Abstract
This paper discusses the optimal preview control problem for a class of linear continuous stochastic control systems in the infinite horizon, based on the augmented error system method. Firstly, an assistant system is designed and the state equation is translated to the assistant system. Then, an integrator is introduced to construct a stochastic augmented error system. As a result, the tracking problem is converted to a regulation problem. Secondly, the optimal regulator is solved based on dynamic programming principle for the stochastic system, and the optimal preview controller of the original system is obtained. Compared with the finite horizon, we simplify the performance index. We also study the stability of the stochastic augmented error system and design the observer for the original stochastic system. Finally, the simulation example shows the effectiveness of the conclusion in this paper.
Highlights
Future reference signals or disturbance signals are known in certain circumstances
We study the stability of the stochastic augmented error system and design the observer for the original stochastic system
All the known future information can be utilized by preview control theory to improve the performance of the dynamic system
Summary
Future reference signals or disturbance signals are known in certain circumstances. All the known future information can be utilized by preview control theory to improve the performance of the dynamic system. According to the maximum principle, the optimal preview controller was obtained by solving a differential equation on reference signals backward in time. This method was extended to systems with previewable disturbance signals in [11] and to singular continuous systems in [12]. The optimal regulator is obtained based on the dynamic programming principle for stochastic systems, which means the optimal preview controller of the original stochastic system is gained For such a system, when the integrator approaches zero at infinity, the error approaches zero. Due to the fact that the relative terms of reference signals are included in the stochastic augmented error system, the conclusion in the infinite horizon cannot be directly employed when solving the optimal regulation problem in this paper. Et0,x0 denotes the expectation of process (t, x) with initial time t0 and state x0. tr(⋅) denotes the trace of a matrix
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