Optimal distributed control with stability guarantees by training a network of neural closed-loop maps

TL;DR

This paper introduces a neural network-based method for distributed control that guarantees stability and allows for arbitrary cost optimization, demonstrated through vehicle formation control simulations.

Contribution

It develops a novel parameterization of stabilizing distributed control policies using neural networks within the Neur-SLS framework, ensuring stability by design.

Findings

Guarantees bounded $\\mathcal{L}_2$ gain for network stability.

Enables fully distributed implementation with local communication.

Successfully applied to vehicle formation control simulation.

Abstract

This paper proposes a novel approach to improve the performance of distributed nonlinear control systems while preserving stability by leveraging Deep Neural Networks (DNNs). We build upon the Neural System Level Synthesis (Neur-SLS) framework and introduce a method to parameterize stabilizing control policies that are distributed across a network topology. A distinctive feature is that we iteratively minimize an arbitrary control cost function through an unconstrained optimization algorithm, all while preserving the stability of the overall network architecture by design. This is achieved through two key steps. First, we establish a method to parameterize interconnected Recurrent Equilibrium Networks (RENs) that guarantees a bounded $\mathcal{L}_2$ gain at the network level. This ensures stability. Second, we demonstrate how the information flow within the network is preserved, enabling a fully distributed implementation where each subsystem only communicates with its neighbors. To showcase the effectiveness of our approach, we present a simulation of a distributed formation control problem for a fleet of vehicles. The simulation demonstrates how the proposed neural controller enables the vehicles to maintain a desired formation while navigating obstacles and avoiding collisions, all while guaranteeing network stability.