Synthesis of Feedback Controller for Nonlinear Control Systems with Optimal Region of Attraction

TL;DR

This paper introduces a novel framework combining stochastic optimization and deep learning to synthesize feedback controllers that maximize the region of attraction in nonlinear systems, improving stability and control performance.

Contribution

It presents a new method that co-optimizes control objectives and ROA using neural networks and stochastic optimization, advancing nonlinear control synthesis.

Findings

Effective estimation of ROA using deep neural networks

Controller synthesis that balances LQR cost and stability region

Validated approach through extensive experiments on nonlinear systems

Abstract

We propose a framework for synthesizing a feedback control policy that maximizes the region of attraction (ROA) of a closed-loop nonlinear dynamical system. Our synthesis technique relies on stochastic optimization, which involves computation of an objective function capturing the ROA for a feedback control law. We employ a machine learning technique based on deep neural network to estimate the ROA for a given feedback controller. Overall, our technique is capable of synthesizing a controller co-optimizing traditional control objectives like LQR cost together with ROA. We demonstrate the efficacy of our technique through exhaustive experiments carried out on various nonlinear systems.