@article{Galbraith:2003,
author = {Galbraith, GN and Vinter, RB},
journal = {J DYN CONTROL SYST},
pages = {563--584},
title = {Optimal control of hybrid systems with an infinite set of discrete states},
volume = {9},
year = {2003}
}

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TY  - JOUR
AB  - Hybrid control systems are described by a family of continuous subsystems and a set of logic rules for switching between them. This paper concerns a broad class of optimization problems for hybrid systems, in which the continuous subsystems are modelled as differential inclusions. The formulation allows endpoint constraints and a general objective function that includes "transaction costs" associated with abrupt changes of discrete and continuous states, and terms associated with continuous control action as well as the terminal value of the continuous state. In consequence of the endpoint constraints, the value function may be discontinuous. It is shown that the collection of value functions (associated with all discrete states) is the unique lower semicontinuous solution of a system of generalized Bensoussan-Lions type quasi-variational inequalities, suitably interpreted for nondifferentiable, extended valued functions. It is also shown how optimal strategies and value functions are related. The proof techniques are system theoretic, i.e., based on the construction of state trajectories with suitable properties. A distinctive feature of the analysis is that it permits an infinite set of discrete states.
AU  - Galbraith,GN
AU  - Vinter,RB
EP  - 584
PY  - 2003///
SN  - 1079-2724
SP  - 563
TI  - Optimal control of hybrid systems with an infinite set of discrete states
T2  - J DYN CONTROL SYST
VL  - 9
ER  - 

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