New Controller Design Approaches for Complex, Nonlinear Dynamic Systems

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This project will create new theories and approaches for ensuring stable behavior and desired performance of complex dynamic systems. Some examples of such systems include network of power plants, interconnected electric vehicles, or biological systems such as normal cell physiology and the alterations that lead to human disease. This project will develop new theories and methods that can help design control systems for such systems based on better understanding of the intrinsic relationships between inherent characteristics of the system and their dynamic behaviors. The theories, tools and approaches can be readily used to solve a wide range of real-world engineering problems, including predicting evolution of damage in bones, developing more energy efficient control algorithms for power generation systems to reduce hazardous emissions, or designing better coordination control for a network of electric vehicles. The traditional approaches to design of control systems for complex nonlinear systems involve simplified model (linearization) of the system which inherently limits the performance of these systems. If successful, the outcome of the work will be a big leap towards finding better control methods for nonlinear systems. The project also has significant broader impacts. Through a structured research activity this project will enhance minority students' education at the University of Texas at San Antonio, a Hispanic serving institution. The project will also promote international collaboration among U.S. students, faculty, and their peers in the global community. This project aims to develop sustained and systematic research to explore new theories and approaches for behavior analysis and controller design of inherently nonlinear dynamic systems. The new framework of multivariant homogeneity will be developed based on recent new concepts in defining homogeneity. The new generalized framework will be instrumental to characterize a boarder range of nonlinear dynamic systems. By establishing the homogeneous center manifold theory, the intrinsic link between the convergence rate of the system trajectory and the monotone homogeneity of the system will be discovered. The innovative design tools will lead to solutions to many open control problems for inherently nonlinear systems. The definitions, theories, and approaches in this project will add much-needed components to complete the theory of homogeneous systems, accelerate the research of control theory and dynamic systems, and facilitate new solutions to real-world engineering problems.This award reflects NSF's statutory mission and has been deemed worthy of support through evaluation using the Foundation's intellectual merit and broader impacts review criteria.