Optimal control for a singularly perturbed linear stochastic system with multiplicative white noise perturbations and Markovian jumping

Abstract

Summary In this study, we investigate the optimal control of a class of singularly perturbed linear stochastic systems with Markovian jumping parameters. After establishing an asymptotic structure for the stabilizing solution of the coupled stochastic algebraic Riccati equations, a parameter‐independent composite controller is derived. Furthermore, the cost degradation in a reduced‐order controller is discussed. Thus, the exactness of the proposed approximate control is discussed for the first time. As an additional important contribution, a numerical algorithm for solving the coupled stochastic algebraic Riccati equations is proposed, and the feature of the resulting higher‐order controller is shown. Finally, a simple example is presented to demonstrate the validity of the proposed method. Copyright © 2016 John Wiley & Sons, Ltd.

Control Optimization of Stochastic Systems Based on Adaptive Correction CKF Algorithm

“…The linear stable feedback control of stochastic systems is carried out by using the antistable rate function, and the optimality of disturbance parameters is analyzed [11]. A control strategy based on coupled asymptotic structure is proposed for stochastic systems with multiplicative white noise disturbances [12]. A dynamic control mechanism of secondary load is proposed for stochastic systems with active demand response, which realizes real-time control of power equipment [13].…”