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

Abstract

In this paper we introduce a transformation for the exact closed‐loop decomposition of the optimal control and Kalman filtering tasks of linear weakly coupled stochastic systems composed of N subsystems. In addition to having obtained N completely independent reduced‐order subsystem Kalman filters working in parallel, we have obtained the exact solution of the algebraic regulator and filter Riccati equations in terms of the solutions of the corresponding reduced‐order subsystem algebraic Riccati equations. The introduced transformation produces a lot of savings especially for on‐line computations since it allows parallel processing of information with lower‐order‐dimensional Kalman filters. The methodology presented is applied to a 17th‐order cold‐rolling mill. Copyright © 1999 John Wiley & Sons, Ltd.

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

“…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…”

“…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.…”

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

“…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…”

“…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.…”

Optimal stabilizing controllers for linear discrete‐time stochastic systems

“…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].…”

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

“…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.…”

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

“…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…”

“…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.…”

Optimal stabilizing controllers for linear discrete‐time stochastic systems

“…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].…”

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

“…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.…”

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

“…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…”

“…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.…”

Optimal stabilizing controllers for linear discrete‐time stochastic systems

“…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].…”

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

“…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.…”