Robust Control of Uncertain Switched Systems

本提案的目的是为复杂系统开发系统的控制器设计工具。PI将使用一组所谓的不确定仿射模型来开发对感兴趣的行为进行建模的程序。在这个标准形式的系统的表示，然后将允许系统的鲁棒控制器设计算法，使控制器合成与可证明的性能的发展。重点将不仅放在理论结果的发展，但也在使用所提出的方法在具体的应用，如反馈控制癫痫发作。智力优点：提出的方法依赖于不确定切换系统的概念。拟议的工作将解决几个开放的问题，在该地区的切换系统及其连接到不确定的系统。具体而言，所提出的研究将开发有效的方法，确定一组仿射模型和不确定性界，解释所观察到的非线性行为，和不确定切换仿射系统的鲁棒控制器设计的工具。与其它复杂系统控制器设计方法相比，该方法的主要优点是：（a）鲁棒系统逼近方法：（B）能够设计出性能可证明的控制器，并且在给定足够的计算资源的情况下，其性能任意地接近可达到的最优值; c）、能够为没有全局模型但只有局部信息可用的复杂系统设计控制器。更广泛的影响。拟议的活动探讨了覆盖复杂系统的概念，动态由一个不确定的切换仿射模型的动态行为集。它将导致开发系统的，独立于问题的控制器设计工具，可用于广泛的应用，如癫痫和其他类似的神经系统疾病的反馈控制。教育是积极融入这个项目，通过纳入非线性控制在本科课程，机器人课程开发，特别强调非线性控制方面，REU补充，以激励本科生追求非线性和混合控制的研究，并将研究成果整合到研究生课程材料。 

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.