The Autonomous Linear Quadratic Control Problem: Theory and Numerical Solution

✍ Scribed by Volker Ludwig Mehrmann (eds.)

• Publisher: Springer-Verlag Berlin Heidelberg
• Year: 1991
• Tongue: English
• Leaves: 178
• Series: Lecture Notes in Control and Information Sciences 163
• Edition: 1
• Category: Library

✦ Synopsis

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.

✦ Table of Contents

Introduction....Pages 1-8
Notation and definitions....Pages 9-14
Existence of solutions....Pages 15-26
Eigenstructure of αA - βB, αA′ - βB′ ....Pages 27-38
Uniqueness and stability of feedback solutions....Pages 39-49
Algebraic Riccati equations and deflating subspaces....Pages 50-54
Schur-forms, Hessenberg-forms and triangular decompositions....Pages 55-65
Perturbation analysis....Pages 66-69
Numerical preprocessing....Pages 70-81
Defect correction....Pages 82-89
Newton's method....Pages 90-97
The sign function method....Pages 98-100
Elementary transformation matrices....Pages 101-104
Schur methods....Pages 105-112
Unitary symplectic algorithms for special Hamiltonian or symplectic eigenvalue problems....Pages 113-130
Nonunitary algorithms for real Hamiltonian or real symplectic eigenvalue problems....Pages 131-139
Closed loop algorithms....Pages 140-142
A combination algorithm for real Hamiltonian and symplectic eigenvalue problems....Pages 143-147
Numerical algorithms for Riccati differential or difference equations....Pages 148-151
A general algorithm....Pages 152-155
Conclusion....Pages 156-156
Statement....Pages 157-157
References....Pages 158-173

✦ Subjects

Control Engineering; Appl.Mathematics/Computational Methods of Engineering; Systems Theory, Control; Calculus of Variations and Optimal Control; Optimization