具有状态和输入量化的分数阶非线性系统自适应模糊控制

Adaptive fuzzy control for fractional-order nonlinear systems with state and input quantization

中文关键词  分数阶非线性系统  状态和输入量化  模糊逻辑系统  反步递推

英文关键词  fractional-order nonlinear systems  state and input quantization  fuzzy logic system  backstepping

中文摘要

      本文主要探讨在状态和输入量化条件下的分数阶非线性系统的模糊自适应控制问题. 首先, 基于状态非量 化的情况, 设计了状态量化下的虚拟控制器和实际控制器, 其偏导数是量化状态的乘积, 以实现最终的控制设计; 其 次, 为确保由于状态量化和输入量化导致的一些列误差有界, 构造了一个足够光滑的分数阶投影算子并设计了一种 模糊自适应反步递推控制策略. 进而建立并严格证明了分数阶一致有界准则, 在已知参数有界的前提下, 解决了分 数阶意义下的误差信号一致有界问题. 在分数阶一致有界准则的保障下, 确保了所有闭环信号的有界性; 最后, 通过 仿真结果验证了该方法的有效性.

英文摘要

      This article mainly discusses the fuzzy adaptive control problem of fractional-order nonlinear systems under state and input quantization conditions. To begin with, based on the case of non-quantized states, virtual and actual controllers under state quantization are designed, where their partial derivatives are the product of the quantized states, to achieve the final control design. Next, to ensure that the series of errors caused by state and input quantization is bounded, a sufficiently smooth fractional-order projection operator is constructed, and a fuzzy adaptive backstepping recursive control strategy is designed. Furthermore, a fractional-order uniform boundedness criterion is established and rigorously proven, addressing the issue of uniform boundedness of the error signal in the fractional-order sense under the premise of known bounded parameters. With the assurance of the fractional-order uniform boundedness criterion, the boundedness of all closed-loop signals is guaranteed. Finally, the effectiveness of this method is validated through simulation results.