基于小增益定理的非线性系统的自适应动态面控制

Adaptive dynamic surface control of nonlinear systems via small gain theorem

针对一类具有未知死区的严格反馈不确定非线性系统,基于输入状态稳定理论和小增益定理,利用T-S模糊系统的逼近能力,提出一种自适应模糊控制方案.该方案取消了死区模型参数上下界已知的假设和虚拟控制增益要求可微的假设;利用动态面控制技术,将一阶滤波器引入后推设计中避免了传统后推方法中对虚拟控制反复求导而导致的计算复杂问题.通过构造2个耦合的子系统满足输入状态稳定条件,利用小增益定理分析证明闭环系统半全局一致终结有界,且选取适当的设计常数,跟踪误差可收敛到零的一个小邻域内.

Based on input-to-state stability （ISS） and small gain theorem, an adaptive fuzzy control scheme is proposed for a class of strict-feedback uncertain nonlinear systems with unknown deadzone by use of the approximation capability of Takagi-Sugeno type fuzzy systems. The approach does not require a priori knowledge of the upper bound and lower bound of dead zone model parameters, and it removes the assumption of the derivative of virtual control gain functions to be known. By using dynamic surface control and introducing first order filter, the explosion of complexity caused by repeated differentiations of virtual control in traditional backstepping design is avoided. By constructing two interconnected subsystems satisfying ISS condition, the closed-loop control system is proven to be semi-globally uniformly ultimately bounded using small gain theorem, and the output tracking error converges to a neighborhood of zero by choosing appropriate parameters.