An ADP-based robust control scheme for nonaffine nonlinear systems with uncertainties and input constraints

doi:10.1088/1674-1056/adbee1

中国物理B ›› 2025, Vol. 34 ›› Issue (6): 60202-060202.doi: 10.1088/1674-1056/adbee1

An ADP-based robust control scheme for nonaffine nonlinear systems with uncertainties and input constraints

Shijie Luo(罗世杰)¹, Kun Zhang(张坤)^1,2,†, and Wenchao Xue(薛文超)³

1 The School of Astronautics, Beihang University, Beijing 100191, China;
2 The State Key Laboratory of High-Efficiency Reusable Aerospace Transportation Technology, Beijing 102206, China;
3 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

收稿日期:2024-12-20 修回日期:2025-02-17 接受日期:2025-03-11 出版日期:2025-05-16 发布日期:2025-05-30
通讯作者: Kun Zhang E-mail:zhangkun22@buaa.edu.cn
基金资助:
Project supported by the National Natural Science Foundation of China (Grant No. 62103408), Beijing Nova Program (Grant No. 20240484516), and the Fundamental Research Funds for the Central Universities (Grant No. KG16314701).

An ADP-based robust control scheme for nonaffine nonlinear systems with uncertainties and input constraints

Shijie Luo(罗世杰)¹, Kun Zhang(张坤)^1,2,†, and Wenchao Xue(薛文超)³

1 The School of Astronautics, Beihang University, Beijing 100191, China;
2 The State Key Laboratory of High-Efficiency Reusable Aerospace Transportation Technology, Beijing 102206, China;
3 Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

Received:2024-12-20 Revised:2025-02-17 Accepted:2025-03-11 Online:2025-05-16 Published:2025-05-30
Contact: Kun Zhang E-mail:zhangkun22@buaa.edu.cn
Supported by:
Project supported by the National Natural Science Foundation of China (Grant No. 62103408), Beijing Nova Program (Grant No. 20240484516), and the Fundamental Research Funds for the Central Universities (Grant No. KG16314701).

摘要/Abstract

摘要： The paper develops a robust control approach for nonaffine nonlinear continuous systems with input constraints and unknown uncertainties. Firstly, this paper constructs an affine augmented system (AAS) within a pre-compensation technique for converting the original nonaffine dynamics into affine dynamics. Secondly, the paper derives a stability criterion linking the original nonaffine system and the auxiliary system, demonstrating that the obtained optimal policies from the auxiliary system can achieve the robust controller of the nonaffine system. Thirdly, an online adaptive dynamic programming (ADP) algorithm is designed for approximating the optimal solution of the Hamilton-Jacobi-Bellman (HJB) equation. Moreover, the gradient descent approach and projection approach are employed for updating the actor-critic neural network (NN) weights, with the algorithm's convergence being proven. Then, the uniformly ultimately bounded stability of state is guaranteed. Finally, in simulation, some examples are offered for validating the effectiveness of this presented approach.

关键词: adaptive dynamic programming, robust control, nonaffine nonlinear system, neural network

Abstract: The paper develops a robust control approach for nonaffine nonlinear continuous systems with input constraints and unknown uncertainties. Firstly, this paper constructs an affine augmented system (AAS) within a pre-compensation technique for converting the original nonaffine dynamics into affine dynamics. Secondly, the paper derives a stability criterion linking the original nonaffine system and the auxiliary system, demonstrating that the obtained optimal policies from the auxiliary system can achieve the robust controller of the nonaffine system. Thirdly, an online adaptive dynamic programming (ADP) algorithm is designed for approximating the optimal solution of the Hamilton-Jacobi-Bellman (HJB) equation. Moreover, the gradient descent approach and projection approach are employed for updating the actor-critic neural network (NN) weights, with the algorithm's convergence being proven. Then, the uniformly ultimately bounded stability of state is guaranteed. Finally, in simulation, some examples are offered for validating the effectiveness of this presented approach.

Key words: adaptive dynamic programming, robust control, nonaffine nonlinear system, neural network

中图分类号: (Control theory)

02.30.Yy

Shijie Luo(罗世杰), Kun Zhang(张坤), and Wenchao Xue(薛文超). An ADP-based robust control scheme for nonaffine nonlinear systems with uncertainties and input constraints[J]. 中国物理B, 2025, 34(6): 60202-060202.

Shijie Luo(罗世杰), Kun Zhang(张坤), and Wenchao Xue(薛文超). An ADP-based robust control scheme for nonaffine nonlinear systems with uncertainties and input constraints[J]. Chin. Phys. B, 2025, 34(6): 60202-060202.

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An ADP-based robust control scheme for nonaffine nonlinear systems with uncertainties and input constraints

An ADP-based robust control scheme for nonaffine nonlinear systems with uncertainties and input constraints

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