Optimal control of hybrid systems and a system of quasi-variational inequalities

Huan Zhang; Matthew R. James

doi:10.1137/050630131

Optimal control of hybrid systems and a system of quasi-variational inequalities

Huan Zhang, Matthew R. James^*

^*Corresponding author for this work

Research output: Contribution to journal › Article › peer-review

18 Citations (Scopus)

Abstract

Optimal control of a. class of hybrid dynamical systems is studied using the method of dynamic programming. It is proved that the value function is a discontinuous viscosity solution of the corresponding Hamilton-Jacobi-Bellman (HJB) equation which appears as a system of quasi-variational inequalities (SQVI) coupled by a nonlocal operator with a variable boundary condition. The comparison theorems are established for the sub- and super-solutions of the SQVI.

Original language	English
Pages (from-to)	722-761
Number of pages	40
Journal	SIAM Journal on Control and Optimization
Volume	45
Issue number	2
DOIs	https://doi.org/10.1137/050630131
Publication status	Published - 2006

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10.1137/050630131

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AB - Optimal control of a. class of hybrid dynamical systems is studied using the method of dynamic programming. It is proved that the value function is a discontinuous viscosity solution of the corresponding Hamilton-Jacobi-Bellman (HJB) equation which appears as a system of quasi-variational inequalities (SQVI) coupled by a nonlocal operator with a variable boundary condition. The comparison theorems are established for the sub- and super-solutions of the SQVI.

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KW - Dynamic programming

KW - Hybrid dynamical systems

KW - Optimal control

KW - System of quasi-variational inequalities

KW - Viscosity solutions

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JF - SIAM Journal on Control and Optimization

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ER -

Optimal control of hybrid systems and a system of quasi-variational inequalities

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