Learning Lyapunov (Potential) Functions from Counterexamples and Demonstrations

Authors: Hadi Ravanbakhsh, Sriram Sankaranarayanan

We present a technique for learning control Lyapunov (potential)functions, which are used in turn to synthesize controllersfor nonlinear dynamical systems. The learning framework uses ademonstrator that implements a black-box, untrusted strategypresumed to solve the problem of interest, a learner thatposes finitely many queries to the demonstrator to infer a candidatefunction and a verifier that checks whether the currentcandidate is a valid control Lyapunov function. The overall learningframework is iterative, eliminating a set of candidates on eachiteration using the counterexamples discovered by the verifier andthe demonstrations over these counterexamples. We prove itsconvergence using ellipsoidal approximation techniques from convexoptimization. We also implement this scheme using nonlinear MPCcontrollers to serve as demonstrators for a set of state andtrajectory stabilization problems for nonlinear dynamical systems. Ourapproach is able to synthesize relatively simple polynomial controlLyapunov functions, and in that process replace the MPC using aguaranteed and computationally less expensive controller.