H&#8734 Optimal Control Problems for Jump

Ivan G. Ivanov; Ivelin G. Ivanov

doi:10.4236/jmf.2015.54029

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JMF> Vol.5 No.4, November 2015

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H_∞ Optimal Control Problems for Jump

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DOI: 10.4236/jmf.2015.54029 2,246 Downloads 2,598 Views

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Ivan G. Ivanov^1,2, Ivelin G. Ivanov²

Affiliation(s)

¹Faculty of Economics and Business Administration, Sofia University “St. Kliment Ohridski”, Sofia, Bulgaria.
²Pedagogical College Dobrich, Shoumen University, Shoumen, Bulgaria.

ABSTRACT

We consider a set of continuous algebraic Riccati equations with indefinite quadratic parts that arise in H￥ control problems. It is well known that the approach for solving such type of equations is proposed in the literature. Two matrix sequences are constructed. Three effective methods are described for computing the matrices of the second sequence, where each matrix is the stabilizing solution of the set of Riccati equations with definite quadratic parts. The acceleration modifications of the described methods are presented and applied. Computer realizations of the presented methods are numerically compared. In addition, a second iterative method is proposed. It constructs one matrix sequence which converges to the stabilizing solution to the given set of Riccati equations with indefinite quadratic parts. The convergence properties of the second method are commented. The iterative methods are numerically compared and investigated.

KEYWORDS

H_∞ Optimal Control Problem, Generalized Riccati Equation, Indefinite Sign, Stabilizing Solution

Conflicts of Interest

The authors declare no conflicts of interest.

Cite this paper

G. Ivanov, I. and Ivanov, I. (2015) H_∞ Optimal Control Problems for Jump. Journal of Mathematical Finance, 5, 337-347. doi: 10.4236/jmf.2015.54029.

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