Alan J. Laub

Michael J. Denham

Computational concepts and techniques have always played a major role in control engineering since the first computer-based control systems were put into operation over twenty years ago. This role has in fact been accelerating over the intervening years as the sophistication of the computing methods and tools available, as well as the complexity of the control problems they have been used to solve, have also increased. In particular, the introduction of the microprocessor and its use as a low-cost computing element in a distributed computer control system has had a profound effect on the way in which the design and implementation of a control system is carried out and, to some extent, on the theory which underlies the basic design strategies. The development of interactive computing has encouraged a substantial growth in the use of computer aided design methods and robust and efficient numerical algorithms have been produced to support these methods. Major advances have also taken place in the languages used for control system implementation, notably the recent introduction of Ada'", a language whose design is based on some very fundamental computer science concepts derived and developed over the past decade. With the extremely high rate of change in the field of computer science, the more recent developments have outpaced their incorporation into new control system design and implementation techniques.

Advanced Computing Concepts and Techniques in Control Engineering

Jan C. Willems

Sergio Bittanti

Conceived by Count Jacopo Francesco Riccati more than a quarter of a millennium ago, the Riccati equation has been widely studied in the subsequent centuries. Since its introduction in control theory in the sixties, the matrix Riccati equation has known an impressive range of applications, such as optimal control, H? optimization and robust stabilization, stochastic realization, synthesis of linear passive networks, to name but a few. This book consists of 11 chapters surveying the main concepts and results related to the matrix Riccati equation, both in continuous and discrete time. Theory, applications and numerical algorithms are extensively presented in an expository way. As a foreword, the history and prehistory of the Riccati equation is concisely presented.

The Riccati Equation

Using an approach that author Alan Laub calls "matrix analysis for grown-ups," this new textbook introduces fundamental concepts of numerical linear algebra and their application to solving certain numerical problems arising in state-space control and systems theory. It is written for advanced undergraduate and beginning graduate students and can be used as a follow-up to Matrix Analysis for Scientists and Engineers (SIAM, 2005), a compact single-semester introduction to matrix analysis for engineers and computational scientists by the same author. Computational Matrix Analysis provides readers with a one-semester introduction to numerical linear algebra; an introduction to statistical condition estimation in book form for the first time; and an overview of certain computational problems in control and systems theory. The book features a number of elements designed to help students learn to use numerical linear algebra in day-to-day computing or research, including a brief review of matrix analysis, including notation, and an introduction to finite (IEEE) arithmetic; discussion and examples of conditioning, stability, and rounding analysis; an introduction to mathematical software topics related to numerical linear algebra; a thorough introduction to Gaussian elimination, along with condition estimation techniques; coverage of linear least squares, with orthogonal reduction and QR factorization; variants of the QR algorithm; and applications of the discussed algorithms.

Alan J. Laub

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