Linear Systems and Optimal Control

✍ Scribed by Professor Dr. Charles K. Chui, Dr. Guanrong Chen (auth.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1989
• Tongue: English
• Leaves: 161
• Series: Springer Series in Information Sciences 18
• Edition: 1
• Category: Library

✦ Synopsis

A knowledge of linear systems provides a firm foundation for the study of optimal control theory and many areas of system theory and signal processing. State-space techniques developed since the early sixties have been proved to be very effective. The main objective of this book is to present a brief and somewhat complete investigation on the theory of linear systems, with emphasis on these techniques, in both continuous-time and discrete-time settings, and to demonstrate an application to the study of elementary (linear and nonlinear) optimal control theory. An essential feature of the state-space approach is that both time-varying and time-invariant systems are treated systematically. When time-varying systems are considered, another important subject that depends very much on the state-space formulation is perhaps real-time filtering, prediction, and smoothing via the Kalman filter. This subject is treated in our monograph entitled "Kalman Filtering with Real-Time Applications" published in this Springer Series in Information Sciences (Volume 17). For time-invariant systems, the recent frequency domain approaches using the techniques of Adamjan, Arov, and Krein (also known as AAK), balanced realization, and oo H theory via Nevanlinna-Pick interpolation seem very promising, and this will be studied in our forthcoming monograph entitled "Mathematical Ap­ proach to Signal Processing and System Theory". The present elementary treatise on linear system theory should provide enough engineering and mathe­ of these two subjects.

✦ Table of Contents

Front Matter....Pages I-VIII
State-Space Descriptions....Pages 1-7
State Transition Equations and Matrices....Pages 8-15
Controllability....Pages 16-25
Observability and Dual Systems....Pages 26-35
Time-Invariant Linear Systems....Pages 36-48
Stability....Pages 49-69
Optimal Control Problems and Variational Methods....Pages 70-80
Dynamic Programming....Pages 81-93
Minimum-Time Optimal Control Problems....Pages 94-105
Notes and References....Pages 106-118
Back Matter....Pages 119-155

✦ Subjects

Systems Theory, Control;Calculus of Variations and Optimal Control;Optimization;Geophysics/Geodesy;Economic Theory;Business Information Systems;Complexity