Linear Systems and Optimal Control

Softcover Nachdruck of the original 1. Auflage 1989
ISBN: 978-3-642-64787-1
Verlag: Springer

Buch, Englisch, Band 18, 155 Seiten, Paperback, Format (B × H): 155 mm x 235 mm, Gewicht: 265 g

Reihe: Springer Series in Information Sciences

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.

Zielgruppe

Research

Autoren/Hrsg.

Chen, Guanrong

Chui, Charles K.

Fachgebiete

• Technische Wissenschaften Elektronik | Nachrichtentechnik Nachrichten- und Kommunikationstechnik Regelungstechnik

Inhaltsverzeichnis

1. State-Space Descriptions.- 1.1 Introduction.- 1.2 An Example of Input-Output Relations.- 1.3 An Example of State-Space Descriptions.- 1.4 State-Space Models.- Exercises.- 2. State Transition Equations and Matrices.- 2.1 Continuous-Time Linear Systems.- 2.2 Picard’s Iteration.- 2.3 Discrete-Time Linear Systems.- 2.4 Discretization.- Exercises.- 3. Controllability.- 3.1 Control and Observation Equations.- 3.2 Controllability of Continuous-Time Linear Systems.- 3.3 Complete Controllability of Continuous-Time Linear Systems.- 3.4 Controllability and Complete Controllability of Discrete-Time Linear Systems.- Exercises.- 4. Observability and Dual Systems.- 4.1 Observability of Continuous-Time Linear Systems.- 4.2 Observability of Discrete-Time Linear Systems.- 4.3 Duality of Linear Systems.- 4.4 Dual Time-Varying Discrete-Time Linear Systems.- Exercises.- 5. Time-Invariant Linear Systems.- 5.1 Preliminary Remarks.- 5.2 The Kalman Canonical Decomposition.- 5.3 Transfer Functions.- 5.4 Pole-Zero Cancellation of Transfer Functions.- Exercises.- 6. Stability.- 6.1 Free Systems and Equilibrium Points.- 6.2 State-Stability of Continuous-Time Linear Systems.- 6.3 State-Stability of Discrete-Time Linear Systems.- 6.4 Input-Output Stability of Continuous-Time Linear Systems.- 6.5 Input-Output Stability of Discrete-Time Linear Systems.- Exercises.- 7. Optimal Control Problems and Variational Methods.- 7.1 The Lagrange, Bolza, and Mayer Problems.- 7.2 A Variational Method for Continuous-Time Systems.- 7.3 Two Examples.- 7.4 A Variational Method for Discrete-Time Systems.- Exercises.- 8. Dynamic Programming.- 8.1 The Optimality Principle.- 8.2 Continuous-Time Dynamic Programming.- 8.3 Discrete-Time Dynamic Programming.- 8.4 The Minimum Principle of Pontryagin.- Exercises.- 9.Minimum-Time Optimal Control Problems.- 9.1 Existence of the Optimal Control Function.- 9.2 The Bang-Bang Principle.- 9.3 The Minimum Principle of Pontryagin for Minimum-Time Optimal Control Problems.- 9.4 Normal Systems.- Exercises.- 10. Notes and References.- 10.1 Reachability and Constructibility.- 10.2 Differential Controllability.- 10.3 State Reconstruction and Observers.- 10.4 The Kalman Canonical Decomposition.- 10.5 Minimal Realization.- 10.6 Stability of Nonlinear Systems.- 10.7 Stabilization.- 10.8 Matrix Riccati Equations.- 10.9 Pontryagin’s Maximum Principle.- 10.10 Optimal Control of Distributed Parameter Systems.- 10.11 Stochastic Optimal Control.- References.- Answers and Hints to Exercises.- Notation.