非匹配不确定非线性系统的鲁棒输出跟踪

Robust Output Tracking for a Certain Class of Nonlinear Systems with Unknown Mismatched Uncertainties

针对一类非匹配不确定非线性系统,提出一种鲁棒自适应渐近输出跟踪控制方法,该方法无须已知不确定性函数及其各阶导数上界。基于Lyapunov函数方法,给出了鲁棒自适应控制律以及GCMAC神经网络权值调整算法,通过后一个状态镇定前一个状态,最终达到了对期望输出的渐近跟踪,同时系统状态有界。应用于电液位置伺服系统的仿真结果表明该控制策略是有效的,对系统不确定性和未知干扰具有较强的鲁棒性。

Aim. Backstepping design requires knowledge of hard-to-specify upper bounds of unknown functions and their derivatives. We obviate this difficulty for a certain class of nonlinear systems with unknown mismatched uncertainties by proposing a new adaptive robust tracking control method using GCMAC （Gauss basis function Cerebellar Model Articulation Controller）. In the full paper, we explain our proposed method in detail; in this abstract, we just add some pertinent remarks to listing the two topics of explanation： （1） description of the class of nonlinear systems to which our proposed method is applicable; （2） design of our robust controllers the subtopics are the function approximation theory of GCMAC neural network （subtopic 2. 1） and the procedure of the design of our robust controller （subtopic 2. 2）; Theorem 1 in subtopic 2.1, the common estimation theorem of GCMAC, is well known and taken from the open literature; in subtopic 2.2, we introduce the tracking error vector and establish the tracking error mathematical model; again, in subtopic 2.2, we use GCMAC neural networks to estimate the system uncertainties and to design the robust adaptive controller; again, still in subtopic 2. 2, we construct Lyapunov functions with state tracking error and GCMAC weight error and design the neural networks weight turn laws, which, together with the robust adaptive controller, can guarantee the output tracking error＇s converging to zero while the states of the nonlinear system and the approximation errors of neural networks are bounded. In short, through our proposed control method, the preceding state of system is stabilized by the succeeding state and the succeeding state, now as the preceding state, is again stabilized by the next succeeding state and so on until the output tracks the instruction precisely. Our proposed control method was applied to designing the electro-hydraulic position servo control system with mismatched uncertainties and unknown external load disturbance of 8 000sin （62.8t） N. The simulation results show that the output tracking error is only 0. 3mm when the desired output is 50＋16sin （31.4t） mm.