On some iterations for optimal control of jump linear equations

We consider different iterative methods for computing Hermitian solutions of the coupled Riccati equations of the optimal control problem for jump linear systems. We have constructed a sequence of perturbed Lyapunov algebraic equations whose solutions define matrix sequences with special properties...

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Veröffentlicht in:	Nonlinear analysis 2008-12, Vol.69 (11), p.4012-4024
1. Verfasser:	Ivanov, Ivan Ganchev
Format:	Artikel
Sprache:	eng
Schlagworte:	Algebra Algebraic geometry Calculus of variations and optimal control Coupled algebraic Riccati equations Exact sciences and technology Linear and multilinear algebra, matrix theory Lyapunov iterations Mathematical analysis Mathematics Newton’s method Numerical analysis Numerical analysis. Scientific computation Numerical linear algebra Positive semidefinite matrix Sciences and techniques of general use
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Beschreibung
Zusammenfassung:	We consider different iterative methods for computing Hermitian solutions of the coupled Riccati equations of the optimal control problem for jump linear systems. We have constructed a sequence of perturbed Lyapunov algebraic equations whose solutions define matrix sequences with special properties proved under proper initial conditions. Several numerical examples are included to illustrate the effectiveness of the considered iterations.
ISSN:	0362-546X 1873-5215
DOI:	10.1016/j.na.2007.10.034