引用本文:王乐,崔凯,蒋秀珊,赵东亚,张维海.线性Markov跳变随机系统的Pareto最优控制[J].控制理论与应用,2025,42(1):59~66.[点击复制]
WANG Le,CUI Kai,JIANG Xiu-shan,ZHAO Dong-ya,ZHANG Wei-hai.Pareto optimal control of linear Markov jump stochastic systems[J].Control Theory and Technology,2025,42(1):59~66.[点击复制]
线性Markov跳变随机系统的Pareto最优控制
Pareto optimal control of linear Markov jump stochastic systems
摘要点击 2742  全文点击 35  投稿时间:2023-01-14  修订日期:2024-11-10
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DOI编号  10.7641/CTA.2024.30019
  2025,42(1):59-66
中文关键词  Markov跳变  随机系统  Pareto控制  最优控制系统
英文关键词  Markov jump  stochastic systems  Pareto control  optimal control systems
基金项目  国家自然科学基金项目(62103442, 12326343, 62373229), 山东省自然科学基金项目(ZR2021QF080), 中央高校基本科研业务费专项资金项目 (23CX06024A), 山东省高校优秀青年创新团队项目(2023KJ061)资助.
作者单位邮编
王乐 中国石油大学(华东) 266580
崔凯 中国石油大学(华东) 266580
蒋秀珊* 中国石油大学(华东) 266580
赵东亚 中国石油大学(华东) 
张维海 山东科技大学 
中文摘要
      目前针对多个主体、多个目标的带有Markov跳变的线性随机系统的控制问题的研究较少且较为浅显. 本文研究了具有乘性噪声的连续时间线性Markov跳变随机系统的Pareto最优控制问题. 假设多个主体、多个性能指标由状态和控制变量中的二次部分和线性部分的线性组合而形成, 证明了Pareto最优与加权和优化之间的关系, 从而将多目标优化问题转化为特殊的单目标加权和最优控制问题. 基于Pareto博弈理论与广义Ito?公式, 系统的Pareto有效策略可以通过一组耦合的广义Riccati微分方程与一组耦合的线性微分方程求解, 并且可以得到每一个控制器的Pareto解. 最后, 本文通过数值仿真验证理论结果的有效性.
英文摘要
      At present, there is relatively little research on the control problem of linear stochastic systems with Markov jumps for multiple agents and objectives. This paper investigates the Pareto optimal control problem for continuous time linear Markov jump stochastic systems with multiplicative noise. Assuming that multiple entities and performance indicators are formed by a linear combination of the quadratic and linear parts of state and control variables, the relationship between Pareto optimality and weighted sum optimization is proved, thereby transforming multi-objective optimization into a special single objective weighted sum optimal control problem. Based on the Paret ogame theory and the generalized Ito formula, the Pareto effective strategy of the system can be obtained by a set of coupled generalized Riccati differential ? equations and a set of coupled linear differential equations, and under this strategy, the Pareto solution of each controller can be obtained. Finally, the validity of the theoretical results is verified by a numerical simulation.