-regression models based on recent results in compressive sensing. It is shown that the proposed scheme provides consistent estimation of sparse models in terms of the so-called oracle property, it is computationally attractive for large-scale over-parameterized models and it is applicable in case of small data sets, i.e., underdetermined estimation problems. The performance of the approach w.r.t. other regularization schemes is demonstrated in an extensive Monte Carlo study. © 2011 IEEE.
Practical Implementations of Advanced Process Control for Linear Systems
DEFF Research Database (Denmark)
Knudsen, Jørgen K . H.; Huusom, Jakob Kjøbsted; Jørgensen, John Bagterp
2013-01-01
Most advanced process control systems are based on Model Predictive Control (MPC). In this paper we discuss three critical issues for the practical implementation of linear MPC for process control applications. The rst issue is related to oset free control and disturbance models; the second issue...... implications for process control. If the control and evaluation intervals are chosen too short, the predicted behaviour of the controllers may have unstable characteristics. Depending of the degrees of freedom, oset-free control of a number of the controlled variables can be achieved by introduction of noise...... models and integration of the innovation errors. If the disturbances increases, oset-free control cannot be achieved without violation of process constraints. A target calculation function is used to calculate the optimal achievable target for the process. The use of soft constraints for process output...
Convergence results on iteration algorithms to linear systems.
Wang, Zhuande; Yang, Chuansheng; Yuan, Yubo
2014-01-01
In order to solve the large scale linear systems, backward and Jacobi iteration algorithms are employed. The convergence is the most important issue. In this paper, a unified backward iterative matrix is proposed. It shows that some well-known iterative algorithms can be deduced with it. The most important result is that the convergence results have been proved. Firstly, the spectral radius of the Jacobi iterative matrix is positive and the one of backward iterative matrix is strongly positive (lager than a positive constant). Secondly, the mentioned two iterations have the same convergence results (convergence or divergence simultaneously). Finally, some numerical experiments show that the proposed algorithms are correct and have the merit of backward methods.
A fault detection and isolation filter for discrete linear systems.
Giovanini, L; Dondo, R
2003-10-01
The problem of fault and/or abrupt disturbances detection and isolation for discrete linear systems is analyzed in this work. A strategy for detecting and isolating faults and/or abrupt disturbances is presented. The strategy is an extension of an already existing result in the continuous time domain to the discrete domain. The resulting detection algorithm is a Kalman filter with a special structure. The filter generates a residuals vector in such a way that each element of this vector is related with one fault or disturbance. Therefore the effects of the other faults, disturbances, and measurement noises in this element are minimized. The necessary stability and convergence conditions are briefly exposed. A numerical example is also presented.
IMPROVING THE PERFORMANCE OF THE LINEAR SYSTEMS SOLVERS USING CUDA
Directory of Open Access Journals (Sweden)
BOGDAN OANCEA
2012-05-01
Full Text Available Parallel computing can offer an enormous advantage regarding the performance for very large applications in almost any field: scientific computing, computer vision, databases, data mining, and economics. GPUs are high performance many-core processors that can obtain very high FLOP rates. Since the first idea of using GPU for general purpose computing, things have evolved and now there are several approaches to GPU programming: CUDA from NVIDIA and Stream from AMD. CUDA is now a popular programming model for general purpose computations on GPU for C/C++ programmers. A great number of applications were ported to CUDA programming model and they obtain speedups of orders of magnitude comparing to optimized CPU implementations. In this paper we present an implementation of a library for solving linear systems using the CCUDA framework. We present the results of performance tests and show that using GPU one can obtain speedups of about of approximately 80 times comparing with a CPU implementation.
Robust mean field games for coupled Markov jump linear systems
Moon, Jun; Başar, Tamer
2016-07-01
We consider robust stochastic large population games for coupled Markov jump linear systems (MJLSs). The N agents' individual MJLSs are governed by different infinitesimal generators, and are affected not only by the control input but also by an individual disturbance (or adversarial) input. The mean field term, representing the average behaviour of N agents, is included in the individual worst-case cost function to capture coupling effects among agents. To circumvent the computational complexity and analyse the worst-case effect of the disturbance, we use robust mean field game theory to design low-complexity robust decentralised controllers and to characterise the associated worst-case disturbance. We show that with the individual robust decentralised controller and the corresponding worst-case disturbance, which constitute a saddle-point solution to a generic stochastic differential game for MJLSs, the actual mean field behaviour can be approximated by a deterministic function which is a fixed-point solution to the constructed mean field system. We further show that the closed-loop system is uniformly stable independent of N, and an approximate optimality can be obtained in the sense of ε-Nash equilibrium, where ε can be taken to be arbitrarily close to zero as N becomes sufficiently large. A numerical example is included to illustrate the results.