Education

Research Description

Dr. Wu is interested in control theory, robust analysis and control, gain-scheduling control design and implementation, model approximation, structure and control interaction analysis, and the application of advanced control and optimization techniques to aerospace, mechanical and chemical engineering problems. Presently, he is working on fault detection algorithms that improve the safety of hypersonic vehicles (for NASA), and the development of computationally efficient algorithms for nonlinear systems that have polynomial nonlinearities. Within MAE he collaborates with Dr. Buckner and Dr. Yuan.

Publications

Almost output regulation of LFT systems via gain-scheduling control

Yuan, C. Z. and Duan, C. and Wu, F. (2018), International Journal of Control, 91(5), 1161-1170.

Cooperative output regulation of multi-agent systems with switched leader dynamics

Yuan, C. Z. and Wu, F. (2018), International Journal of Systems Science, 49(7), 1463-1477.

Stability analysis and controller design for a novel nonlinear system: Fuzzy parameter varying system

Zhang, H. Y. and Ban, X. J. and Wu, F. (2018), Journal of Intelligent & Fuzzy Systems, 34(6), 4387-4395.

Almost output regulation of switched linear dynamics with switched exosignals

Yuan, C. Z. and Wu, F. (2017), International Journal of Robust and Nonlinear Control, 27(16), 3197-3217.

Consensus for multi-agent systems with time-varying input delays

Yuan, C. Z. and Wu, F. (2017), International Journal of Systems Science, 48(14), 2956-2966.

Cooperative output regulation of multi-agent systems with switched leader dynamics via smooth switching

Yuan, C. Z. and Wu, F. and Duan, C. (2017), Proceedings of the ASME 10th Annual Dynamic Systems and Control Conference, 2017, vol 2, (), .

Dynamic output feedback control for continuous-time T-S fuzzy systems using fuzzy lyapunov functions

Liu, Y. and Wu, F. and Ban, X. J. (2017), IEEE Transactions on Fuzzy Systems, 25(5), 1155-1167.

Exact-memory and memoryless control of linear systems with time-varying input delay using dynamic IQCs

Yuan, C. Z. and Wu, F. (2017), Automatica, 77(), 246-253.

Gain-scheduling control of T-S fuzzy systems with actuator saturation

Liu, Y. and Ban, X. J. and Wu, F. and Lam, H. K. (2017), Journal of Intelligent & Fuzzy Systems, 32(3), 2579-2589.

New developments in multibody system dynamics and its applications 2015

Rui, X. T. and Zhang, C. Z. and Wang, S. M. and Wu, F. (2017), Advances in Mechanical Engineering, 9(3), .

Output feedback control for fuzzy systems subject to actuator saturation based on fuzzy Lyapunov functions

Ban, X. J. and Liu, Y. and Huang, X. L. and Wu, F. (2017), Proceedings of the ASME 9th Annual Dynamic Systems and Control Conference, 2016, Vol 1, (), .

Time-based switching control of genetic regulatory networks: toward sequential drug intake for cancer therapy

Oduola, W. O. and Li, X. F. and Duan, C. and Qian, L. J. and Wu, F. and Dougherty, E. R. (2017), Cancer Informatics, 16(), .

Tracking control of hybrid systems with state-triggered jumps and stochastic events and its application

Yang, T. and Wu, F. and Zhang, L. X. (2017), IET Control Theory and Applications, 11(7), 1024-1033.

Aggregate control of clustered networks with inter-cluster time delays

Boker, A. M. and Yuan, C. Z. and Wu, F. and Chakrabortty, A. (2016), Proceedings of the American Control Conference, (), 5340-5345.

Analysis and control of genetic regulatory systems with switched drug inputs

Oduola, W. and Li, X. F. and Duan, C. and Qian, L. J. and Wu, F. and Dougherty, E. R. (2016), 2016 3rd IEEE EMBS International Conference on Biomedical and Health Informatics, (), 533-536.

Dynamic IQC-based analysis and synthesis of networked control systems

Yuan, C. Z. and Wu, F. (2016), Proceedings of the American Control Conference, (), 5346-5351.

Dynamic IQC-based control of uncertain LFT systems with time-varying state delay

Yuan, C. Z. and Wu, F. (2016), IEEE Transactions on Cybernetics, 46(12), 3320-3329.

H-infinity state-feedback control of linear systems with time-varying input delays

Yuan, C. Z. and Wu, F. (2016), IEEE Conference on Decision and Control, (), 586-591.

Hybrid almost output regulation of linear impulsive systems with average dwell-time

Yuan, C. Z. and Wu, F. (2016), Nonlinear Analysis-Hybrid Systems, 20(), 82-94.

