一类纯反馈非线性系统的反推近似滑模控制

Backstepping Approximate Sliding Mode Control for a Class of Pure-Feedback Nonlinear Systems

在非线性控制系统的优化过程中,针对一类含有未知函数项和外界干扰的不确定纯反馈非线性系统,提出了一种自适应反推近似滑模变结构控制方法。基于中值定理和隐函数定理将未知非仿射输入函数进行分解,使其含有显式的控制输入,利用神经网络逼近未知非线性函数,动态面控制技术解决了反推设计中对虚拟控制反复求导而导致的"微分爆炸"问题。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,取消了不确定干扰上界先验已知条件。最后,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,为控制系统性能优化提供了有效方法。

An adaptive 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 neural networks are 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 and priori known conditions for the upper bound of uncertainties are cancelled. At last, the proposed controller ensures the semi-global uniformly ultimately boundedness for all the closed loop signals.