基于Backstepping的非一致轨迹迭代学习控制研究

Backstepping Based Non-Uniform Trajectory Iterative learning Control

针对一类在有限时间区间上可重复运行的高阶混合参数化非线性系统,利用改进Backstepping方法,将参数重组技巧和分段积分机制相结合,提出了一种混合自适应迭代学习控制算法。该算法由参数的微分-差分型自适应律和学习控制律组成,可以处理目标轨线迭代可变的跟踪问题。通过构造Lyapunov-like泛函使得跟踪误差的平方在一个有限时间区间上的积分收敛于零,同时保证所有信号均在有限时间区间内有界。仿真结果说明了所提算法的有效性。

For a class of high-order hybrid parametric nonlinear systems, which are repeatable on a finite time interval, an adaptive iterative learning control algorithm is proposed, by using modified Backstepping method, which combines the parameters reconstructed technique and piecewise integration mechanism. The algorithm is consisted of a difference-difficulty type parameters update law and a learning control, which can deal with the tracking problem with iterative changing desired trajectory. By constructing a Lyapunov-like functional, one can guarantee the tracking error converges to zero in terms of mean-square on the finite interval and guarantee all signals bounded in a finite time interval. The results of simulated example illustrate the effectiveness of algorithm proposed in this paper.