Linear Quadratic Control of Continuous-time Singular Stochastic Affine Systems

Zhu Huai-nian; Zhang Cheng-ke; Cao Ming; Bin Ning

doi:10.3969/j.issn.1007-7162.2016.02.005

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Linear Quadratic Control of Continuous-time Singular Stochastic Affine Systems

更新时间：2026-05-27

- Linear Quadratic Control of Continuous-time Singular Stochastic Affine Systems
- Vol. 33, Issue 2, Pages: 24-30(2016)
- 作者机构：
- 作者简介：
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- DOI：10.3969/j.issn.1007-7162.2016.02.005
  CLC：
- Online First：23 March 2016，
  
  Published：2016
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朱怀念, 张成科, 曹铭, 宾宁. 广义随机仿射系统的线性二次控制[J]. 广东工业大学学报, 2016, 33(2): 24-30.

Zhu Huai-nian, Zhang Cheng-ke, Cao Ming, et al. Linear Quadratic Control of Continuous-time Singular Stochastic Affine Systems[J]. 2016, 33(2): 24-30.
朱怀念, 张成科, 曹铭, 宾宁. 广义随机仿射系统的线性二次控制[J]. 广东工业大学学报, 2016, 33(2): 24-30. DOI： 10.3969/j.issn.1007-7162.2016.02.005.

Zhu Huai-nian, Zhang Cheng-ke, Cao Ming, et al. Linear Quadratic Control of Continuous-time Singular Stochastic Affine Systems[J]. 2016, 33(2): 24-30. DOI： 10.3969/j.issn.1007-7162.2016.02.005.

摘要

研究了一类连续时间广义随机仿射系统的线性二次(Linear Quadratic

LQ)控制问题.在定义了广义随机系统稳定性的相关概念后，通过一个线性矩阵不等式(Linear Matrix Inequality

LMI)给出了系统稳定性的条件.然后，利用Riccati方程法分别研究了有限时间广义随机仿射系统的LQ问题和无限时间广义随机系统的LQ问题，得到了有限时间最优反馈控制的存在条件等价于一个推广的微分Riccati方程和一个推广的倒向微分方程存在解，而对应的无限时间最优反馈控制的存在条件等价于一个推广的代数Riccati方程存在解，同时给出了最优反馈控制的显式表达及最优性能指标值.

Abstract

Linear quadratic control of a class of continuous-time singular stochastic affine systems is investigated. After establishing some concepts of the stability for stochastic singular systems

the condition of the stability is presented by means of a linear matrix inequality. Then

by utilizing Riccati equation approach

the existent conditions of optimal feedback control in finite horizon and infinite horizon are respectively obtained by means of a generalized differential Riccati equation or a generalized algebraic Riccati equation. And explicit expressions of the optimal feedback controls and optimal cost function are given.

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