H∞-Optimal Control via Game-Theoretic Differential Dynamic Programming and Gaussian Processes

In this paper, we present a nonlinear 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 no...

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Bibliographic Details
Published in:Journal of optimization theory and applications Vol. 204; no. 3; p. 40
Main Authors: Sun, Wei, Trafalis, Theodore B.
Format: Journal Article
Language:English
Published: New York Springer US 01.03.2025
Springer Nature B.V
Subjects:
Algorithms
Applications of Mathematics
Artificial neural networks
Calculus of Variations and Optimal Control; Optimization
Control algorithms
Control systems
Control theory
Differential games
Dynamic programming
Engineering
Game theory
Gaussian process
H-infinity control
Machine learning
Mathematics
Mathematics and Statistics
Noise control
Nonlinear control
Nonlinear dynamics
Operations Research/Decision Theory
Optimal control
Optimization
Theory of Computation
Zero sum games
control
Gaussian process
Differential game
Differential dynamic programming
ISSN:0022-3239, 1573-2878
Online Access:Get full text
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Summary:In this paper, we present a nonlinear 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 ∞ -optimal control is then formulated to synthesis the 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.
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ISSN:0022-3239
1573-2878
DOI:10.1007/s10957-024-02572-6