Robust Controller Synthesis for Hybrid Systems Using Modal Logic

In this paper, we formulate and robustly solve a quite general class of hybrid controller synthesis problems. The type of controller we investigate is the switching control mechanism of a hybrid automaton (via guard and mode invariant sets), and the robustness result is with respect to variations in the right hand sides of the differential equations that depend continuously on a parameter. We present a novel methodology for controller design and synthesis which uses modal logic as a formalism for reasoning about sets of plant states, and various operators on sets arising from the differential equations and from metric tolerance relations on the state space.