一类严反馈块控非线性MIMO系统的动态面控制

Dynamic Surface Control for a Class of Strict-Feedback MIMO Systems in Nonlinear Block Controllable Form

针对一类具有未知不确定性的严反馈块控非线性多输入多输出(MIMO)系统,提出一种满足L_∞跟踪性能的动态面鲁棒控制律设计方法.通过非线性阻尼项对未知不确定性进行补偿,动态面控制方法消除了反向递推(backstepping)设计方法中由于对虚拟控制反复求导而导致的复杂性问题.基于李亚普诺夫稳定性定理证明了闭环系统的所有信号半全局一致最终有界,通过适当选择设计参数及初始化动态面变量,跟踪误差可收敛到原点的一个任意小邻域内,且可以保证系统各个输出跟踪误差的L_∞性能.数值仿真验证了方法的有效性.

A robust dynamic surface control law design method with guaranteed L∞ tracking performance is proposed for a class of strict-feedback MIMO （multiple-input multiple-output） systems in nonlinear block controllable form with unknown uncertainty. A nonlinear damping item is employed to compensate unknown uncertainty. The problem of explosion of terms in backstepping design caused by repeated derivations of certain nonlinear functions in virtual control, is overcome by the dynamic surface control method. All signals in the closed loop are guaranteed to be semi-globally uniformly ultimately bounded by Lyapunov stability theorem. The output tracking error is proved to converge to an arbitrarily small neighborhood around zero and the L∞ performance of system tracking error can be guaranteed by appropriately choosing design parameters and initializing the dynamic surfaces. Simulation results demonstrate the effectiveness of the proposed method.