Fuzzy Approximator Based Adaptive Dynamic Surface Control for Unknown Time Delay Nonlinear Systems With Input Asymmetric Hysteresis Nonlinearities
针对一类未知时滞非线性系统，提出一种基于模糊逼近器的自适应动态面控制方法，利用模糊逻辑系统和有限覆盖引理处理时滞，无需逆模型即可补偿非对称滞回非线性，保证闭环系统信号有界。
In this paper, a fuzzy approximator based adaptive dynamic surface control scheme is proposed for a class of unknown time delay nonlinear systems preceded by asymmetric hysteresis nonlinearities. The features of the proposed method are: 1) by combining the approximated property of the fuzzy logic systems (FLSs) with the finite covering lemma, the Krasovskii functionals are disposed of, achieving the <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">${L}_{{\infty }}$ </tex-math></inline-formula> norm of the tracking error by using the initializing technique; 2) the assumptions on the time-delay functions are removed due to the use of the finite covering lemma and the FLSs; and 3) the proposed adaptive fuzzy dynamic surface control scheme can also compensate the asymmetric shifted Prandtl-Ishlinskii (ASPI) hysteresis without constructing the inverse of the ASPI model with the density function of ASPI model being unknown and estimated online to compensate the hysteresis. It is proved that all the signals in the closed-loop system are ultimately uniformly bounded and can be made arbitrarily small. Simulation results show the validity of the proposed method.