Sun Wei, Diao Shuzhen, Su Shun-Feng, Sun Zong-Yao
IEEE Trans Neural Netw Learn Syst. 2023 Apr;34(4):1911-1920. doi: 10.1109/TNNLS.2021.3105664. Epub 2023 Apr 4.
This study concentrates on the tracking control problem for nonlinear systems subject to actuator saturation. To improve the performance of the controller, we propose a fixed-time tracking control scheme, in which the upper bound of the convergence time is independent of the initial conditions. In the control scheme, first, a smooth nonlinear function is employed to approximate the saturation function so that the controller can be designed under the framework of backstepping. Then, the effect of input saturation is compensated by introducing an auxiliary system. Furthermore, a fixed-time adaptive neural network control method is given with the help of fixed-time control theory, in which the dynamic order of controllers is reduced to a certain extent since there is only one updating law in the entire control design. Through rigorous theoretical analysis, it is concluded that the proposed control scheme can guarantee that: 1) the output tracking error can converge to a small neighborhood near the origin in a fixed time and 2) all signals in the closed-loop system are bounded. Finally, a numerical example and a practical example based on the single-link manipulator are provided to verify the effectiveness of the proposed method.
本研究聚焦于受执行器饱和影响的非线性系统的跟踪控制问题。为提高控制器的性能，我们提出一种固定时间跟踪控制方案，其中收敛时间的上限与初始条件无关。在该控制方案中，首先，采用一个光滑非线性函数来逼近饱和函数，以便在反步设计框架下设计控制器。然后，通过引入一个辅助系统来补偿输入饱和的影响。此外，借助固定时间控制理论给出了一种固定时间自适应神经网络控制方法，由于在整个控制设计中只有一个更新律，控制器的动态阶数在一定程度上得以降低。通过严格的理论分析，得出所提出的控制方案能够保证：1）输出跟踪误差可在固定时间内收敛到原点附近的一个小邻域；2）闭环系统中的所有信号都是有界的。最后，给出了一个数值例子和一个基于单连杆机械手的实际例子，以验证所提方法的有效性。
