The Autonomous Linear Quadratic Control Problem

1. Front Matter

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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

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.

• Algebra
• Algebraische Differentialgleichung
• Differentialgleichung
• Newton's method
• Numerische Mathematik
• algorithm
• algorithms
• control
• feedback
• numerical methods
• optimal control
• stability
• transformation

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