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具有非严格反馈结构的非线性时滞系统的模糊自适应控制

王锐1, 文国兴2, 刘士虎3   

  1. 1. 山西财经大学应用数学学院, 太原 030006;
    2. 滨州学院理学院, 滨州 256603;
    3. 云南民族大学数学与计算机科学学院, 昆明 650031
  • 收稿日期:2022-02-27 修回日期:2022-04-20 发布日期:2022-12-13
  • 基金资助:
    国家自然科学基金(12102236, 62073045, 61966039)资助课题, 山西省自然科学基金(20210302124258, 201901D211411)资助课题.

王锐, 文国兴, 刘士虎. 具有非严格反馈结构的非线性时滞系统的模糊自适应控制[J]. 系统科学与数学, 2022, 42(11): 2902-2913.

WANG Rui, WEN Guoxing, LIU Shihu. Adaptive Fuzzy Control for a Class of Nonlinear Non-Strict Feedback Systems with Time-Delays[J]. Journal of Systems Science and Mathematical Sciences, 2022, 42(11): 2902-2913.

Adaptive Fuzzy Control for a Class of Nonlinear Non-Strict Feedback Systems with Time-Delays

WANG Rui1, WEN Guoxing2, LIU Shihu3   

  1. 1. School of Applied Mathematics, Shanxi University of Finance and Economics, Taiyuan 030006;
    2. School of Mathematics, Binzhou University Binzhou 256603;
    3. School of Mathematics and Computer Science, Yunnan Minzu University, Kunming 650031
  • Received:2022-02-27 Revised:2022-04-20 Published:2022-12-13
针对一类具有不确定时滞输入和未知非光滑函数的非线性非严格反馈结构系统, 提出了一种新颖的自适应模糊减少计算量状态反馈跟踪控制方法. 采用模糊逻辑系统作为未知函数的逼近器, 利用变量分离技术处理非严格反馈结构且不要求系统函数满足严格单调递增. 未知常数作为最优逼近向量范数和逼近误差模的界, 在每一步反步递推过程中只需要调节这两个自适应参数即可. 该方法不仅 补偿了未知时滞输入的影响, 同时还减少了在线逼近参数数目. 基于~Lyapunov~ 稳定性 理论分析闭环非严格反馈系统的一致有界性. 最后给出数值仿真例子验证所提控制 方法的有效性.
This paper investigates an adaptive fuzzy state feedback tracking control design problems for a class of non-strict feedback nonlinear systems with unknown functions and uncertain time-delay inputs. Fuzzy logic systems are used as the approximators of unknown functions, variable separation technology is used to deal with the non-strict feedback structure, and this method does not require the system function to meet the strict monotonic increasing condition. Unknown constants are used as the bounds of optimal approximation vector norm and approximation error. Therefore, at each step of backstepping design procedure, only these two adaptive parameters need to be adjusted. This method can not only compensate the influence of unknown time-delay input, but also reduce the number of online approximation parameters. Based on Lyapunov stability theory, the boundedness of closed-loop non-strict {feedback system} is analyzed. Finally, a numerical simulation example is given to verify the effectiveness of the proposed control method.

MR(2010)主题分类: 

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