Advances in Statistical Control, Algebraic Systems Theory, and Dynamic Systems Characteristics

Life has many surprises. One of the best surprises is meeting a caring mentor, an encouraging collaborator, or an enthusiastic friend. This volume is a tribute to P- fessor Michael K. Sain, who is such a teacher,colleague,and friend.On the beautiful fall day of October 27, 2007, friends, families, colleagues, and former students ga- ered at a workshop held in Notre Dame, Indiana. This workshop brought together many people whose lives have been touched by Mike to celebrate his milestone 70th birthday, and to congratulate him on his contributions in the elds of systems, c- cuits, and control. Mike was born on March 22, 1937, in St. Louis, Missouri. After obtaining his B.S.E.E. and M.S.E.E. at St. Louis University, he went on to study at the University of Illinois at Urbana-Champaignfor his doctoral degree. With his Ph.D. degree c- plete, he came to the University of Notre Dame in 1965 as an assistant professor. He became an associate professor in 1968, a full professor in 1972, and the Frank M. Freimann Chair in Electrical Engineering in 1982. He has remained at and loved the University of Notre Dame for over 40 years. Mike also held a number of consu- ing jobs throughout his career. Most notably, he consulted with the Energy Controls Division of Allied-Bendix Aerospace from 1976 to 1988 and the North American Operations branch of the Research and Development Laboratory of General Motors Corporation for a decade, 1984–1994.

This volume―dedicated to Michael K. Sain on the occasion of his seventieth birthday―is a collection of chapters covering recent advances in stochastic optimal control theory and algebraic systems theory. Written by experts in their respective fields, the chapters are thematically organized into four parts:

* Part I focuses on statistical control theory, where the cost function is viewed as a random variable and performance is shaped through cost cumulants. In this respect, statistical control generalizes linear-quadratic-Gaussian and H-infinity control.

* Part II addresses algebraic systems theory, reviewing the use of algebraic systems over semirings, modules of zeros for linear multivariable systems, and zeros in linear time-delay systems.

* Part III discusses advances in dynamical systems characteristics. The chapters focus on the stability of a discontinuous dynamical system, approximate decentralized fixed modes, direct optimal adaptive control, and stability of nonlinear systems with limited information.

* Part IV covers engineering education and includes a unique chapter on theology and engineering, one of Sain's latest research interests.

The book will be a useful reference for researchers and graduate students in systems and control, algebraic systems theory, and applied mathematics. Requiring only knowledge of undergraduate-level control and systems theory, the work may be used as a supplementary textbook in a graduate course on optimal control or algebraic systems theory.