The Autonomous Linear Quadratic Control Problem: Theory and Numerical Solution

ISBN-13: 9783540541707 / Angielski / Miękka / 1991 / 180 str.

Mehrmann, Volker L.

Opis

Covers the theory and numerical solution of general autonomous linear quadratic optimal control problems (continuous and discrete) with differential algebraic equation constraints. This book incorporates developments on differential algebraic equations, Riccati equations and invariant subspace problems.

Spis treści

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.