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

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  • Dao, Phuong Nam
  • Dao, Quang Huy

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.

Suggested Citation

  • Dao, Phuong Nam & Dao, Quang Huy, 2025. "H∞ tracking control for perturbed discrete-time systems using On/Off policy Q-learning algorithms," Chaos, Solitons & Fractals, Elsevier, vol. 197(C).
    • Handle: RePEc:eee:chsofr:v:197:y:2025:i:c:s0960077925004722
    DOI: 10.1016/j.chaos.2025.116459
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    References listed on IDEAS

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    1. Ijaz, Salman & Fuyang, Chen & Hamayun, Mirza Tariq & Anwaar, Haris, 2021. "Adaptive integral-sliding-mode control strategy for maneuvering control of F16 aircraft subject to aerodynamic uncertainty," Applied Mathematics and Computation, Elsevier, vol. 402(C).
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