Trajectory-based controller design for hybrid systems with affine continuous dynamics

In this paper we propose a method for feedback controller synthesis using the concept of control autobisimulation function. Control autobisimulation function (CAF) is the analog of control Lyapunov function for approximate bisimulation. Approximate bisimulation has been used to establish robustness (in ℓ_∞ sense) of execution trajectories of dynamical systems and hybrid systems, resulting in trajectory-based safety verification procedures. CAF is used to characterize the family of all feedback control laws that result in a close loop system with an autobisimulation function. Further, we use a heuristic potential function based idea to construct a safe feedback control law for a nominal initial state, and use the trajectory-robustness property to guarantee that the control law is also safe for other initial states in a neighborhood of the nominal initial state.