不确定非线性系统的鲁棒自适应跟踪简化算法

Simplified algorithm of robust adaptive tracking controller for uncertain nonlinear systems

传统的Backstepping自适应控制方法需要对虚拟控制律进行求导,从而导致“计算复杂性膨胀”。动态平面控制技术能够克服这一缺陷。将这一技术扩展到一类具有参数严格反馈形式的不确定非线性系统输出跟踪,这类系统同时包含线性参数和未知非线性函数两种不确定性。所设计的控制算法比现有算法大大简化,解决了“计算复杂性膨胀”问题;运用Lyapunov理论证明了闭环系统一致最终有界,仿真结果表明了算法的有效性。

The traditional adaptive backstepping method can result in ＂an explosion of computation complexity＂ because of the reguirement to differentiate the virtual controls at each backstepping step. The dynamic surface control （DSC） technique can overcome this shortcoming. In this paper, the DSC method is extended to robust adaptive tracking control for a class of nonlinear systems in parametric-strict-feedback form. The systems may possess both parametric uncertainties and unknown nonlinear functions that may represent modeling errors and external disturbances. The designed control algorithm is simplifier than the existing algorithms based on the traditional backstepping method and overcomes the problem of ＂the explosion of computation complexity＂. It is shown to guarantee the closed-loop system signals are uniformly ultimately bounded using Lyapunov theory. The steady-tracking errors stay in the prescribed bound. The numerical simulation results verify the proposed algorithm effectiveness.