Viability theory
Lower semicontinuous solutions of Hamilton-Jacobi-Bellman equations
SIAM Journal on Control and Optimization
Dynamic Programming for Nonlinear Systems Driven by Ordinaryand Impulsive Controls
SIAM Journal on Control and Optimization
Nonsmooth analysis and control theory
Nonsmooth analysis and control theory
Proximal Analysis and the Minimal Time Function
SIAM Journal on Control and Optimization
Theorem of abstraction for equivalent controllers in hybrid systems
Information Sciences—Informatics and Computer Science: An International Journal
Theorem of abstraction for equivalent controllers in hybrid systems
Information Sciences: an International Journal
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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 m ay 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.