不确定非线性系统的自适应滑模区域到达控制

孙晓明; 马辛; 刘烨; 周悦; 邢博闻

doi:10.13700/j.bh.1001-5965.2022.0647

不确定非线性系统的自适应滑模区域到达控制

doi: 10.13700/j.bh.1001-5965.2022.0647

孙晓明^{1, 2},
马辛^3, ,,
刘烨⁴,
周悦¹,
邢博闻¹

1.
上海海洋大学工程学院上海深渊科学工程技术研究中心，上海 201306
2.
复旦大学智能信息处理重点实验室，上海 200433
3.
北京航空航天大学仪器科学与光电工程学院，北京 100191
4.
上海工程技术大学电子电气工程学院，上海 201620

基金项目: 国家自然科学基金(61873196)；中央高校基本科研业务费专项资金(YWF-23-L-826)；上海巿智能信息处理重点实验室开放基金(IIPL201904)；上海海洋大学科技发展专项基金(A2-2006-21-200207)；科技创新2030-“量子通信与量子计算机”重大项目(2021ZD0303400)；高性能船舶技术重点实验室开放基金(GXNC23052801)

详细信息

通讯作者:
E-mail：maxin@buaa.edu.cn

中图分类号: V249.1；TP273
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出版历程
- 收稿日期: 2022-07-27
- 录用日期: 2023-07-14
- 网络出版日期: 2023-12-19
- 整期出版日期: 2024-08-28

Adaptive sliding mode region reaching control for uncertain nonlinear systems

SUN Xiaoming^{1, 2},
MA Xin^{3
, ,},
LIU Ye⁴,
ZHOU Yue¹,
XING Bowen¹

1.
Shanghai Engineering Research Center of Hadal Science and Technology，College of Engineering Science and Technology，Shanghai Ocean University，Shanghai 201306，China
2.
Key Lab of Intelligent Information Processing，Fudan University，Shanghai 200433，China
3.
School of Instrumentation and Optoelectronic Engineering，Beihang University，Beijing 100191，China
4.
School of Electronic and Electrical Engineering，Shanghai University of Engineering Science，Shanghai 201620，China

Funds: National Natural Science Foundation of China (61873196); The Fundamental Research Funds for the Central Universities (YWF-23-L-826); Open Research Program of Shanghai Key Lab of Intelligent Information Processing (IIPL201904); Development of Science and Technology Foundation of Shanghai Ocean University (A2-2006-21-200207); Science and Technology Innovation 2030-Quantum Communication and Quantum Computer Major Projects (2021ZD0303400); Open Fund of Key Laboratory of High Performance Ship Technology (GXNC23052801)

More Information

Corresponding author: E-mail：maxin@buaa.edu.cn

摘要

摘要:
针对一类参数严格反馈型不确定非线性系统，考虑存在外界干扰的情况下，设计一种基于反推方法的自适应滑模区域到达控制器，提高系统对非匹配不确定性及未知干扰的鲁棒性。与传统的设定点控制或位置控制不同，区域到达算法的控制目标是一个以期望点为中心的目标区域。所设计控制器综合了人工势场法、自适应控制、反推技术、滑模控制和Lyapunov方法。利用人工势场法设计目标势能函数，将区域误差引入势能函数中，结合Lyapunov方法，可以实现对目标区域的到达跟踪控制。采用基于反推的区域控制思想，将高阶整体模型分解为低阶子系统，并分别设计相应的滑模面，同时在前n-1步中结合自适应律，能够在线估计非线性系统的不确定参数项，增加所设计控制器的适用性。基于Lyapunov理论证明闭环系统的全局渐近稳定性，仿真结果表明：所设计控制器有效。
- 严格反馈 /
- 区域到达控制 /
- 人工势场 /
- 自适应控制 /
- 滑模控制
Abstract:
In this paper, considering the existence of external disturbances, an adaptive backstepping-based sliding mode region reaching controller is designed for a class of uncertain nonlinear systems in parametric strict-feedback form. The robustness of the system for mismatched uncertainties and unknown disturbances was recovered and strengthened. The designed controller is based on the fusion of the artificial potential field method, adaptive control, backstepping techniques, sliding mode control and the Lyapunov synthesis approach. The control target in the region reaching control technique is created as a desirable spatial region, which sets it apart from the conventional set-point control or position control. The target potential function and new Lyapunov functions are designed with the region control error in mind using the artificial potential field method in order to achieve the goal of region reaching control. The backstepping method can be used to break down large and high-order nonlinear systems into smaller, more manageable subsystems, making the suggested approach more applicable to real-world scenarios. The online estimation of the unknown parameters is obtained by the adaptive method which is combined with the first n-1 steps of the backstepping method. The Lyapunov theorem is utilized to prove the globally asymptotic stability of the closed-loop system, and simulation results are presented to show the effectiveness of the designed controller.
- strict feedback /
- region reaching control /
- artificial potential field /
- adaptive control /
- sliding mode control

HTML全文

图 1 目标区域示例

Figure 1. Examples of the desired target region

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图 2 x轴方向区域跟踪曲线

Figure 2. Tracking curve of region reaching on the x-axis

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图 3 y轴方向区域跟踪曲线

Figure 3. Tracking curve of region reaching on the y-axis

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图 4 区域误差

Figure 4. Regional errors

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图 5 目标区域到达势能函数${P}(\Delta {\boldsymbol{X}})$

Figure 5. Target region reaching potential energy function ${P}(\Delta {\boldsymbol{X}})$

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图 6 系统输出跟踪曲线

Figure 6. Trajectory tracking curve of the system output

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图 7 参数估计${\hat \theta _i}$

Figure 7. Parameters estimation ${\hat \theta _i}$

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图 8 方形区域到达控制

Figure 8. Region reaching control for a square

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图 9 方形区域到达误差

Figure 9. Arrival error in square area

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图 10 方形区域到达势能函数${P}(\Delta {\boldsymbol{X}})$

Figure 10. Potential energy function ${P}(\Delta {\boldsymbol{X}})$ of region reaching for a square

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