基于未知高频增益的非线性系统自适应迭代学习控制

Adaptive iterative learning control for nonlinear systems with unknown high-frequency gain

针对一类单输入单输出不确定非线性重复跟踪系统 ,提出一种基于完全未知高频反馈增益的自适应迭代学习控制。与普通迭代学习控制需要学习增益稳定性前提条件不同 ,自适应迭代学习控制通过不断修改 Nussbaum形式的高频学习增益达到收敛。经证明当迭代次数 i→∞时 ,重复跟踪误差可一致收敛到任意小界δ。

An adaptive iterative learning control approach is proposed for a class of single input, single output uncertain nonlinear systems with completely unknown high frequency learning gain. Unlike the common iterative learning control which requires some preconditions of stability on the learning gain, the adaptive iterative learning control obtains the convergence through the change of high frequency learning gain in a Nussbaum type function. The repetitive tracking error sequence is shown to converge uniformly into an arbitrary small bound δ as the iterative sequence i→∞ . Simulation shows the validity of the proposed control method.