有限时区非线性系统的最优切换控制

数学季刊 ›› 2006, Vol. 21 ›› Issue (2): 185-195.

有限时区非线性系统的最优切换控制

Department of Mathematics, University of Zhengzhou, Zhengzhou 450052, China

收稿日期:2005-06-08 出版日期:2006-06-30 发布日期:2023-12-05
作者简介:MU Xiao-wu(1963-),male,native of Wenxian,Henan,a professor of Zhengzhou University, Ph.D.,engagas in nonlinear systems
基金资助:
Supported by the SRFEB of Henan Province(2003110002)；

Optimal Switching Control for Nonlinear Systems in A Finite Duration

Department of Mathematics, University of Zhengzhou, Zhengzhou 450052, China

Received:2005-06-08 Online:2006-06-30 Published:2023-12-05
About author:MU Xiao-wu(1963-),male,native of Wenxian,Henan,a professor of Zhengzhou University, Ph.D.,engagas in nonlinear systems
Supported by:
Supported by the SRFEB of Henan Province(2003110002)；

摘要/Abstract

摘要： This paper proposes a optimal control problem for a general nonlinear systems with finitely many admissible control settings and with costs assigned to switching of controls. With dynamic programming and viscosity solution theory we show that the switching lower-value function is a viscosity solution of the appropriate systems of quasi-variational inequalities(the appropriate generalization of the Hamilton-Jacobi equation in this context) and that the minimal such switching-storage function is equal to the continuous switching lower-value for the game. With the lower value function a optimal switching control is designed for minimizing the cost of running the systems.

关键词: switching , systems;optimal , control;viscosity , solution;value , function;cost function

Abstract: This paper proposes a optimal control problem for a general nonlinear systems with finitely many admissible control settings and with costs assigned to switching of controls. With dynamic programming and viscosity solution theory we show that the switching lower-value function is a viscosity solution of the appropriate systems of quasi-variational inequalities(the appropriate generalization of the Hamilton-Jacobi equation in this context) and that the minimal such switching-storage function is equal to the continuous switching lower-value for the game. With the lower value function a optimal switching control is designed for minimizing the cost of running the systems.

Key words: switching , systems;optimal , control;viscosity , solution;value , function;cost function

中图分类号:

O231.2

慕小武, 刘海军. 有限时区非线性系统的最优切换控制[J]. 数学季刊, 2006, 21(2): 185-195.

MU Xiao-wu, LIU Hai-jun . Optimal Switching Control for Nonlinear Systems in A Finite Duration[J]. Chinese Quarterly Journal of Mathematics, 2006, 21(2): 185-195.

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