The Autonomous Linear Quadratic Control Problem: Theory and Numerical Solution

by Volker L. Mehrmann

Overview

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.

Product Details

ISBN-13:	9783540541707
Publisher:	Springer Berlin Heidelberg
Publication date:	10/28/1991
Series:	Lecture Notes in Control and Information Sciences , #163
Edition description:	1991
Pages:	176
Product dimensions:	6.69(w) x 9.84(h) x 0.01(d)

Table of Contents

Notation and definitions.- Existence of solutions.- Eigenstructure of—A -—B,—A? -—B?.- Uniqueness and stability of feedback solutions.- Algebraic Riccati equations and deflating subspaces.- Schur-forms, Hessenberg-forms and triangular decompositions.- Perturbation analysis.- Numerical preprocessing.- Defect correction.- Newton's method.- The sign function method.- Elementary transformation matrices.- Schur methods.- Unitary symplectic algorithms for special Hamiltonian or symplectic eigenvalue problems.- Nonunitary algorithms for real Hamiltonian or real symplectic eigenvalue problems.- Closed loop algorithms.- A combination algorithm for real Hamiltonian and symplectic eigenvalue problems.- Numerical algorithms for Riccati differential or difference equations.- A general algorithm.- Conclusion.- Statement.- References.