Theory, Methods, and Applications of Nonlinear Control Systems with Time Delays

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Objective: This project will develop cutting edge stabilization and tracking methods for important classes of deterministic nonlinear control problems that ensure good controller performance under uncertainty or time delays. The work will include engineering applications that will guide the research and ensure the practical usefulness of the results. One application will be to a delayed model of neuromuscular electrical stimulation, which is a technique that has the potential to help restore function to patients with neurological disorders. Another will be to experimental real time implementation of surface or underwater autonomous vehicles in collaboration with Fumin Zhang from Georgia Tech.Intellectual Merit: Delays and uncertainty are common in chemical process control, combustion, networked systems, teleoperation, and other areas because of modeling uncertainty, sensor designs, time consuming information processing, and transport phenomena, but they are often ignored to simplify the analysis or because the delays are short. In practice, many controllers typically perform well under small uncertainty, but rigorous analysis is needed to understand how the disturbances impact performance, and how big the delays and disturbances can be before stability is destroyed. This project will address these crucial issues using adaptive or delayed controllers that respect the bounds that often arise in applications.Broader Impacts: The project will combine the PI's mathematical approaches with the work of his engineering collaborators. This will increase the control engineering community's understanding of more rigorous methods. While the applications will focus on neuromuscular electrical stimulation and marine vehicles, we anticipate that the work will be general enough to eventually apply to other areas where time delays are important, such as aerospace and mechanical engineering. The project will also promote interdisciplinary learning. The work will be carried out at an institution that attracts many minorities, and special efforts will be made to recruit students from under- represented groups.