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

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.