Imitation Learning of Stabilizing Policies for Nonlinear Systems

TL;DR

This paper extends stabilizing imitation learning methods from linear to polynomial systems using sum of squares techniques, proposing algorithms and demonstrating their effectiveness through experiments.

Contribution

It introduces a novel extension of stabilizing imitation learning to polynomial systems via sum of squares methods, with practical algorithms and numerical validation.

Findings

Algorithms effectively stabilize polynomial systems

Sum of squares techniques enable extension from linear to nonlinear systems

Numerical experiments demonstrate practical performance

Abstract

There has been a recent interest in imitation learning methods that are guaranteed to produce a stabilizing control law with respect to a known system. Work in this area has generally considered linear systems and controllers, for which stabilizing imitation learning takes the form of a biconvex optimization problem. In this paper it is demonstrated that the same methods developed for linear systems and controllers can be readily extended to polynomial systems and controllers using sum of squares techniques. A projected gradient descent algorithm and an alternating direction method of multipliers algorithm are proposed as heuristics for solving the stabilizing imitation learning problem, and their performance is illustrated through numerical experiments.