Stochastic Lagrangian Adaptation

This book introduces a cutting-edge continuous time stochastic linear quadratic (LQ) adaptive control algorithm for fully observed linear stochastic systems with unknown parameters. The adaptive estimation algorithm is engineered to drive the maximum likelihood estimate into the set of parameters representing the true closed-loop dynamics. By incorporating a performance monitoring feature, this approach ensures that the estimate converges to the true system parameters. Concurrently, it delivers optimal long-term LQ closed-loop performance. This groundbreaking work offers a significant advancement in the field of stochastic control systems.

The Stochastic Lagrangian Adaptation control algorithm is completely recursive Non-compact unbounded parameter sets are permitted sharply distinguishing the work from standard analyses The work is based upon a geometric analysis of parameter sets yielding optimal closed loop LQ performance

Autorentext

Peter E. Caines received the BA in mathematics from Oxford University in 1967 and the PhD in systems and control theory in 1970 from Imperial College, University of London, supervised by David Q. Mayne, FRS. Following PDF and visiting positions,a he joined McGill University in 1980, where he is Distinguished James McGill Professor and Macdonald Chair in the Department of Electrical and Computer Engineering. He received the IEEE Control Systems Society Bode Lecture Prize (2009), is a Fellow of IFAC, CIFAR, SIAM, IEEE, the IMA (UK) and the Royal Society of Canada (2003), and is a member of Professional Engineers Ontario. His monograph, Linear Stochastic Systems (Wiley, 1988), is now published as a SIAM Classic and his research interests include stochastic and hybrid systems, and mean field (control and games) systems on large networks. David Levanony (BSc., Aerospace Eng., 1985, MSc., Aerospace Eng., 1988, DSc., Electrical Eng., 1992, Technion, Haifa, Israel) is a Senior Lecturer with the School of Electrical and Computer Engineering, Ben Gurion University, Beer Sheva, Israel and a consultant with the defense industry in Israel.

Inhalt

Introduction.- Problem Statement.- Asymptotic Maximum Likelihood Identification.- Geometric Results.- Lagrangian Adaptation.- Proof of Theorem 5.2.- Index.