Switching Control with Minimal Data

这笔赠款将允许我们在解决控制问题所需的最小数据量的理解方面取得新的突破。对于一个给定的控制目标，现代控制设计师不仅面临着开发控制算法的任务，而且还面临着决定是否可以用可用数据实现目标的问题，或者是通过适当的控制设计可以实现任务的最小数据量是多少的问题。通过采用现代系统理论工具，围绕动态系统的熵概念以及表征系统对扰动的鲁棒性的方法，该项目将开发在数据速率限制的情况下进行控制设计的系统方法。预计这些结果将对几个应用领域产生重大影响，包括人口动态，机械系统的控制，以及电气或机械系统网络的同步。该项目还包括将研究与人员培训和教育活动相结合的组成部分。该项目的总体目标是深入了解表征控制任务可实现的最小数据的挑战，并将此见解转化为设计通信和控制方案的协同方法。在现代理论和应用中感兴趣的高级控制问题中，人们经常会遇到过程动态，或控制器动态，或控制任务本身的切换行为。切换动态提出了重大挑战，该项目计划通过部署新的概括和拓扑熵和输入到状态鲁棒性概念的组合来克服。该项目最初将集中在三个基准类的控制问题：1）切换系统的控制; 2）非完整机械系统的控制;和3）鲁棒的领导者-跟随者同步。该项目从每个问题类别的具体案例研究出发，旨在为复杂系统设计开关控制器提供一种通用方法，该方法利用现有数据以最佳或接近最佳的方式进行设计。该奖项反映了NSF的法定使命，并通过使用基金会的知识价值和更广泛的影响审查标准进行评估，被认为值得支持。

This grant will allow breaking new ground in our understanding of the minimal amount of data required for solving control problems. For a given control objective, a modern control designer is faced not just with the task of developing a control algorithm, but also with deciding whether the objective is achievable with the available data, or with the question of what is the smallest amount of data with which the task is achievable by proper control design. By employing modern system-theoretic tools, centered around the notion of entropy for dynamical systems as well as methods for characterizing robustness of system response to perturbations, the project will develop systematic approaches to control design in the presence of data-rate constraints. The results are expected to have significant impact on several application domains, including population dynamics, control of mechanical systems, and synchronization of networks of electrical or mechanical systems. The project also includes components for integrating the research with personnel training and educational activities. The overarching goal of the project is to gain insight into the challenge of characterizing the minimal data with which a control task is achievable, and to translate this insight into synergistic methods for designing communication and control schemes. In advanced control problems of interest in modern theory and applications, one frequently encounters switching behavior in either the process dynamics, or in the controller dynamics, or in the control task itself. Switching dynamics present significant challenges, which the project plans to overcome by deploying novel generalizations and combinations of topological entropy and input-to-state robustness concepts. The project will initially focus on three benchmark classes of control problems: 1) control of switched systems; 2) control of nonholonomic mechanical systems; and 3) robust leader--follower synchronization. Building from specific case studies within each of these problem classes, the project aims to achieve a general methodology for designing switching controllers for complex systems which utilize available data in optimal or near-optimal fashion.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.