Regularity of optimal solutions and the optimal cost for hybrid dynamical systems via reachability analysis

For a general optimal control problem for dynamical systems with hybrid dynamics, we study the dependency of cost on perturbations to constraints and mappings. The former limits allowable values state, input, initial terminal condition, time, while latter is given by right-hand sides differential/difference inclusions defining as well functions functional We show that upper lower semicontinuous dependence solutions conditions – properties are captured outer inner well-posedness, respectively lead existence solution upper/lower semicontinuity cost. In particular, exploiting finite horizon reachable sets systems, varies semicontinuously when system well-posed, it well-posed an additional assumption requiring partial knowledge holds. Consequently, both aforementioned holds, continuously, vary outer/upper semicontinuously. further even in absence this solution-based assumption, (respectively, solutions) can be continuously semicontinuously) approximated. Results demonstrated examples, theoretically numerically.