Fen Wu

There are many switched systems emerging recently in engineering practice that involve an interaction between continuous time and discrete event dynamics. Switched systems provide a useful mechanism to model complex dynamics that are subject to abrupt parameter variations and sudden changes of system configurations. Nevertheless, hybrid/switched systems are not only hard to analyze but also difficult to design and control. Therefore, effective control of these systems poses significant challenges for control engineers. Moreover, current switching control techniques often fail to address important practical issues such as restricted switches and actuator nonlinearities. Bridging over adaptive and gain-scheduling control techniques, the PI will establish a switching control design framework for nonlinear systems, with ultimate goal of developing efficient control design algorithms. It is expected that the new switching control approaches will optimize controlled performance, augment design capability with balanced robustness and adaptation. Moreover, the study on generalized Lyapunov functions for control synthesis may expand classical Lyapunov control horizon. Computationally efficient algorithm development would exploit the structure of non-convex BMIs and dramatically reduce computational cost of BMI optimization problems. The research on advanced switching control is envisioned to foster competitive nonlinear control paradigm, and overcome long-standing theoretical and practical limitations of existing switching control theory. The application of newly developed switching control techniques to hypersonic aircraft could realize the full potential of ultrahigh speed aircraft flight, which has critical importance for lethal military mission and fast global transportation. The outcome of the proposed research thus would have significant commercial, military, and national security impact. Because of the general nature of the proposed research, it is expected to have large impacts on other areas including the control of automobile transmission, switching power converters, and robot manipulators. The success of this project can serve as a catalyst for the widespread use of high-performance, switching control approaches in engineering society. The proposed educational activities will enhance NCSU educational program by fostering under-represented students and facilitate university-industry collaboration and technology transfer.

Nonlinear control has been a very active research area in recent years, motivated by the fact that in many practical control problems, the controlled dynamics of the systems are dominated by nonlinear effects. Unfortunately, current nonlinear control techniques cannot satisfy stability and performance requirements simultaneously and often result in compromised designs. On the other hand, the availability of increasingly more powerful and less expensive microprocessors and the need for better performance have motivated control engineers to explore new nonlinear control algorithms for advanced applications. Nevertheless, significant progress in computational mathematics and convex optimization techniques in recent years has not been fully utilized in nonlinear control designs. Therefore, it is highly desirable to develop innovative control design methodologies and nonlinear control solution approaches to address these deficiencies. Intellectual Merit This proposal is aimed at developing a novel control approach to overcome limitations and computational complexity of existing nonlinear control techniques and applying it to a spacecraft control problem. By exploiting the polynomial nonlinear vector field, significantly improved control techniques could be obtained using non-quadratic Lyapunov functions and SOS programming techniques. The systematic control design approach is applicable to a larger class of nonlinear systems, and will solve challenging nonlinear robust control problem with optimized performance. The synergy among optimization techniques, control theory, and applications has the potential for substantial gains in all three areas and would greatly increase our ability to design, build and control the increasingly complex nonlinear systems. The proposed research could also help automate the control design process and verification of high performance nonlinear control laws, thus dramatically reducing the cost and the design circle of nonlinear control systems. We envision the proposed nonlinear control approach will not only provide effective design and computational tools for nonlinear systems, it will also lead to the invention of competitive nonlinear control theory. Broader Impact The application of proposed nonlinear control approach to the spacecraft control problem promises to enhance its maneuver capability and robustness properties, and improve spacecraft performance by optimizing its nonlinear control strategy. Through close collaboration with NASA Johnson Space Center, the research outcome will be disseminated to aerospace industry and the benefits of automated nonlinear control design techniques are expected to be widely appreciated. Because of its general nature, it is anticipated that the proposed research will have major impacts on other applications including aircraft, robot manipulators, automotive engines, and magnetic-levitated rotory machines, etc. Moreover, the developed on-line control course and virtual experiment testbed could provide a unique platform for learning, and enhance the educational program of North Carolina State University by attracting non-traditional students and providing students with hands-on experience. With the help of computer-aided nonlinear control design toolbox, this project could serve as a catalyst for the widespread use of high performance, nonlinear control techniques in engineering society.

Hypersonic air-breathing vehicles offer a very attractive and potentially safer alternative to traditional rockets. However, Hypersonic vehicle flight presents significant challenges for control engineers including variable operating conditions, large modeling uncertainties and possible sensor/actuator failures. In this project, we will develop effective control approaches to address challenging control tasks during hypersonic flight. By synthesizing fault detection and identification (FDI), switching control, and gain-scheduling control techniques, we will develop reconfigurable control systems for enhanced fault-tolerant capability and design flexibility. Moreover, the study on probabilistic robust control will provide new perspective on robust control techniques. It will overcome the complexity of non-convex control problems and achieve practically acceptable engineering designs. The advantages of the proposed control approach for hypersonic flight will be demonstrated through high-fidelity nonlinear simulations. The success of the proposed research will realize the potential of hypersonic aircraft as launch vehicle and global transporter, thus has critical importance in achieving NASA's strategic goal. Throughout the project, the PIs will collaborate with researchers in NASA research centers for the verification of integrated control techniques and technology transfer.

Spacecraft and reusable launch vehicles have inherent nonlinear characteristics that cannot be ignored. In space missions, global/semi-global stability is a desired property for the safety of these systems. Increasingly stringent operation requirements of spacecraft have continually been demanding sophisticated high performance flight control systems. Although significant progress has been made over the last decade in developing nonlinear control theories and numerical algorithms, it appears that there are significant limitations in these methods to effectively address global stability and optimal controlled performance altogether. For instance, most results of nonlinear control theory only consider global stability of nonlinear systems without addressing performance issues. The solutions to optimal control synthesis problems such as nonlinear H_inf control are difficult not only to compute but also to represent. Therefore, new nonlinear control approaches and effective control design methodologies are highly desirable. The proposed research efforts will be focused on the development of novel nonlinear control theory and its application to space vehicle control problems. Towards this goal, a comprehensive nonlinear control theory with global/semi-global stability and optimized performance will be developed for polynomial nonlinear systems. Encouraged by his preliminary study on the sum-of-squares (SOS) technique, the PI will further explore this powerful tool to solve challenging nonlinear optimal and robust control problems. A direct application of the proposed nonlinear control techniques will be high-precision and robust spacecraft attitude control problem, which presents significant technical challenges and has significant importance in achieving NASA strategic goal in space exploration. Close collaboration with NASA Johnson Space Center (JSC) will be established to ensure technical relevance of proposed nonlinear control techniques to the needs of aerospace industry.