Optimal control of discrete-time hybrid automata under safety and liveness constraints

In this contribution we address an optimal control problem for a class of discrete-time hybrid automata under safety and liveness constraints. The solution is based on a hierarchical decomposition of the problem, where the low-level controller enforces safety and liveness constraints while the high-level controller exploits the remaining degrees of freedom for performance optimization. Lower-level control is based on a discrete abstraction of the continuous dynamics. The action of low-level control can be interpreted as restricting invariants in the hybrid automaton representing the plant model. A state feedback solution for the high-level control is provided, based on the off-line construction of an appropriate partition of the state space.