Provably-Stable Neural Network-Based Control of Nonlinear Systems

TL;DR

This paper introduces a systematic method for designing neural network-based controllers for nonlinear systems that guarantees stability and convergence, validated through simulations and experiments.

Contribution

It provides the first comprehensive approach to ensure provable stability in NN-based control of nonlinear systems.

Findings

Guarantees closed-loop system stability with NN control.

Ensures asymptotic convergence to a neighborhood of the equilibrium.

Validated on inverted pendulum and drone experiments.

Abstract

In recent years, Neural Networks (NNs) have been employed to control nonlinear systems due to their potential capability in dealing with situations that might be difficult for conventional nonlinear control schemes. However, to the best of our knowledge, the current literature on NN-based control lacks theoretical guarantees for stability and tracking performance. This precludes the application of NN-based control schemes to systems where stringent stability and performance guarantees are required. To address this gap, this paper proposes a systematic and comprehensive methodology to design provably-stable NN-based control schemes for affine nonlinear systems. Rigorous analysis is provided to show that the proposed approach guarantees stability of the closed-loop system with the NN in the loop. Also, it is shown that the resulting NN-based control scheme ensures that system states asymptotically converge to a neighborhood around the desired equilibrium point, with a tunable proximity threshold. The proposed methodology is validated and evaluated via simulation studies on an inverted pendulum and experimental studies on a Parrot Bebop 2 drone.