Continuous Time Dynamical Systems

State Estimation and Optimal Control with Orthogonal Functions
 
 
CRC Press
  • erschienen am 8. Oktober 2018
  • |
  • 247 Seiten
 
E-Book | ePUB mit Adobe DRM | Systemvoraussetzungen
978-1-351-83223-6 (ISBN)
 

Optimal control deals with the problem of finding a control law for a given system such that a certain optimality criterion is achieved. An optimal control is a set of differential equations describing the paths of the control variables that minimize the cost functional.

This book, Continuous Time Dynamical Systems: State Estimation and Optimal Control with Orthogonal Functions, considers different classes of systems with quadratic performance criteria. It then attempts to find the optimal control law for each class of systems using orthogonal functions that can optimize the given performance criteria.

Illustrated throughout with detailed examples, the book covers topics including:

    • Block-pulse functions and shifted Legendre polynomials
    • State estimation of linear time-invariant systems
    • Linear optimal control systems incorporating observers
    • Optimal control of systems described by integro-differential equations
    • Linear-quadratic-Gaussian control
    • Optimal control of singular systems
    • Optimal control of time-delay systems with and without reverse time terms
    • Optimal control of second-order nonlinear systems
    • Hierarchical control of linear time-invariant and time-varying systems

    • Englisch
    • London
    • |
    • Großbritannien
    Taylor & Francis Ltd
    • Für höhere Schule und Studium
    66 schwarz-weiße Abbildungen, 28 schwarz-weiße Tabellen
    978-1-351-83223-6 (9781351832236)

    <strong>Introduction
    </strong>Optimal Control Problem
    Historical Perspective
    Organization of the Book
    <b>
    </b><strong>Orthogonal Functions and Their Properties</strong><b>
    </b>Introduction
    Block-Pulse Functions (BPFs)
    Legendre Polynomials (LPs)
    Shifted Legendre Polynomials (SLPs)
    Nonlinear Operational Matrix
    Rationale for Choosing BPFs and SLPs
    <b>
    </b><strong>State Estimation</strong><b>
    </b>Introduction
    Inherent Filtering Property of OFs
    State Estimation
    Illustrative Examples
    Conclusion
    <b>
    </b><strong>Linear Optimal Control Systems Incorporating Observers</strong><b>
    </b>Introduction
    Analysis of Linear Optimal Control Systems Incorporating Observers
    Illustrative Example
    Conclusion
    <b>
    </b><strong>Optimal Control of Systems Described by Integro-Differential Equations</strong><b>
    </b>Introduction
    Optimal Control of LTI Systems Described by Integro-Differential Equations
    Illustrative Example
    Conclusion
    <b>
    </b><strong>Linear-Quadratic-Gaussian Control</strong><b>
    </b>Introduction
    LQG Control Problem
    Unified Approach
    Illustrative Example
    Recursive Algorithms
    Conclusion
    <b>
    </b><strong>Optimal Control of Singular Systems</strong><b>
    </b>Introduction
    Recursive Algorithms
    Unified Approach
    Illustrative Examples
    Conclusion
    <b>
    </b><strong>Optimal Control of Time-Delay Systems</strong><b>
    </b>Introduction
    Optimal Control of Multi-Delay Systems
    Optimal Control of Delay Systems with Reverse Time Terms
    Conclusion
    <b>
    </b><strong>Optimal Control of Nonlinear Systems</strong><b>
    </b>Introduction
    Computation of the Optimal Control Law
    Illustrative Examples
    Conclusion
    <b>
    </b><strong>Hierarchical Control of Linear Systems</strong><b>
    </b>Introduction
    Hierarchical Control of LTI Systems with Quadratic Cost Functions
    Solution of Hierarchical Control Problem via BPFs
    Extension to Linear Time-Varying Systems
    Computational Algorithm
    Illustrative Examples
    Conclusion

    "... provides a good introduction of using orthogonal function approaches for state estimation and optimal control problems. ... the first book I've seem that puts it all together in one text. ... The authors provide several detailed examples that clearly explain how the shown theory can be applied. This makes it much easier to understand the basic algorithms."
    -John L. Crassidis, University at Buffalo, State University of New York


    "The approach and selection of topics are very appropriate, because the book has considered all the important components of optimal control problems using orthogonal functions. ... Overall, the book is quite good and comprehensive."
    -Anish Deb, University of Caluctta, India


    "A majority of the presentation relies on existing results; the authors main contribution is contained in Chapters 7-10. This book may be useful to postgraduate and doctoral students interested in system and control theory as well as inspiring to control engineers."
    -Zentralblatt Math,Vol. 1272
     

    "... provides a good introduction of using orthogonal function approaches for state estimation and optimal control problems. ... the first book I've seem that puts it all together in one text. ... The authors provide several detailed examples that clearly explain how the shown theory can be applied. This makes it much easier to understand the basic algorithms."
    -John L. Crassidis, University at Buffalo, State University of New York


    "The approach and selection of topics are very appropriate, because the book has considered all the important components of optimal control problems using orthogonal functions. ... Overall, the book is quite good and comprehensive."
    -Anish Deb, University of Caluctta, India


    "A majority of the presentation relies on existing results; the authors main contribution is contained in Chapters 7-10. This book may be useful to postgraduate and doctoral students interested in system and control theory as well as inspiring to control engineers."
    <i>-Zentralblatt Math,Vol. 1272
    </i>

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