The Autonomous Linear Quadratic Control Problem

Volker L. Mehrmann

ISBN 10: 3540541705 / ISBN 13: 9783540541707

Editore: Springer Berlin Heidelberg, Springer Berlin Heidelberg Okt 1991, 1991

Riguardo questo articolo

Neuware -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.Springer Verlag GmbH, Tiergartenstr. 17, 69121 Heidelberg 180 pp. Englisch.

Codice articolo 9783540541707

Dati bibliografici

• Titolo: The Autonomous Linear Quadratic Control Problem
• Editore: Springer Berlin Heidelberg, Springer Berlin Heidelberg Okt 1991
• Data di pubblicazione: 1991
• Lingua: Inglese
• ISBN 10: 3540541705
• ISBN 13: 9783540541707
• Rilegatura: Taschenbuch
• Condizione: Neu
• Dimensioni: 254 L x 178 A x 11 P (millimetri) 254 millimetri di larghezza per 178 millimetri di altezza per 11 millimetri di profondità
• Peso: 351 grammi

Descrizione articolo

Riassunto

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.

Contenuti

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.