A framework of learning controller with Lyapunov-based constraint and application

TL;DR

This paper introduces a novel framework for designing stable nonlinear controllers using Lyapunov constraints and deep learning, enabling direct optimization-based controller synthesis with guaranteed stability.

Contribution

It proposes a new optimization-based approach for controller design with Lyapunov constraints, integrating neural networks and deep learning to improve stability and robustness.

Findings

High convergence speed in simulations

Effective tracking error minimization

Robustness to disturbances and uncertainties

Abstract

In this paper, we focus on the problem about direct way to design a stable controller for nonlinear system. A framework of learning controller with Lyapunov-based constraint is proposed, which is intended to transform designing and analyis of a controller to straightforward way to make controller by solving an optimization with the Lyapunov constraint, and which can be a novel way to design a global stability guaranteed controller directly. Firstly, an optimization problem subject to Lyapunov-based constraints is formulated, in which the tracking error is the objective function to minimize. Secondly, the controller combines with PID and feedforward is given in form of neural networks, Finally, the solution of controller method to the optimization problem is analyzed, in which we leverage some deep learning technologies to boost the capbility of solution. The results of two simulations of 2 order linear and nonlinear systems demonstrate that the method proposed has some high performance in speed of convergence, tracking error and smoothness and amplitude of control output. The results of simulation to the nonlinear system with disturbance, noise, uncertainty of parameters and the difference of reference output demostrate that our method has high performance in robustness and generalization.