A Guaranteed-Stable Neural Network Approach for Optimal Control of Nonlinear Systems

TL;DR

This paper introduces a neural network-based control method for nonlinear systems that guarantees stability and convergence by transforming the control optimization into a trainable neural network, reducing computational complexity.

Contribution

It develops a Neural Optimization Machine (NOM) that converts complex control optimization problems into neural network training, ensuring stability and asymptotic convergence.

Findings

System states converge to a neighborhood of the equilibrium

All signals remain bounded under the proposed control scheme

Simulation and experiments validate effectiveness

Abstract

A promising approach to optimal control of nonlinear systems involves iteratively linearizing the system and solving an optimization problem at each time instant to determine the optimal control input. Since this approach relies on online optimization, it can be computationally expensive, and thus unrealistic for systems with limited computing resources. One potential solution to this issue is to incorporate a Neural Network (NN) into the control loop to emulate the behavior of the optimal control scheme. Ensuring stability and reference tracking in the resulting NN-based closed-loop system requires modifications to the primary optimization problem. These modifications often introduce non-convexity and nonlinearity with respect to the decision variables, which may surpass the capabilities of existing solvers and complicate the generation of the training dataset. To address this issue, this paper develops a Neural Optimization Machine (NOM) to solve the resulting optimization problems. The central concept of a NOM is to transform the optimization challenges into the problem of training a NN. Rigorous proofs demonstrate that when a NN trained on data generated by the NOM is used in the control loop, all signals remain bounded and the system states asymptotically converge to a neighborhood around the desired equilibrium point, with a tunable proximity threshold. Simulation and experimental studies are provided to illustrate the effectiveness of the proposed methodology.