Hybrid switched gain-scheduling control for missile autopilot design

Yuan, C. Z. and Liu, Y. and Wu, F. and Duan, C. (2016), Journal of Guidance Control and Dynamics, 39(10), 2352-2363.

New results on switched linear systems with actuator saturation

Duan, C. and Wu, F. (2016), International Journal of Systems Science, 47(5), 1008-1020.

Output feedback control of linear fractional transformation systems subject to actuator saturation

Ban, X. J. and Wu, F. (2016), International Journal of Systems Science, 47(15), 3646-3655.

Robust H-2 and H-infinity switched feedforward control of uncertain LFT systems

Yuan, C. Z. and Wu, F. (2016), International Journal of Robust and Nonlinear Control, 26(9), 1841-1856.

Robust switching output-feedback control of time-varying polytopic uncertain systems

Yuan, C. Z. and Wu, F. (2016), International Journal of Control, 89(11), 2262-2276.

robust gain-scheduling output feedback control of state-delayed lft systems using dynamic IQCS

Yuan, C. Z. and Wu, F. and Duan, C. (2016), Proceedings of the ASME 8th Annual Dynamic Systems and Control Conference, 2015, vol 3, (), .

A gain-scheduling control approach for takagi-sugeno fuzzy systems based on linear parameter-varying control theory

Liu, Y. and Ban, X. J. and Wu, F. and Lam, H. K. (2016), Journal of Dynamic Systems, Measurement, and Control, 138(1), .

A new hybrid LFT control method for missile autopilot design

Yuan, C. Z. and Wu, F. (2016), Chinese Control Conference, (), 5852-5857.

A nonlinear gain-scheduling compensation approach using parameter-dependent Lyapunov functions

Wu, F. and Song, X. and Ren, Z. (2016), Journal of Dynamic Systems, Measurement, and Control, 138(1), .

An optimization-based approach for prosthesis dynamic modeling and parameter identification

Yang, T. and Wu, F. and Liu, M. and Huang, H. (2016), Proceedings of the ASME 8th Annual Dynamic Systems and Control Conference, 2015, vol 1, (), .

Almost output regulation of discrete-time switched linear systems

Yuan, C. Z. and Duan, C. and Wu, F. (2015), Proceedings of the American Control Conference, (), 4042-4047.

Asynchronous switching output feedback control of discrete-time switched linear systems

Yuan, C. Z. and Wu, F. (2015), International Journal of Control, 88(9), 1766-1774.

Gain scheduling output feedback control of linear plants with actuator saturation

Ban, X. J. and Wu, F. (2015), Journal of the Franklin Institute, 352(10), 4163-4187.

Hybrid control for switched linear systems with average dwell time

Yuan, C. Z. and Wu, F. (2015), IEEE Transactions on Automatic Control, 60(1), 240-245.

Preface

Rui, X. T. and Pfeiffer, F. G. and Zhang, C. Z. and Wang, S. M. and Wu, F. (2015), Advances in Mechanical Engineering, 7(9), .

Robust fault detection filter design for linear uncertain systems with unknown inputs

Liu, Y. and Wu, F. and Ban, X. J. (2015), Proceedings of the American Control Conference, (), 886-891.

Robust switching output feedback control of discrete-time linear polytopic uncertain systems

Yuan, C. Z. and Wu, F. and Duan, C. (2015), 2015 34th Chinese Control Conference (CCC), (), 2973-2978.

Switching control of linear systems subject to asymmetric actuator saturation

Yuan, C. Z. and Wu, F. (2015), International Journal of Control, 88(1), 204-215.

Analysis and control of switched linear systems via dwell-time min-switching

Duan, C. and Wu, F. (2014), Systems and Control Letters, 70(), 8-16.

Analysis and control of switched linear systems via modified Lyapunov-Metzler inequalities

Duan, C. and Wu, F. (2014), International Journal of Robust and Nonlinear Control, 24(2), 276-294.

Analysis and synthesis of linear hybrid systems with state-triggered jumps

Yuan, C. Z. and Wu, F. (2014), Nonlinear Analysis-Hybrid Systems, 14(), 47-60.

Control of polynomial nonlinear systems using higher degree Lyapunov functions

Yang, S. W. and Wu, F. (2014), Journal of Dynamic Systems, Measurement, and Control, 136(3), .

Dwell-time min-switching for discrete-time switched linear systems

Duan, C. and Wu, F. (2014), 2014 European Control Conference (ECC), (), 2540-2545.

Dynamic output feedback controller design for T-S fuzzy plants with actuator saturation using linear fractional transformation

Liu, Y. and Ban, X. J. and Wu, F. and Lam, H. K. (2014), IEEE International Fuzzy Systems Conference Proceedings, (), 2125-2132.

