Designing System Level Synthesis Controllers for Nonlinear Systems with Stability Guarantees

We introduce a method for controlling systems with nonlinear dynamics and full actuation by approximating the dynamics with polynomials and applying a system level synthesis controller. We show how to optimize over this class of controllers using a neural network while maintaining stability guarantees, without requiring a Lyapunov function. We give bounds for the domain over which the use of the class of controllers preserves stability and gives bounds on the control costs incurred by optimized controllers. We then numerically validate our approach and show improved performance compared with feedback linearization -- suggesting that the SLS controllers are able to take advantage of nonlinearities in the dynamics while guaranteeing stability.