#### Reference

#### Abstract

We present a technique for learning control Lyapunov (potential) functions, which are used in turn to synthesize controllers
for nonlinear dynamical systems. The learning framework uses a *demonstrator* that implements a black-box, untrusted strategy presumed to solve the problem of interest, a *learner* that poses finitely many queries to the demonstrator to infer a candidate function and a *verifier* that checks whether the current candidate is a valid control Lyapunov function. The overall learning framework is iterative,
eliminating a set of candidates on each iteration using the counterexamples discovered by the verifier and the demonstrations
over these counterexamples. We prove its convergence using ellipsoidal approximation techniques from convex optimization.
We also implement this scheme using nonlinear MPC controllers to serve as demonstrators for a set of state and trajectory
stabilization problems for nonlinear dynamical systems. Our approach is able to synthesize relatively simple polynomial control
Lyapunov functions, and in that process replace the MPC using a guaranteed and computationally less expensive controller.

#### BibTeX

@string{RSS = " Robotics: Science and Systems (RSS)"} @inproceedings{clf-learning-rss17, author = {Hadi RavanbakhshSriram Sankaranarayanan}, title = {Learning Lyapunov (Potential) Functions from Counterexamples and Demonstrations}, booktitle = RSS, year = {2017}, }