Output feedback reset control of general MIMO LTI systems

Yuan, C. Z. and Wu, F. (2014), 2014 European Control Conference (ECC), (), 2334-2339.

Feedback design for saturated polynomial nonlinear systems via higher order Lyapunov functions

Yang, S. W. and Wu, F. (2013), Proceedings of the ASME 5th Annual Dynamic Systems and Control Division Conference and JSME 11th Motion and Vibration Conference, DSCC 2012, vol 2, (), 645-652.

Gain-scheduling compensator synthesis for output regulation of nonlinear systems

Song, X. and Ren, Z. and Wu, F. (2013), Proceedings of the American Control Conference, (), 6078-6083.

New results on continuous-time switched linear systems with actuator saturation

Duan, C. and Wu, F. (2013), ASME 2013 Dynamic Systems and Control Conference, vol 2, (), .

Nonlinear gain-scheduling output-feedback control for polynomial nonlinear systems subject to actuator saturation

Wu, F. and Hays, S. (2013), International Journal of Control, 86(9), 1607-1619.

Robust control of switched linear systems via min of quadratics

Yuan, C. Z. and Wu, F. (2013), Proceedings of the ASME 2013 Dynamic Systems and Control Conference (DSCC2013), vol. 1, (), .

Robust switched filtering for time-varying polytopic uncertain systems

Duan, C. and Wu, F. (2013), Journal of Dynamic Systems, Measurement, and Control, 135(6), .

Switching fault-tolerant control of a flexible air-breathing hypersonic vehicle

Wu, F. and Cai, X. J. (2013), Proceedings of the Institution of Mechanical Engineers Part I-Journal of Systems and Control Engineering, 227(I1), 24-38.

Nonlinear robust H-infinity control with state-dependent scaling

Hays, S. and Wu, F. (2012), Proceedings of the ASME Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control (DSCC 2011), vol 1, (), 581-588.

Output feedback control for continuous-time switched linear systems subject to actuator saturation

Duan, C. and Wu, F. (2012), Proceedings of the ASME Dynamic Systems and Control Conference and Bath/ASME Symposium on Fluid Power and Motion Control (DSCC 2011), vol 1, (), 449-456.

Output-feedback control for switched linear systems subject to actuator saturation

Duan, C. and Wu, F. (2012), International Journal of Control, 85(10), 1532-1545.

Adaptive control design for uncertain polynomial nonlinear systems with parametric uncertainties

Zheng, Q. and Wu, F. (2011), International Journal of Adaptive Control and Signal Processing, 25(6), 502-518.

Generalized nonlinear H(infinity) synthesis condition with its numerically efficient solution

Zheng, Q. and Wu, F. (2011), International Journal of Robust and Nonlinear Control, 21(18), 2079-2100.

Multiobjective fault detection and isolation for flexible air-breathing hypersonic vehicle

Cai, X. J. and Wu, F. (2011), Journal of Systems Engineering and Electronics, 22(1), 52-62.

Robust fault detection and isolation for parameter-dependent LFT systems

Cai, X. J. and Wu, F. (2010), International Journal of Robust and Nonlinear Control, 20(7), 764-776.

Robust parameter-dependent fault-tolerant control for actuator and sensor faults

Cai, X. J. and Wu, F. (2010), International Journal of Control, 83(7), 1475-1484.

Disturbance attenuation by output feedback for linear systems subject to actuator saturation

Wu, F. and Zheng, Q. and Lin, Z. L. (2009), International Journal of Robust and Nonlinear Control, 19(2), 168-184.

Lyapunov redesign of adaptive controllers for polynomial nonlinear systems

Zheng, Q. and Wu, F. (2009), Proceedings of the American Control Conference, (), 5144-5149.

Nonlinear H-infinity control designs with axisymmetric spacecraft control

Zheng, Q. and Wu, F. (2009), Journal of Guidance Control and Dynamics, 32(3), 850-859.

Online switching control of LFT parameter-dependent systems

Dong, K. and Wu, F. (2009), Journal of Dynamic Systems, Measurement, and Control, 131(2), .

Regional stabilisation of polynomial non-linear systems using rational Lyapunov functions

Zheng, Q. and Wu, F. (2009), International Journal of Control, 82(9), 1605-1615.

A Robust fault tolerant control approach for LTI systems with actuator and sensor faults

Cai, X. J. and Wu, F. (2009), CCDC 2009: 21st Chinese Control and Decision Conference, vols 1-6, Proceedings, (), 890-895.

Almost output regulation for parameter-dependent linear fractional transformation systems

Dong, K. and Wu, F. (2008), IET Control Theory and Applications, 2(3), 200-209.

Output feedback control of saturated discrete-time linear systems using parameter-dependent Lyapunov functions

Zheng, Q. and Wu, F. (2008), Systems and Control Letters, 57(11), 896-903.

