乘性噪声和多重时滞下离散奇异系统的最优控制

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中图分类号：TP13 文献标识码：A

Optimal Control for Discrete-time Singular Systems with Multiplicative Noise and Multiple Time Delays

KONG Xiangtong，QIU Yongxin，LIU Zhenbing，XIE Jing （School of Information and Control Engineering，Qingdao University of Technology，Qingdao 26652o，China）

Abstract： Due to the presence of the singular matrix in discrete-time singular systems， state variables cannot be directly updated，which makes the traditional optimal control method diffcult to apply directly. This paper investigates the finite-horizon linear quadratic optimal control problem for discrete-time singular systems with stochastic multiplicative noise and multiple input delays. To address this issue，the paper constructs an augmented matrix to transform the discrete singular stochastic system with multiple time delays into a standard discrete stochastic system while ensuring its regularity and causality. Then， based on the maximum principle，the optimal control conditions are derived，and the optimal control law and minimum cost function are obtained using coupled Riccati difference equations. Finally，simulation results demonstrate that under the influence of random disturbances and input delays，the proposed method effectively stabilizes the system state，verifying its effectiveness.

Keywords： discrete-time singular system； linear quadratic optimal control; multiple time delays; coupled Riccati difference equation

最优控制理论在最省燃料控制系统、线性调节器、电力系统控制等方面应用广泛[1-4]。（剩余6481字）