Optimal control of a class of deterministic switched systems
一类有限时间切换系统的最优控制问题

A class of deterministic switched control problems with end-point constraint in finite horizon is addressed. An end-point constraint makes the value-functions being not differentiable everywhere or even discontinuous. As a result, the former conclusion that the value-functions for infinite horizon are the unique viscosity solutions to a Bensoussan-Lions type quasi-variational inequality(QVI) is no longer valid. We extend the viscosity solutions to the lower semi-continuous case by using the dynamic programming and the viability theory.