Learning over All Stabilizing Nonlinear Controllers for a Partially-Observed Linear System

TL;DR

This paper introduces a novel nonlinear control policy architecture for partially-observed linear systems that guarantees stability, leveraging a universal approximator based on recurrent equilibrium networks and a nonlinear Youla parameterization.

Contribution

The paper presents a new Youla-REN architecture that ensures stability and universal approximation of stabilizing nonlinear controllers, with improved learning efficiency and scalability.

Findings

Faster convergence to better controllers in simulations

Guarantees stability during learning transients

Scalable learning with both model-based and reinforcement learning methods

Abstract

This paper proposes a nonlinear policy architecture for control of partially-observed linear dynamical systems providing built-in closed-loop stability guarantees. The policy is based on a nonlinear version of the Youla parameterization, and augments a known stabilizing linear controller with a nonlinear operator from a recently developed class of dynamic neural network models called the recurrent equilibrium network (REN). We prove that RENs are universal approximators of contracting and Lipschitz nonlinear systems, and subsequently show that the the proposed Youla-REN architecture is a universal approximator of stabilizing nonlinear controllers. The REN architecture simplifies learning since unconstrained optimization can be applied, and we consider both a model-based case where exact gradients are available and reinforcement learning using random search with zeroth-order oracles. In simulation examples our method converges faster to better controllers and is more scalable than existing methods, while guaranteeing stability during learning transients.