Fundamental Limitations in Control of Nonlinear Systems with Application to Biology

University Of Illinois At Urbana-Champaign, Urbana IL

Investigators

Abstract

Objective: The motivation for the proposed research comes from the brain, where nonlinear dynamics are believed to be at the heart of computation, signal processing and control. The brain suggests that nonlinear dynamics and control have a robust, synergistic relationship. This proposal offers an integrated research program for the fundamental limitations and robustness analysis of nonlinear systems with control. Intellectual Merit: The intellectual merit derives from the proposed unified framework for fundamental limitations and robustness analysis of nonlinear feedback systems. A variety of system theoretic problems can be cast within the proposed framework, which can lead to transformative advances in the fundamental understanding of nonlinear dynamics in brain functions. The project will develop algorithms and software for model reduction, enunciation of control architectures that are best suited to exploit synergies between nonlinear dynamics and control and development of software tools for modeling the neural circuits in the brain. Broader Impacts: The theoretical aspects of the proposed research address fundamental limitations in control of nonlinear systems, which have broad applicability. The brain itself offers a unique paradigm that can lead to novel ways to leverage nonlinear dynamics in current and future engineering applications. In addition the research plan is closely integrated with an educational plan. Several educational initiatives will help disseminate the methods, outcomes and the interdisciplinary synergies. This project seeks to develop a strong undergraduate involvement in research, interdisciplinary outreach activities, exposure to the central role of dynamics and control and to foster symbiotic relationships between university research and the industry.