Ebook: Linear Systems and Optimal Control
- Tags: Systems Theory Control, Calculus of Variations and Optimal Control, Optimization, Geophysics/Geodesy, Economic Theory, Business Information Systems, Complexity
- Series: Springer Series in Information Sciences 18
- Year: 1989
- Publisher: Springer-Verlag Berlin Heidelberg
- Edition: 1
- Language: English
- pdf
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.
Content:
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
Content:
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
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