Pareto optimal control of linear Markov jump stochastic systems
WANG Le
CUI Kai
JIANG Xiu-shan
ZHAO Dong-ya
ZHANG Wei-hai
Abstract：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 indi-cators 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 Itô 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.
Keywords：Markov jumpstochastic systemsPareto controloptimal control systems
Publication Date：2025-01-27
Online Publishing Date：2025-08-15(First online date of this platform, not the publication date of the document)
Pages：8( 59-66 )