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.
