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

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 exact 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 closedloop 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.

Safety Certification for Stochastic Systems via Neural Barrier Functions

“…In contrast, our approach does not require the computation of any Lipschitz constant and can scale to larger networks of hundreds of neurons and multiple hidden layers as we will show in Section IV. A novel approach to neural certification of systems is Neural System Level Synthesis where a closed loop system is synthesized to guarantee stability [15].…”

Robust Nonlinear Optimal Control via System Level Synthesis

“…In particular, for linear systems, SLS allows to jointly optimize a linear error feedback policy and nominal trajectory and thereby provide a tight reachable set at least for linear systems. There exist conceptual extensions of the SLS framework to nonlinear systems [25]- [27], however these existing approaches do not consider (robust) constraint satisfaction.…”