$$H^\infty $$ H ∞ -Optimal Control via Game-Theoretic Differential Dynamic Programming and Gaussian Processes

Wei Sun () and Theodore B. Trafalis ()
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Wei Sun: University of Oklahoma
Theodore B. Trafalis: University of Oklahoma

Journal of Optimization Theory and Applications, 2025, vol. 204, issue 3, No 5, 20 pages

Abstract: Abstract In this paper, we present a nonlinear $$H^\infty $$ H ∞ -optimal control algorithm for a system whose dynamics can be described by the summation of two terms: a known function obtained from system modeling and an unknown function that represents the model error induced by the disturbance and the noise that are not captured by the original model. A Gaussian Process (GP) is utilized as an alternative to a supervised artificial neural network to update the nominal dynamics of the system and provide disturbance estimates based on data gathered through interaction with the system. A soft-constrained two-player zero-sum differential game that is equivalent to the disturbance attenuation problem in nonlinear $$H^\infty $$ H ∞ -optimal control is then formulated to synthesis the $$H^\infty $$ H ∞ controller. The differential game is solved through the Game-Theoretic Differential Dynamic Programming (GT-DDP) algorithm in continuous time. In addition we provide a proof of quadratic convergence of the proposed GT-DDP algorithm. Simulation results on a quadcopter system demonstrate the efficiency of the learning-based control algorithm in handling model uncertainties and external disturbances.

Keywords: Differential game; Differential dynamic programming; Gaussian process; $$H^\infty $$ H ∞ control (search for similar items in EconPapers)
Date: 2025
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DOI: 10.1007/s10957-024-02572-6

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