2016/07/31 by Myong-Song Ho, Ho, Myong-Song, Kwang-Nam Oh +3
Computer Science · Engineering · Mathematics · #Advanced Control Systems Optimization #Aerospace Engineering and Control Systems #Artificial intelligence #Bellman equation #Computer science #Control (management) #Control theory (sociology) #FOS: Electrical engineering #FOS: Mathematics #Function (biology) #Mathematical analysis #Mathematical optimization #Mathematics #Optimal control #Optimization and Control (math.OC) #Optimization and Variational Analysis #Set (abstract data type) #Statistics #Systems and Control (eess.SY) #Uniqueness #Value (mathematics) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1608.00828
published in arXiv (Cornell University) (Cornell University)
openalex publication_date 2016/07/31 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
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.