Continuous Time Dynamical Systems

Continuous Time Dynamical Systems

by B.M. Mohan, S.K. Kar
Released October 2018
Publisher(s): CRC Press
ISBN: 9781351832236

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Book description

This book presents the developments in problems of state estimation and optimal control of continuous-time dynamical systems using orthogonal functions since 1975. It deals with both full and reduced-order state estimation and problems of linear time-invariant systems. It also addresses optimal control problems of varieties of continuous-time systems such as linear and nonlinear systems, time-invariant and time-varying systems, as well as delay-free and time-delay systems. Content focuses on development of recursive algorithms for studying state estimation and optimal control problems.

Table of contents

  1. Cover
  2. Title Page
  3. Copyright Page
  4. Dedication
  5. Table of Contents
  6. List of Abbreviations
  7. Preface
  8. Acknowledgements
  9. About the Authors
  10. 1 Introduction
    1. 1.1 Optimal Control Problem
    2. 1.2 Historical Perspective
    3. 1.3 Organisation of the Book
  11. 2 Orthogonal Functions and Their Properties
    1. 2.1 Introduction
    2. 2.2 Block-Pulse Functions (BPFs)
      1. 2.2.1 Integration of B(t)
      2. 2.2.2 Product of two BPFs
      3. 2.2.3 Representation of C(t)f(t) in terms of BPFs
      4. 2.2.4 Representation of a time-delay vector in BPFs
      5. 2.2.5 Representation of reverse time function vector in BPFs
    3. 2.3 Legendre Polynomials (LPs)
    4. 2.4 Shifted Legendre Polynomials (SLPs)
      1. 2.4.1 Integration of L(t)
      2. 2.4.2 Product of two SLPs
      3. 2.4.3 Representation of C(t)f(t) in terms of SLPs
      4. 2.4.4 Representation of a time-delay vector function in SLPs
      5. 2.4.5 Derivation of a time-advanced matrix of SLPs
      6. 2.4.6 Algorithm for evaluating the integral in Eq. (2.75)
      7. 2.4.7 Representation of a reverse time function vector in SLPs
    5. 2.5 Nonlinear Operational Matrix
    6. 2.6 Rationale for Choosing BPFs and SLPs
  12. 3 State Estimation
    1. 3.1 Introduction
    2. 3.2 Inherent Filtering Property of OFs
    3. 3.3 State Estimation
      1. 3.3.1 Kronecker product method
      2. 3.3.2 Recursive algorithm via BPFs
      3. 3.3.3 Recursive algorithm via SLPs
      4. 3.3.4 Modification of the recursive algorithm of Sinha and Qi-Jie
    4. 3.4 Illustrative Examples
    5. 3.5 Conclusion
  13. 4 Linear Optimal Control Systems Incorporating Observers
    1. 4.1 Introduction
    2. 4.2 Analysis of Linear Optimal Control Systems Incorporating Observers
      1. 4.2.1 Kronecker product method
      2. 4.2.2 Recursive algorithm via BPFs
      3. 4.2.3 Recursive algorithm via SLPs
    3. 4.3 Illustrative Example
    4. 4.4 Conclusion
  14. 5 Optimal Control of Systems Described by Integro-Differential Equations
    1. 5.1 Introduction
    2. 5.2 Optimal Control of LTI Systems Described by Integro-Differential Equations
    3. 5.3 Illustrative Example
    4. 5.4 Conclusion
  15. 6 Linear-Quadratic-Gaussian Control
    1. 6.1 Introduction
    2. 6.2 LQG Control Problem
    3. 6.3 Unified Approach
      1. 6.3.1 Illustrative example
    4. 6.4 Recursive Algorithms
      1. 6.4.1 Recursive algorithm via BPFs
      2. 6.4.2 Recursive algorithm via SLPs
      3. 6.4.3 Illustrative example
    5. 6.5 Conclusion
  16. 7 Optimal Control of Singular Systems
    1. 7.1 Introduction
    2. 7.2 Recursive Algorithms
      1. 7.2.1 Recursive algorithm via BPFs
      2. 7.2.2 Recursive algorithm via SLPs
    3. 7.3 Unified Approach
    4. 7.4 Illustrative Examples
    5. 7.5 Conclusion
  17. 8 Optimal Control of Time-Delay Systems
    1. 8.1 Introduction
    2. 8.2 Optimal Control of Multi-Delay Systems
      1. 8.2.1 Using BPFs
      2. 8.2.2 Using SLPs
      3. 8.2.3 Time-invariant systems
      4. 8.2.4 Delay free systems
      5. 8.2.5 Illustrative examples
    3. 8.3 Optimal Control of Delay Systems with Reverse Time Terms
      1. 8.3.1 Using BPFs
      2. 8.3.2 Using SLPs
      3. 8.3.3 Illustrative example
    4. 8.4 Conclusion
  18. 9 Optimal Control of Nonlinear Systems
    1. 9.1 Introduction
    2. 9.2 Computation of the Optimal Control Law
    3. 9.3 Illustrative Examples
    4. 9.4 Conclusion
  19. 10 Hierarchical Control of Linear Systems
    1. 10.1 Introduction
    2. 10.2 Hierarchical Control of LTI Systems with Quadratic Cost Functions
      1. 10.2.1 Partial feedback control
      2. 10.2.2 Interaction prediction approach
    3. 10.3 Solution of Hierarchical Control Problem via BPFs
      1. 10.3.1 State transition matrix
      2. 10.3.2 Riccati matrix and open-loop compensation vector
      3. 10.3.3 State vector
      4. 10.3.4 Adjoint vector and local control
      5. 10.3.5 Coordination
      6. 10.3.6 Error
    4. 10.4 Extension to Linear Time-Varying Systems
    5. 10.5 Computational Algorithm
    6. 10.6 Illustrative Examples
    7. 10.7 Conclusion
  20. 11 Epilogue
  21. Bibliography
  22. Index

Product information

  • Title: Continuous Time Dynamical Systems
  • Author(s): B.M. Mohan, S.K. Kar
  • Release date: October 2018
  • Publisher(s): CRC Press
  • ISBN: 9781351832236