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Optimal finite-horizon tracking control in affine nonlinear systems: A Stackelberg game approach with H2/H∞ framework

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  • Dong, Xu
  • Zhang, Huaguang
  • Ming, Zhongyang
  • Luo, Yanhong

Abstract

In this paper, we address the finite-time optimal tracking control problem within the context of a Stackelberg game structure, characterized by the mixed H2/H∞ framework. This objective is accomplished through the innovative design and implementation of a novel Adaptive Dynamic Programming (ADP) algorithm. Initially, we establish a time-varying coupled Hamilton-Jacobi-Isaacs (HJI) equations, posing a significant challenge in deriving an analytical solution for the optimal leader. Subsequently, we elucidate the existence of Nash equilibrium points, confirming the algorithm's convergence and providing theoretical foundations for its practical application. Furthermore, we introduce a novel ADP algorithm that incorporates time-varying activation functions. The use of the Lyapunov direct method ensures the stability of the closed-loop affine nonlinear system under the ADP control scheme, thereby guaranteeing the system's uniformly ultimately bounded (UUB). Finally, the effectiveness of the aforementioned ADP-based control approach is validated through numerical simulations.

Suggested Citation

  • Dong, Xu & Zhang, Huaguang & Ming, Zhongyang & Luo, Yanhong, 2025. "Optimal finite-horizon tracking control in affine nonlinear systems: A Stackelberg game approach with H2/H∞ framework," Applied Mathematics and Computation, Elsevier, vol. 495(C).
    • Handle: RePEc:eee:apmaco:v:495:y:2025:i:c:s0096300325000037
    DOI: 10.1016/j.amc.2025.129276
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    References listed on IDEAS

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    1. Cui, Lili & Xie, Xiangpeng & Guo, Hongyan & Luo, Yanhong, 2022. "Dynamic event-triggered distributed guaranteed cost FTC scheme for nonlinear interconnected systems via ADP approach," Applied Mathematics and Computation, Elsevier, vol. 425(C).
    2. Liu, Xikui & Ge, Yingying & Li, Yan, 2019. "Stackelberg games for model-free continuous-time stochastic systems based on adaptive dynamic programming," Applied Mathematics and Computation, Elsevier, vol. 363(C), pages 1-1.
    3. Ming, Zhongyang & Zhang, Huaguang & Liang, Yuling & Su, Hanguang, 2022. "Nonzero-sum differential games of continuous-Time nonlinear systems with uniformly ultimately ε-bounded by adaptive dynamic programming," Applied Mathematics and Computation, Elsevier, vol. 430(C).
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