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Hybrid control and dynamic programming. (English) Zbl 0897.49022
Quasi-variational inequalities are used to present a unified model of hybrid control, including most of the known cases with complete information. Dynamic programming and viscosity solutions are the main tools used in this approach. Autonomous and controlled jumps/switching are modeled, with or without time-delay. Under suitable conditions existence and continuous dependency on the data are proved for the trajectories. Next a characterization of the value function is given.
MSC:
49N25Impulsive optimal control problems
49L20Dynamic programming method (infinite-dimensional problems)
49J40Variational methods including variational inequalities
49L25Viscosity solutions (infinite-dimensional problems)
93C15Control systems governed by ODE