Learning-Based Nonlinear $H^\infty$ Control via Game-Theoretic Differential Dynamic Programming

TL;DR

This paper introduces a learning-based nonlinear $H^$ control method using game-theoretic differential dynamic programming, leveraging Gaussian Process regression to adapt to system dynamics and disturbances, demonstrated on a quadcopter.

Contribution

It develops a novel control algorithm combining Gaussian Process learning with game-theoretic DDP for nonlinear $H^$ control, addressing disturbance attenuation in a data-driven manner.

Findings

Effective disturbance handling demonstrated on quadcopter simulations.

The proposed method adapts to learned dynamics and disturbance estimates.

Simulation results show improved control performance over traditional methods.

Abstract

In this work, we present a learning-based nonlinear $H^\infty$ control algorithm that guarantee system performance under learned dynamics and disturbance estimate. The Gaussian Process (GP) regression is utilized to update the nominal dynamics of the system and provide disturbance estimate based on data gathered through interaction with the system. A soft-constrained differential game associated with the disturbance attenuation problem in nonlinear $H^\infty$ control is then formulated to obtain the nonlinear $H^\infty$ controller. The differential game is solved through the min-max Game-Theoretic Differential Dynamic Programming (GT-DDP) algorithm in continuous time. Simulation results on a quadcopter system demonstrate the efficiency of the learning-based control algorithm in handling external disturbances.