Subsystem-level optimal control of weakly coupled linear stochastic systems composed ofN subsystems

Lim, Myo Taeg; Gajić, Zoran

doi:10.1002/(sici)1099-1514(199903/04)20:2<93::aid-oca648>3.0.co;2-g

Cited by 13 publications

(4 citation statements)

References 20 publications

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“…It should be noted that the assumption of this structure is also made in [4,5,6]. Using the implicit function theorem, let us prove the existence of the implicit functions P i = P i (ε) and P 12 = P 12 (ε) of ε such that…”

Section: Lemma 1 Under Assumption 1 There Exists An Admissible Contrmentioning

confidence: 99%

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Numerical computation for H∞ output feedback control for strongly coupled large-scale systems

Mukaidani

2008

Applied Mathematics and Computation

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In this paper, H∞ output feedback control for strongly coupled large-scale systems are discussed. When the positive coupling parameter ε which connect the other subsystems is large, a successive algorithm for solving the algebraic Riccati equations (ARE) is developed for the first time. Since the proposed algorithm is derived using Newton's method, it is noteworthy that the quadratic convergence and uniqueness of the obtained solution are both guaranteed for strongly coupled parameter ε. Moreover, in order to reduce the computation in the resulting Newton's method, the gradient-based iterative (GI) algorithm is combined. As a result, it is shown that the reduced-order computation is attained. Finally, in order to demonstrate the efficiency of the proposed algorithms, computational examples are provided.

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Section: Lemma 1 Under Assumption 1 There Exists An Admissible Contrmentioning

confidence: 99%

“…For large-scale systems, the stability analysis and control and filtering problems have been investigated extensively (see e.g., [4,5,6]). In practice, it is known that such systems are represented by multiarea power systems [4], distillation columns [5], and cold rolling [6]. They are widely used to represent system dynamics.…”

Section: Introductionmentioning

confidence: 99%

Numerical computation for H∞ output feedback control for strongly coupled large-scale systems

Mukaidani

2008

Applied Mathematics and Computation

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“…The control problems of weakly coupled large-scale systems have been studied by several researchers (see [3], [4] and references therein). In practice, it is known that such systems are represented by multi-area power systems [3], distillation columns [11] and cold-rolling mills [12]. They are widely used to represent the system dynamics.…”

Section: Introductionmentioning

confidence: 99%

Efficient Numerical Computations of Soft Constrained Nash Strategy for Weakly Coupled Large-Scale Systems

Sagara¹,

Mukaidani²,

Yamamoto³

2008

JCP

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In this paper, a high-order soft constrained Nash strategy for weakly coupled large-scale systems is investigated. In order to solve the cross-coupled sign-indefinite algebraic Riccati equations (CSAREs) corresponding to strategy, the iterative algorithm on the basis of the Newton’s method is first applied. Second, the recursive algorithm for solving the CSAREs is also established to reduce the amount of algebraic computation as compared with the Newton’s method. Using these iterative solutions, a highorder soft-constrained Nash strategy is designed. As a result, it is proved that the proposed high-order approximate equilibrium strategies achieve better performance. Finally, in order to demonstrate the efficiency of the algorithm, a numerical example is given.

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“…In [6], a controllable set of a class of nonlinear stochastic control systems was characterized using optimal control theory of diffusion processes. Linear-quadratic optimal control and filtering problems have been solved for linear, weakly coupled continuous stochastic systems composed of N subsystems in [7]. Delay-dependent stability in the mean-square sense has been studied for stochastic systems with time-varying delays, Markovian switching and nonlinearities in article [8].…”

mentioning

confidence: 99%

Optimal stabilizing controllers for linear discrete‐time stochastic systems

Feng

Lam

et al. 2007

Optim Control Appl Methods

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The relationship between the spectral radius and the decay rate for discrete stochastic systems is investigated. Several equivalent conditions are obtained, which guarantee a specified decay rate of the closed-loop systems. Based on the relationship, this paper provides a design method for state feedback controllers, which ensure that the closed-loop systems converge as fast as possible. Finally, a numerical example is used to illustrate the developed method.where the diffusion term in dynamics depends on both the state and the control variables. The H ∞ model reduction problem was studied in [5] for both continuous and discrete stochastic systems, in which necessary and sufficient conditions for the solvability of the problem were obtained in terms of LMIs and a coupling non-convex rank constraint. In [6], a controllable set of a class of nonlinear stochastic control systems was characterized using optimal control theory of diffusion processes. Linear-quadratic optimal control and filtering problems have been solved for linear, weakly coupled continuous stochastic systems composed of N subsystems in [7]. Delay-dependent stability in the mean-square sense has been studied for stochastic systems with time-varying delays, Markovian switching and nonlinearities in article [8]. Basic theory and applications can be found in the book by Meyn and Tweedie [9] on Markov chains evolving in discrete time and on general state spaces.Stability and stabilization of stochastic systems have been studied extensively by many researchers. Some necessary and sufficient conditions were obtained via stochastic algebraic Riccati equations and LMIs in [4,10]. The problems of absolute stabilization and minimax control were investigated in [11] in the context of uncertain stochastic systems, while the issue of decentralized stabilization for a class of interconnected stochastic nonlinear systems was addressed in [12]. Characterizations of stability radii of a stable linear stochastic Itô system with respect to structured multi-perturbations were presented in [13]. Four types of definitions of exponential stability in the mean square are discussed for a more general class of discrete-time linear stochastic systems in [14], and they are equivalent for the system considered in this paper.This paper is organized as follows. Section 2 describes the problem studied in this paper, and some necessary lemmas are also introduced in this section. Section 3 investigates the equivalent relationship between the spectral radius and the decay rate. It can be explained that the spectral radius is associated with the decay rate in the sense of convergence speed. Based on this result, an optimal controller is designed. Finally, Section 4 presents an illustrative example and Section 5 concludes the paper.Notation: Throughout this paper, R n , C n , R m×n and C m×n are, respectively, the n-dimensional Euclidean space, the n-dimensional complex vector space, the set of all m ×n real matrices and the set of all m ×n complex matrices. N denotes the set of natura...

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Subsystem-level optimal control of weakly coupled linear stochastic systems composed ofN subsystems

Cited by 13 publications

References 20 publications

Numerical computation for H∞ output feedback control for strongly coupled large-scale systems

Numerical computation for H∞ output feedback control for strongly coupled large-scale systems

Efficient Numerical Computations of Soft Constrained Nash Strategy for Weakly Coupled Large-Scale Systems

Optimal stabilizing controllers for linear discrete‐time stochastic systems

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