Developing High Performance, Computationally Efficient Nonlinear Control Techniques for Polynomial Nonlinear Systems

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This proposal is aimed at developing a novel control approach to overcome limitations and computational complexity of existing nonlinear control techniques. By exploiting the polynomial nonlinear vector field through power transformation, computationally efficient control techniques could be obtained using non-quadratic Lyapunov functions and Sum-of-Squares programming techniques. The systematic control design approach has the potential to solve challenging nonlinear optimal and robust control problems for polynomial nonlinear systems. The proposed research could also help automate the control design process and verification of high performance nonlinear control laws, thus significantly reducing the cost and design cycle of nonlinear control systems. It is expected that the new nonlinear control approach will not only provide effective control designs and computational tools for polynomial nonlinear systems, it may also lead to the invention of competitive nonlinear control theory. The application of proposed nonlinear control approach to spacecraft control could enhance its robustness and improve spacecraft operating performance by optimizing its nonlinear control strategy. Because of its general nature, the proposed research is also expected to have major impacts on other applications including aircraft, robotic manipulators, automotive engines, and magnetic-levitated rotary machines, etc. Through close collaboration with NASA Johnson Space Center and out-reach activities, the research results will be disseminated to aerospace industry/control community and will result in automated nonlinear control design techniques. In addition, the development of an on-line controls course and a virtual experiment testbed could provide a unique platform for learning, and enhance the educational program at North Carolina State University by attracting non-traditional students and providing students with hands-on experience. These out-reach and educational activities will also strongly promote human resource development and diversity.