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The hybrid optimal control problem with reach time to a target set isaddressed and the continuity and uniqueness of the associated value function isproved. Hybrid systems involves interaction of different types of dynamics:continuous and discrete dynamics. The state ofa continuous system is evolved byan ordinary differential equation until the trajectory hits the predefined jumpsets: an autonomous jump set and a controlled jump set . At each jump thetrajectory is moved discontinuously to another Euclidean space by a discretesystem. We study the hybrid optimal control problem with reach time to a targetset, prove the continuity of the associated value function with respect to theinitial point under the assumption that is lower semicontinuous on the boundaryof a target set, and also characterize it as an unique solution of aquasi-variational inequality in a viscosity sense using the dynamic programmingprinciple.

The continuity and uniqueness of the value function of the hybrid optimal control problem with reach time to a target set