Stability and Continuity of Nonlinear Model Predictive Control Stability and Continuity of Nonlinear Model Predictive Control Stability and Continuity of Nonlinear Model Predictive Control

Acknowledgments I would like to express my appreciation to my advisor, Dr. James B. Rawl-ings. His diicult questions have pushed this work forward when it stalled and his insight has allowed me to progress when it seemed impossible. His vision of computing in this profession has provided his research group with the best computer facilities at the University. The work reported in this dis-sertation would have been impossible without the hardware and software tools he provided. I would like to thank my committee members, Rafael de for their contributions. Professors Himmelblau, Edgar and Rawlings have provided a superb atmosphere of collaboration among Chemical Engineering students and faculty. Of the other students and former students with whom I have worked, several deserve special thanks: Tony Mullins, for listening to my mathematical speculations, John Eaton for masterfully administering our computer facilities and providing octave, and Ken Muske, whose contributions provided a foundation for parts of this work. This work provides an analysis of some important properties of model pre-dictive control (MPC), an algorithm for feedback control of dynamic systems. This dissertation contains a record of work in four related areas: stability of model predictive control, continuity of model predictive control feedback laws and objective functions, resolution of some implementation issues for model predictive control using linear models, and the use of model predictive control for stochastic systems. It makes connections between some well known results for linear quadratic optimal control, which may be viewed as an MPC method, and dynamic programming. Suucient conditions for stability are provided for general nonlinear systems. They include non-negativity of the objective and continuity at the origin. Stability is obtained through a Lyapunov stability argument using the MPC objective as a Lyapunov function. A matrix rank condition related to the constraint set that ensures continuity is also provided. Continuity of the feedback control law derived using model predictive control and the corresponding objective function can have important consequences for the stability and performance of the closed-loop system. Through use of an unusual example, this dissertation investigates continuity and provides a suucient condition to ensure that the objective function and feedback control law are continuous with respect to the state. Some of the results reported here concerning implementation of linear model predictive control are based on previous work by Rawlings and Muske at the University of Texas. The issues discussed herein are technical issues important for applications, including …