Adaptive Control and Robustness in the Gap Metric
Adaptive Control and Robustness in the Gap Metric
复制标题
间隙度量中的自适应控制和鲁棒性
DOI：
10.1109/tac.2008.916659
复制
发表时间：
2008
影响因子：
6.8
通讯作者：
M. French
中科院分区：
文献类型：
--
作者：
M. French
研究了最小相位线性系统在间隙度量意义下实现非零鲁棒裕度的自适应控制器的构造。对于较大的扰动和较大的参数不确定性，间隙摄动裕度可能更受约束。在非线性间隙度量的框架下，首先给出了通用自适应控制器实现一阶标称对象的镇定，然后将结果推广到相对一级标称对象。引入了半通用控制设计的概念，即存在一个独立于先验已知不确定性水平的性能界，并给出了半通用设计何时优于无记忆控制器类和线性定常控制器类的表征。在自适应控制的经典假设下，给出了标称对象的鲁棒半通用自适应控制设计。结果应用于包括Rohrs示例在内的未建模动力学的显式类。
We consider the construction of adaptive controllers for minimum phase linear systems that achieve nonzero robustness margins in the sense of the gap metric. The gap perturbation margin may be more constrained for larger disturbances and for larger parametric uncertainties. Working in both and settings, and within the framework of the nonlinear gap metric, universal adaptive controllers are first given achieving stabilization for first-order nominal plants, and the results are then generalized to relative degree one nominal plants. A notion of a semiuniversal control design is introduced, which is the property that a bound on performance exists that is independent of the a priori known uncertainty level, and a characterization is given for when semiuniversal designs outperform the class of memoryless controllers and the class of linear time-invariant controllers. Robust semiuniversal adaptive control designs are given for nominal plants under the classical assumptions of adaptive control in both the and settings. The results are applied throughout to explicit classes of unmodeled dynamics including the Rohrs example.