Global/Semi-Global Stabilizing, Local Optimized Gain-Scheduling Control Design for Nonlinear Systems

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Although significant progress has been made over the last decade in developing nonlinear control theories and numerical algorithms, it appears that these methods are limited in their abilities to effectively address global stability and optimal controlled performance altogether. One control design approach with great potential for nonlinear systems is gain-scheduling control. With moderate increase in controller complexity, multiple control schemes (such as switching and gain-scheduling) will enhance the capacity of nonlinear control systems and decouple the nonlinear control design task. As a result, overall nonlinear control design objective with improved stability and performance will be achieved. This project will focus on global gain-scheduling control development and its application to unmanned aerial vehicle (UAV), as well as the integration of research results into the educational program of North Carolina State University (NCSU). The global gain-scheduling control framework will provide a systematic control design technique with optimized local performance and guaranteed global/semi-global stability, and overcome the computational complexity of nonlinear optimal control problem. By exploiting the functional dependency of nonlinear vector field, significantly improved LPV analysis and control design techniques will be developed using the sum-of-squares (SOS) decomposition. More importantly, the application of the powerful SOS tool will offer new insights into existing fields, such as robust and adaptive controls, and lead to the development of next generation of advanced control techniques. The application of proposed gain-scheduling control technique to UAVs will demonstrate increased UAV capabilities, and would greatly improve the performance and safety of commercial, military, and personal aircraft. With the development of computer-aided control design software, we envision the resulting gain-scheduled control systems to be widely used to enhance the performance of nonlinear control systems, including ground/underwater autonomous vehicles, robot manipulators, and automotive engines. The development of innovative education approaches will enhance NCSU educational program by providing students at both undergraduate and graduate levels with strong theoretical background and practical skills. Furthermore, the developed toolbox on LPV analysis and control designs will serve as a vehicle to disseminate research outcomes to students and researchers, and facilitate technology transfer to industrial practitioners. Active collaboration with NASA Langley Research Center will be emphasized to achieve research and educational objectives.