Inductively Inferring Valid Logical Models of Continuous-State Dynamical Systems

Hybrid control systems consist of a discrete event (DES) controller supervising a continuousstate (CSS) plant. A controller can be synthesized by obtaining a DES controller for an equivalent DES representation (DES plant) of the CSS plant. An important issue concerns the logical invariance (stability) of DES plant transitions to variations in the initial CSS plant state. This paper provides a set of sufficient conditions for the existence of stable transitions in the DES plant. For CSS plants which are affine in their control policies, these conditions form a system of linear inequalities over the space of control vectors used by the CSS plant. Feasible points to this inequality system are inductively determined using a method of centers algorithm known as the ellipsoid method.