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

Access to Document

10.1137/050630131

Cite this

@article{51d1f50325ad4dd396df644c4d6b8290,

title = "Optimal control of hybrid systems and a system of quasi-variational inequalities",

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.",

keywords = "Comparison theorem, Dynamic programming, Hybrid dynamical systems, Optimal control, System of quasi-variational inequalities, Viscosity solutions",

author = "Huan Zhang and James, \{Matthew R.\}",

year = "2006",

doi = "10.1137/050630131",

language = "English",

volume = "45",

pages = "722--761",

journal = "SIAM Journal on Control and Optimization",

issn = "0363-0129",

publisher = "Society for Industrial and Applied Mathematics Publications",

number = "2",

}

TY - JOUR

T1 - Optimal control of hybrid systems and a system of quasi-variational inequalities

AU - Zhang, Huan

AU - James, Matthew R.

PY - 2006

Y1 - 2006

N2 - 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.

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.

KW - Comparison theorem

KW - Dynamic programming

KW - Hybrid dynamical systems

KW - Optimal control

KW - System of quasi-variational inequalities

KW - Viscosity solutions

UR - https://www.scopus.com/pages/publications/33947281595

U2 - 10.1137/050630131

DO - 10.1137/050630131

M3 - Article

SN - 0363-0129

VL - 45

SP - 722

EP - 761

JO - SIAM Journal on Control and Optimization

JF - SIAM Journal on Control and Optimization

IS - 2

ER -

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

Abstract

Access to Document

Other files and links

Fingerprint

Cite this