Neural System Level Synthesis: Learning over All Stabilizing Policies for Nonlinear Systems

TL;DR

This paper introduces Neural SLS, a neural network-based method for designing stabilizing control policies for nonlinear systems that guarantees stability during learning and can handle complex nonlinear dynamics.

Contribution

It develops a novel parametrization of stabilizing policies for nonlinear systems and leverages deep neural networks to learn stable operators, ensuring stability without constraints.

Findings

Neural SLS guarantees stability during and after training.

The approach effectively handles complex nonlinear dynamics.

Numerical examples demonstrate the method's effectiveness.

Abstract

We address the problem of designing stabilizing control policies for nonlinear systems in discrete-time, while minimizing an arbitrary cost function. When the system is linear and the cost is convex, the System Level Synthesis (SLS) approach offers an effective solution based on convex programming. Beyond this case, a globally optimal solution cannot be found in a tractable way, in general. In this paper, we develop a parametrization of all and only the control policies stabilizing a given time-varying nonlinear system in terms of the combined effect of 1) a strongly stabilizing base controller and 2) a stable SLS operator to be freely designed. Based on this result, we propose a Neural SLS (Neur-SLS) approach guaranteeing closed-loop stability during and after parameter optimization, without requiring any constraints to be satisfied. We exploit recent Deep Neural Network (DNN) models based on Recurrent Equilibrium Networks (RENs) to learn over a rich class of nonlinear stable operators, and demonstrate the effectiveness of the proposed approach in numerical examples.