H_∞ Optimal Control Problems for Jump

Ivan G. Ivanov^1,2, Ivelin G. Ivanov²

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

DOI: 10.4236/jmf.2015.54029                

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.

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