Synthesis of Stabilizing Recurrent Equilibrium Network Controllers

TL;DR

This paper introduces a novel recurrent equilibrium network controller that guarantees stability for nonlinear systems and uses convex optimization-based policy gradient methods for synthesis, demonstrated on simulated nonlinear plants.

Contribution

It presents a new parameterization of nonlinear controllers ensuring stability and a synthesis method using projected policy gradients with convex optimization.

Findings

Controller guarantees exponential stability.

Method successfully controls nonlinear plants in simulations.

Applicable to neural network modeled systems.

Abstract

We propose a parameterization of a nonlinear dynamic controller based on the recurrent equilibrium network, a generalization of the recurrent neural network. We derive constraints on the parameterization under which the controller guarantees exponential stability of a partially observed dynamical system with sector bounded nonlinearities. Finally, we present a method to synthesize this controller using projected policy gradient methods to maximize a reward function with arbitrary structure. The projection step involves the solution of convex optimization problems. We demonstrate the proposed method with simulated examples of controlling nonlinear plants, including plants modeled with neural networks.