一类非线性系统的自适应模糊反推近似滑模控制

针对一类含有未知非线性函数项和外界干扰的不确定纯反馈非线性系统,提出了一种自适应模糊反推近似滑模变结构控制方法。采用中值定理和隐函数定理使未知非仿射输入函数拥有显式的控制输入,利用模糊系统逼近未知非线性函数,动态面控制技术解决了反推设计中出现的"微分爆炸"问题。所提出的自适应近似滑模控制方案削弱了传统滑模控制中的抖振现象。从理论上证明了所设计的控制器能够保证闭环系统所有信号半全局一致终结有界。仿真算例验证了算法的有效性。

Adaptive Fuzzy Backstepping Approximate Sliding Mode Control for A Class of Nonlinear Systems

An adaptive fuzzy backstepping approximate sliding mode variable structure control approach is presented for a class of pure-feedback nonlinear systems with uncertainties and external interference. By using implicit function theorem and mean value theorem,unknown non-affine input functions can be transformed to partially affine forms,the fuzzy system is used to approximate the unknown nonlinearities in systems,the problem of explosion of complexity in traditional backstepping design is eliminated by utilizing dynamic surface control. By using adaptive approximate sliding mode control,the earthquake shaking phenomenon in traditional sliding mode control is decreased. At last, the proposed controller ensures the semi-global uniformly ultimately boundedness for all the closed loop signals. A numerical example is presented to demonstrate the effectiveness of the proposed algorithm.