Robust Control of Uncertain Switched Systems

该提案的目标是开发用于复杂系统的系统化控制器设计工具。PI将开发使用一组所谓的不确定仿射模型对感兴趣的行为进行建模的程序。有了这个标准形式的系统表示，将允许开发系统的鲁棒控制器设计算法，使控制器综合具有可证明的性能。不仅强调理论结果的发展，还将强调将所提出的方法用于癫痫发作的反馈控制等具体应用。智能优点：所提出的方法依赖于不确定切换系统的概念。这项拟议的工作将解决切换系统及其与不确定系统的联系领域中的几个公开问题。具体地说，提出的研究将开发有效的方法来确定一组仿射模型和解释所观察到的非线性行为的不确定性界，以及用于不确定切换仿射系统的鲁棒控制器设计的工具。与其他复杂系统控制器设计方法相比，该方法的主要优点是：a)稳健的系统逼近过程；b)能够设计具有可证明性能的控制器，并且在给定足够的计算资源的情况下，其性能可以任意接近于可实现的最优值；c)对于没有全局模型但只有局部信息可用的复杂系统，能够设计控制器。它将导致系统的、与问题无关的控制器设计工具的开发，这些工具可用于广泛的应用，如癫痫和其他类似神经疾病的反馈控制。通过将非线性控制纳入本科课程，开发了一门特别强调非线性控制方面的机器人课程，REU补充材料以激励本科生学习非线性和混合控制，以及将研究成果整合到研究生课程材料中，教育被积极地整合到这个项目中。

The objective of this proposal is to develop systematic controller design tools for complex systems. The PIs will develop procedures for modeling the behavior of interest using a set of so-called uncertain affine models. Having a representation of the system in this standard form will then allow for the development of systematic robust controller design algorithms that enable controller synthesis with provable performance. Emphasis will be put not only on the development of theoretical results but also on using the proposed approach in concrete applications such as feedback control of epileptic seizures.Intellectual Merit: The approach presented relies on the concept of uncertain switched systems. The proposed work will address several open problems in the area of switched systems and their connection to uncertain systems. Specifically, the proposed research will develop efficient methods that determine a set of affine models and the uncertainty bound that explain the observed nonlinear behavior, and tools for robust controller design for uncertain switched affine systems. The main advantages of the proposed approach, as compared to other approaches to controller design for complex systems, are: a) Robust system approximation procedures; b) Ability to design controllers with provable performance and, given enough computational resources, with performance arbitrarily close to the achievable optimum; c) Ability to design controllers for complex systems for which one does not have a global model but only local information is available.Broader Impact.The proposed activity explores the concept of covering complex dynamics by the set of dynamic behaviors of an uncertain switched affine model. It will lead to the development of systematic, problem-independent tools for controller design that can be used in a wide range of applications such as feedback control of epilepsy and other similar neurological disorders. Education is proactively integrated into this project through incorporation of nonlinear control in the undergraduate curriculum, a robotics course developed with particular emphasis on the nonlinear control aspects, REU supplements to motivate undergraduate students to pursue studies in nonlinear and hybrid control, and integration of the research outcomes into graduate course materials.