H∞ tracking control for perturbed discrete-time systems using On/Off policy Q-learning algorithms

Phuong Nam Dao and Quang Huy Dao

Chaos, Solitons & Fractals, 2025, vol. 197, issue C

Abstract: The widely studied H∞ zero-sum game problem guarantees the integration of external disturbance into the optimal control problem. In this article, two model-free Q-learning algorithms based on H∞ tracking control are proposed for perturbed discrete-time systems in the presence of external disturbance. Moreover, modification of the output optimal control problem is also made. For the optimal tracking control problem, the existence of a discount factor is necessary to guarantee the final value of the cost function, and the Ricatti equation is modified. With the aid of the deviation between Q functions at two consecutive times and the original principle of Off/On policy, the consideration of H∞ zero-sum game problem, two On/Off Q-learning algorithms based on H∞ tracking control are proposed. Then, by computing the Q function, the influence of probing noise on the Q function is considered. The analysis of solution equivalence proves that convergence and tracking are guaranteed in the proposed algorithm. Eventually, simulation studies are carried out on F-16 aircraft to assess the validity of the presented control schemes.

Keywords: Perturbed discrete-time systems; Q-learning; On/off policy algorithm; Model-free control; Reinforcement learning control (search for similar items in EconPapers)
Date: 2025
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Persistent link: https://EconPapers.repec.org/RePEc:eee:chsofr:v:197:y:2025:i:c:s0960077925004722

DOI: 10.1016/j.chaos.2025.116459

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