Linear Systems and Optimal Control [E-Book] /

Linear Systems and Optimal Control [E-Book] / by Charles K. Chui, Guanrong Chen.

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 brie...

More

Saved in:
Full text
Chui, Charles K., author
Chen, Guanrong, author
Berlin, Heidelberg : Springer, 1989
VIII, 155 p. 1 illus. online resource.
englisch
9783642613128
10.1007/978-3-642-61312-8
Springer Series in Information Sciences ; 18
Business
Calculus of variations.
Complexity, Computational.
Economic theory.
Geophysics.
Information technology.
Mathematics.
System theory.
Data processing.



  • 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.