Intellectual Merits: The proposed work aims to explore the best performances of control systems with limited control capacity and resources. Non-quadratic Lyapunov functions will be developed and applied to the construction of nonlinear feedback laws, possibly with switching and hybrid structures. It is expected that nonlinear control laws are able to incorporate various constraints and utilize the limited resources more effectively than linear controllers. The nonlinear controllers will be constructed for the optimization of various performances, including stability region, robustness and disturbance rejection, under input and output constraints. To bridge the gap between theory and practice, this work emphasizes the realizablility of the Lyapunov approach and the design problems will be formulated into numerically tractable linear/bilinear matrix inequalities.
Broader Impact: Constraints are ubiquitous in control systems. All actuators have limited capacity and all physical quantities are bounded. Magnetic suspension systems are typical examples with severe constraints. They have been utilized in a variety of engineering systems ranging from artificial heart pumps to maglev trains. The outcome of the project will benefit the society with methodologies for the development of high performance, low power, economical and compact devices. Computational software will be made available along with published articles to promote the application of the results and to stimulate the development of nonlinear control design methods. An embedded magnetic suspension system will be constructed for both research and educational purposes. Female and minority students will be actively engaged in the project. Collaboration with local industrial partners will be established to promote the application of research results.
