| 有限时区非线性系统的最优切换控制 |
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| 引用本文： | 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. |
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| 作者姓名： | 慕小武 刘海军 |
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| 作者单位： | Department of Mathematics，University of Zhengzhou，Zhengzhou 450052，China |
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| 基金项目： | Supported by the SRFEB of Henan Province(2003110002) |
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| 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.
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| 关 键 词： | 开关系统 最佳控制 粘度解 价值函数 成本函数 |
Optimal Switching Control for Nonlinear Systems in A Finite Duration |
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| 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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| Authors: | MU Xiao-wu LIU Hai-jun |
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| Institution: | Department of Mathematics, University of Zhengzhou, Zhengzhou 450052, China |
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| 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. |
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| Keywords: | switching systems optimal control viscosity solution value function cost function |
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