Uncertainty and risk are integral to engineering because real systems have inherent ambiguities that arise naturally or due to our inability to model complex physics. The authors discuss probability theory, stochastic processes, estimation, and stochastic control strategies and show how probability can be used to model uncertainty in control and estimation problems. The material is practical and rich in research opportunities. The authors provide a comprehensive treatment of stochastic systems from the foundations of probability to stochastic optimal control. The book covers discrete- and continuous-time stochastic dynamic systems leading to the derivation of the Kalman filter, its properties, and its relation to the frequency domain Wiener filter as well as the dynamic programming derivation of the linear quadratic Gaussian (LQG) and the linear exponential Gaussian (LEG) controllers and their relation to H2 and H-inf controllers and system robustness. Stochastic Processes, Estimation, and Control is divided into three related sections. First, the authors present the concepts of probability theory, random variables, and stochastic processes, which lead to the topics of expectation, conditional expectation, and discrete-time estimation and the Kalman filter. After establishing this foundation, stochastic calculus and continuous-time estimation are introduced. Finally, dynamic programming for both discrete-time and continuous-time systems leads to the solution of optimal stochastic control problems, resulting in controllers with significant practical application.
Professor Jason L. Speyer received his B.S. in Aeronautics and Astronautics from M.I.T. (1960) and his Ph.D. in Applied Mathematics from Harvard University (1968). His industrial experience includes research at Boeing, Raytheon, Analytical Mechanics Associated, and the Charles Stark Draper Laboratory. He was the Harry H. Power Professor in Engineering Mechanics, University of Texas, Austin. Currently, he is a Distinguished Professor in the Mechanical and Aerospace Engineering Department and the Electrical Engineering Department at the University of California, Los Angeles. Professor Speyer has twice been an elected member of the Board of Governors of the IEEE Control Systems Society. He served as Associate Editor for Technical Notes and Correspondence (1975-76) and Stochastic Control (1978-79), IEEE Transactions on Automatic Control, for AIAA Journal of Spacecraft and Rockets (1976-77), AIAA Journal of Guidance and Control (1977-78), and for Journal of Optimization Theory and Applications, 1981-present. He is fellow of AIAA and IEEE (Life Fellow) and was awarded AIAA Mechanics and Control of Flight Award, AIAA Dryden Lectureship in Research, Air Force Exceptional Civilian Decoration (1991 and 2001), IEEE Third Millennium Medal, and membership in the National Academy of Engineering. In 2002 the UCLA Autonomous Vehicle System Instrumentation Laboratory under his direction was awarded the NASA Public Service Group Achievement Award for exceptional service, commitment, and dedication toward the successful development of the Dryden Flight Research Center Autonomous Flight Formation project. Walter Chung received his B.S. in Aeronautics and Astronautics from M.I.T. (1990), his M.S. in Aeronautics and Astronautics from Stanford University (1992) and his Ph.D. in Aerospace Engineering from the University of California, Los Angeles (1997). He currently works in the aerospace industry and has taught gradaute courses in stochastic processes, estimation and control at UCLA since 1997.
Preface Chapter 1:Probability Theory Chapter 2: Random Variables and Stochastic Processes Chapter 3: Conditional Expectations and Discrete-Time Kalman Filtering Chapter 4: Least Squares, the Orthogonal Projection Lemma, and Discrete-Time Kalman Filtering Chapter 5: Stochastic Processes and Stochastic Calculus Chapter 6: Continuous-Time Gauss--Markov Systems: Continuous-Time Kalman Filter, Stationarity, Power Spectral Density, and the Wiener Filter Chapter 7: The Extended Kalman Filter Chapter 8: A Selection of Results from Estimation Theory Chapter 9: Stochastic Control and the Linear Quadratic Gaussian Control Problem Chapter 10: Linear Exponential Gaussian Control and Estimation Bibliography Index
Covers stochastic systems beginning with the foundations of probability and ending with stochastic optimal control.
