Neural System Level Synthesis: Learning over All Stabilizing Policies for Nonlinear Systems
This addresses the challenge of stabilizing nonlinear systems in control theory, offering a novel method for learning over all stabilizing policies, though it appears incremental as it builds on existing SLS and REN frameworks.
The paper tackles the problem of designing stabilizing control policies for nonlinear systems while minimizing an arbitrary cost function, proposing a Neural SLS approach that guarantees closed-loop stability without constraints and demonstrates effectiveness in numerical examples.
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.