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A Robust Event-Triggered Approach for Fast Sampled-Data Extremization and Learning

机译：一种鲁棒的事件触发方法，用于快速采样数据的极值化和学习

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摘要

This paper presents a general framework for the analysis and design of a class of model-free, robust, and efficient sampled-data-based algorithms for extremization and learning in continuous-time nonlinear systems that generate response maps with an optimal operational set. In particular, we consider plants described by differential inclusions, interconnected in a sampled-data setting with a robust learning algorithm characterized by a constrained difference inclusion. In contrast to standard sampled-data-based approaches, where the learning dynamics are updated after a fixed sufficiently long sampling time has passed, we design a robust dynamic event-based mechanism that triggers the control action as soon as the rate of change of the output of the plant is sufficiently small. By using this event-based update rule, a significant improvement in the convergence time of the closed-loop system can be achieved. Using the framework of set-valued hybrid dynamical systems, we establish for the closed-loop system the existence of a uniformly asymptotically stable compact set, which, by an appropriate tuning of the control parameters, can be made arbitrarily close to the optimal operational set. Our results generalize existing results for periodic sampled-data extremum seeking, and can be used to solve model-free multivariable smoothonsmooth constrained optimization problems, as well as learning problems in game theoretical scenarios.
机译：本文提出了一个通用的框架，用于分析和设计一类基于模型的，无模型的，鲁棒的，高效的，基于采样数据的算法，用于在连续时间非线性系统中进行极端化和学习，从而生成具有最佳操作集的响应图。特别是，我们考虑用差异包含物描述的植物，这些植物在采样数据设置中与以受限差异包含为特征的鲁棒学习算法互连。与标准的基于采样数据的方法（在经过足够长的固定采样时间后更新学习动态）相比，我们设计了一种强大的基于动态事件的机制，该机制会在事件发生率变化时立即触发控制操作。设备的输出足够小。通过使用基于事件的更新规则，可以显着改善闭环系统的收敛时间。使用集值混合动力系统的框架，我们为闭环系统建立了一个一致渐近稳定的紧集的存在，通过适当地调节控制参数，可以使该紧集任意接近最佳操作集。 。我们的研究结果概括了现有的定期采样数据极值搜索结果，可用于解决无模型的多变量平滑/非平滑约束优化问题，以及博弈论中的学习问题。

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