Neural-NPV Control: Learning Parameter-Dependent Controllers and Lyapunov Functions

Abstract

This paper presents Neural-NPV Control, a learning-based framework for joint synthesis of a parameter-dependent (PD) controller and a PD Lyapunov function using neural networks for an NPV system under input constraints. At the first stage, the proposed framework utilizes a gradient-based counterexample-guided procedure to synthesize a PD controller and a PD Lyapunov function candidate. The second stage relies on a level-set guided procedure to refine the controller and Lyapunov function candidate while maximizing the robust region of attraction (R-ROA). The learned controller, Lyapunov function, and R-ROA are empirically evaluated. We demonstrate the advantages of Neural-NPV over SOS-based methods in terms of applicability, performance, and scalability through numerical experiments involving a simple inverted pendulum with one scheduling parameter and a quadrotor system with three scheduling parameters.