Nonsmooth Extremum Seeking Control With User-Prescribed Fixed-Time Convergence
Nonsmooth Extremum Seeking Control With User-Prescribed Fixed-Time Convergence
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DOI：
10.1109/tac.2021.3063700
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发表时间：
2021-03
影响因子：
6.8
通讯作者：
J. Poveda;M. Krstić
中科院分区：
文献类型：
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作者：
J. Poveda;M. Krstić
本文介绍了一类新的非光滑极值搜索控制器（ESC）的收敛界给出类-$\mathcal {K}\mathcal {L}$功能，具有一致有界的调整时间。这些ESC的特点是标称平均系统，使一致的全球固定时间稳定（UGFxTS），一个稳定的非线性植物的响应映射的最小值集。考虑到在适当调整控制器参数的情况下，ESC继承了其平均系统的收敛特性，与基于梯度下降或牛顿流的传统ESC相比，所提出的动态可以实现更好的瞬态性能。此外，对于当植物是一个静态地图的情况下，所提出的算法的收敛时间可以预先规定的用户为所有的初始条件，而不需要重新调整的ESC的学习动力学的增益。由于具有固定时间收敛特性的自主反馈控制器必然是非Lipschitz连续的，因此传统上用于ESC的标准平均和奇异摄动工具不再适用。我们解决这个问题，通过使用平均和奇异摄动工具的非光滑和集值系统，这进一步使我们能够考虑ESCS建模的不连续向量场，是典型的固定时间和有限时间优化问题。
This article introduces a new class of nonsmooth extremum seeking controllers (ESCs) with convergence bounds given by class-$\mathcal {K}\mathcal {L}$ functions that have a uniformly bounded settling time. These ESCs are characterized by nominal average systems that render uniformly globally fixed-time stable (UGFxTS), the set of minimizers of the response map of a stable nonlinear plant. Given that, under suitable tuning of the parameters of the controllers, the ESCs inherit the convergence properties of their average systems, the proposed dynamics can achieve a better transient performance compared to the traditional ESCs based on gradient descent or Newton flows. Moreover, for the case when the plant is a static map, the convergence time of the proposed algorithms can be prescribed a priori by the users for all initial conditions without the need of retuning the gain of the learning dynamics of the ESC. Since autonomous feedback controllers with fixed-time convergence properties are necessarily non-Lipschitz continuous, standard averaging and singular perturbation tools, traditionally used in ESC, are not applicable anymore. We address this issue by using averaging and singular perturbation tools for nonsmooth and set-valued systems, which further allows us to consider ESCs modeled by discontinuous vector fields that are typical in fixed-time and finite-time optimization problems.