2016/07/31 by Ho, Myong-Song, Oh, Kwang-Nam, Hwang, Chol-Jun
#FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · doi:10.48550/arxiv.1608.00828
The hybrid optimal control problem with reach time to a target set is addressed and the continuity and uniqueness of the associated value function is proved. Hybrid systems involves interaction of different types of dynamics: continuous and discrete dynamics. The state ofa continuous system is evolved by an ordinary differential equation until the trajectory hits the predefined jump sets: an autonomous jump set and a controlled jump set . At each jump the trajectory is moved discontinuously to another Euclidean space by a discrete system. We study the hybrid optimal control problem with reach time to a target set, prove the continuity of the associated value function with respect to the initial point under the assumption that is lower semicontinuous on the boundary of a target set, and also characterize it as an unique solution of a quasi-variational inequality in a viscosity sense using the dynamic programming principle.