LyLA-Therm: Lyapunov-based Langevin Adaptive Thermodynamic Neural Network Controller

TL;DR

This paper introduces LyLA-Therm, a novel Lyapunov-based Langevin thermodynamic neural network controller that employs stochastic differential equations to improve control and estimation performance with probabilistic convergence.

Contribution

It develops a new stochastic control law inspired by thermodynamics and Langevin dynamics, enhancing stability and exploration-exploitation balance in neural network control.

Findings

Achieves probabilistic convergence of errors to an ultimate bound.

Improves tracking errors by up to 20.66%.

Enhances function approximation errors by up to 20.89%.

Abstract

Thermodynamic principles can be employed to design parameter update laws that address challenges such as the exploration vs. exploitation dilemma. In this paper, inspired by the Langevin equation, an update law is developed for a Lyapunov-based DNN control method, taking the form of a stochastic differential equation. The drift term is designed to minimize the system's generalized internal energy, while the diffusion term is governed by a user-selected generalized temperature law, allowing for more controlled fluctuations. The minimization of generalized internal energy in this design fulfills the exploitation objective, while the temperature-based stochastic noise ensures sufficient exploration. Using a Lyapunov-based stability analysis, the proposed Lyapunov-based Langevin Adaptive Thermodynamic (LyLA-Therm) neural network controller achieves probabilistic convergence of the tracking and parameter estimation errors to an ultimate bound. Simulation results demonstrate the effectiveness of the proposed approach, with the LyLA-Therm architecture achieving up to 20.66% improvement in tracking errors, up to 20.89% improvement in function approximation errors, and up to 11.31% improvement in off-trajectory function approximation errors compared to the baseline deterministic approach.