Imitation Learning of Stabilizing Policies for Nonlinear Systems
This work addresses the challenge of ensuring stability in imitation learning for nonlinear systems, which is incremental as it builds on existing linear methods.
The paper tackles the problem of extending stabilizing imitation learning from linear to polynomial systems and controllers using sum of squares techniques, proposing two heuristic algorithms and demonstrating their performance through numerical experiments.
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.