Neural Lyapunov Differentiable Predictive Control

TL;DR

The paper introduces Neural Lyapunov Differentiable Predictive Control (NLDPC), a learning-based method that uses differentiable programming and Lyapunov functions to ensure stability in predictive control, demonstrated on double integrator and aircraft models.

Contribution

It proposes a novel neural network-based predictive control framework with integrated Lyapunov stability certification and probabilistic guarantees, offering a scalable alternative to traditional MPC.

Findings

Successfully stabilizes the double integrator model.

Controls an aircraft model demonstrating practical applicability.

Provides probabilistic stability guarantees during training.

Abstract

We present a learning-based predictive control methodology using the differentiable programming framework with probabilistic Lyapunov-based stability guarantees. The neural Lyapunov differentiable predictive control (NLDPC) learns the policy by constructing a computational graph encompassing the system dynamics, state and input constraints, and the necessary Lyapunov certification constraints, and thereafter using the automatic differentiation to update the neural policy parameters. In conjunction, our approach jointly learns a Lyapunov function that certifies the regions of state-space with stable dynamics. We also provide a sampling-based statistical guarantee for the training of NLDPC from the distribution of initial conditions. Our offline training approach provides a computationally efficient and scalable alternative to classical explicit model predictive control solutions. We substantiate the advantages of the proposed approach with simulations to stabilize the double integrator model and on an example of controlling an aircraft model.