Adaptive Fuzzy Backstepping Control of Fractional-Order Nonlinear Systems
针对一类带有未知外部扰动的分数阶非线性系统，提出一种自适应模糊反步控制方法，用模糊逻辑系统逼近复杂未知函数，基于分数阶李雅普诺夫稳定性准则设计虚拟控制律，最终构建自适应模糊控制器确保跟踪误差收敛。
Backstepping control is effective for integer-order nonlinear systems with triangular structures. Nevertheless, it is hard to be applied to fractional-order nonlinear systems as the fractional-order derivative of a compound function is very complicated. In this paper, we develop an adaptive fuzzy backstepping control method for a class of uncertain fractional-order nonlinear systems with unknown external disturbances. In each step, a complicated unknown nonlinear function produced by differentiating a compound function with a fractional order is approximated by a fuzzy logic system, and a virtual control law is designed based on the fractional Lyapunov stability criterion. At the last step, an adaptive fuzzy controller that ensures convergence of the tracking error is constructed. The effectiveness of the proposed method has been verified by two simulation examples.