Learning to Boost the Performance of Stable Nonlinear Systems

TL;DR

This paper introduces a method combining nonlinear control principles with deep learning to enhance system performance while guaranteeing stability, even with model uncertainties and early stopping in training.

Contribution

It presents a novel approach that integrates Internal Model Control with advanced optimization to learn stable, performance-boosting controllers for nonlinear systems with stability guarantees.

Findings

Guarantees L_p closed-loop stability despite early stopping.

Enables learning over deep neural network classes for nonlinear control.

Demonstrates effectiveness through numerical experiments.

Abstract

The growing scale and complexity of safety-critical control systems underscore the need to evolve current control architectures aiming for the unparalleled performances achievable through state-of-the-art optimization and machine learning algorithms. However, maintaining closed-loop stability while boosting the performance of nonlinear control systems using data-driven and deep-learning approaches stands as an important unsolved challenge. In this paper, we tackle the performance-boosting problem with closed-loop stability guarantees. Specifically, we establish a synergy between the Internal Model Control (IMC) principle for nonlinear systems and state-of-the-art unconstrained optimization approaches for learning stable dynamics. Our methods enable learning over arbitrarily deep neural network classes of performance-boosting controllers for stable nonlinear systems; crucially, we guarantee L_p closed-loop stability even if optimization is halted prematurely, and even when the ground-truth dynamics are unknown, with vanishing conservatism in the class of stabilizing policies as the model uncertainty is reduced to zero. We discuss the implementation details of the proposed control schemes, including distributed ones, along with the corresponding optimization procedures, demonstrating the potential of freely shaping the cost functions through several numerical experiments.