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The Autonomous Linear Quadratic Control Problem

Theory and Numerical Solution

  • Book
  • © 1991

Overview

Editors:
  1. Volker Ludwig Mehrmann
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Part of the book series: Lecture Notes in Control and Information Sciences (LNCIS, volume 163)

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Table of contents (23 chapters)

  1. Front Matter

    Download chapter PDF

  2. Introduction

    Pages 1-8

  3. Notation and definitions

    Pages 9-14

  4. Existence of solutions

    Pages 15-26

  5. Eigenstructure of αA - βB, αA′ - βB′

    Pages 27-38

  6. Uniqueness and stability of feedback solutions

    Pages 39-49

  7. Algebraic Riccati equations and deflating subspaces

    Pages 50-54

  8. Schur-forms, Hessenberg-forms and triangular decompositions

    Pages 55-65

  9. Perturbation analysis

    Pages 66-69

  10. Numerical preprocessing

    Pages 70-81

  11. Defect correction

    Pages 82-89

  12. Newton's method

    Pages 90-97

  13. The sign function method

    Pages 98-100

  14. Elementary transformation matrices

    Pages 101-104

  15. Schur methods

    Pages 105-112

  16. Unitary symplectic algorithms for special Hamiltonian or symplectic eigenvalue problems

    Pages 113-130

  17. Nonunitary algorithms for real Hamiltonian or real symplectic eigenvalue problems

    Pages 131-139

  18. Closed loop algorithms

    Pages 140-142

  19. A combination algorithm for real Hamiltonian and symplectic eigenvalue problems

    Pages 143-147

  20. Numerical algorithms for Riccati differential or difference equations

    Pages 148-151
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About this book

A survey is given on the state of the art in theory and numerical solution of general autonomous linear quadratic optimal control problems (continuous and discrete) with differential algebraic equation constraints. It incorporates the newest developments on differential algebraic equations, Riccati equations and invariant subspace problems. In particular, it gives a decision chart of numerical methods, that can be used to determine the right numerical method according to special properties of the problem. The book closes a gap between mathematical theory, numerical solution and engineering application. The mathematical tools are kept as basic as possible in order to address the different groups of readers, mathematicians and engineers.

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