Output feedback stabilization of linear systems with actuator saturation

Wu, F. and Lin, Z. L. and Zheng, Q. (2007), IEEE Transactions on Automatic Control, 52(1), 122-128.

Robust and gain-scheduling control of LFT systems through duality and conjugate Lyapunov functions

Dong, K. and Wu, F. (2007), International Journal of Control, 80(4), 555-568.

Robust receding horizon control for constrained linear fractional transformation parameter-dependent systems

Wu, F. and Chen, Y. (2007), IET Control Theory and Applications, 1(5), 1423-1430.

Gain-scheduling control of LFT systems using parameter-dependent Lyapunov functions

Wu, F. and Dong, K. (2006), Automatica, 42(1), 39-50.

Probabilistic robust linear parameter-varying control of an F-16 aircraft

Lu, B. and Wu, F. (2006), Journal of Guidance Control and Dynamics, 29(6), 1454-1460.

Distributed parameter-dependent modeling and control of flexible structures

Wu, F. and Yildizoglu, S. E. (2005), Journal of Dynamic Systems, Measurement, and Control, 127(2), 230-239.

Linear parameter-varying antiwindup compensation for enhanced flight control performance

Lu, B. and Wu, F. and Kim, S. W. (2005), Journal of Guidance Control and Dynamics, 28(3), 494-505.

SOS-based solution approach to polynomial LPV system analysis and synthesis problems

Wu, F. and Prajna, S. (2005), International Journal of Control, 78(8), 600-611.

Anti-windup control design for exponentially unstable LTI systems with actuator saturation

Wu, F. and Lu, B. (2004), Systems and Control Letters, 52(04-Mar), 305-322.

On convexified robust control synthesis

Wu, F. and Lu, B. (2004), Automatica, 40(6), 1003-1010.

Computationally efficient algorithm for frequency-weighted optimal H-infinity model reduction

Wu, F. and Jaramillo, J. J. (2003), Asian Journal of Control, 5(3), 341-349.

Distributed control for interconnected linear parameter dependent systems

Wu, F. (2003), IEE Proceedings, Control Theory and Applications, 150(5), 518-527.

H-infinity and L-2-to-L-infinity gain control of linear parameter-varying systems with parameter-varying delays

Tan, K. and Grigoriadis, K. M. and Wu, F. (2003), IEE Proceedings, Control Theory and Applications, 150(5), 509-517.

Robust quadratic performance for time-delayed uncertain linear systems

Wu, F. (2003), International Journal of Robust and Nonlinear Control, 13(2), 153-172.

Output-feedback control of LPV sampled-data systems

Tan, K. and Grigoriadis, K. M. and Wu, F. (2002), International Journal of Control, 75(4), 252-264.

LMI-based robust model predictive control and its application to an industrial CSTR problem

Wu, F. (2001), Journal of Process Control, 11(6), 649-659.

LPV Systems with parameter-varying time delays: analysis and control

Wu, F. and Grigoriadis, K. M. (2001), Automatica, 37(2), 221-229.

A generalized LPV system analysis and control synthesis framework

Wu, F. (2001), International Journal of Control, 74(7), 745-759.

Anti-windup controller design using linear parameter-varying control methods

Wu, F. and Grigoriadis, K. M. and Packard, A. (2000), International Journal of Control, 73(12), 1104-1114.

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Grants

Advanced Switching Control Techniques For Switched Systems Subject to Physical Constraints

National Science Foundation (NSF)(6/01/12 - 8/31/16)

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Advanced Switching Control Techniques For Switched Systems Subject to Physical Constraints

Sponsor: National Science Foundation (NSF)

Start Date: 6/01/12

End Date: 8/31/16

Abstract

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.

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

National Science Foundation (NSF)(6/01/08 - 5/31/12)

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

Sponsor: National Science Foundation (NSF)

Start Date: 6/01/08

End Date: 5/31/12

Abstract

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.

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Reconfigurable Robust Gain-Scheduled Control for Air-Breathing Hypersonic Vehicles

National Aeronautics & Space Administration (NASA)(1/05/07 - 12/31/11)

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Reconfigurable Robust Gain-Scheduled Control for Air-Breathing Hypersonic Vehicles

Sponsor: National Aeronautics & Space Administration (NASA)

Start Date: 1/05/07

End Date: 12/31/11

Abstract

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.

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Developing Nonlinear Optimal and Robust Control Techniques for Space Exploration

NCSU NC Space Grant Consortium(7/01/06 - 6/30/07)

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Developing Nonlinear Optimal and Robust Control Techniques for Space Exploration

Sponsor: NCSU NC Space Grant Consortium

Start Date: 7/01/06

End Date: 6/30/07

Abstract

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.

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