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Dragan, V. and Ivanov, I. (2011) Computation of the Stabilizing Solution of Game Theoretic Riccati Equation Arising in Stochastic H∞ Control Problems. Numerical Algorithms, 57, 357-375.
http://dx.doi.org/10.1007/s11075-010-9432-7

has been cited by the following article:

  • TITLE: On the Iterative Solution to H∞ Control Problems

    AUTHORS: Ivan G. Ivanov, Ivelin G. Ivanov, Nikolay C. Netov

    KEYWORDS: Continuous-Time Riccati Equation, Indefinite Sign, Iterative Computation, Stabilizing Solution

    JOURNAL NAME: Applied Mathematics, Vol.6 No.8, July 17, 2015

    ABSTRACT: This paper addresses the problem for solving a Continuous-time Riccati equation with an indefinite sign of the quadratic term. Such an equation is closely related to the so called full information H∞ control of linear time-invariant system with external disturbance. Recently, a simultaneous policy update algorithm (SPUA) for solving H∞ control problems is proposed by Wu and Luo (Simultaneous policy update algorithms for learning the solution of linear continuous-time H∞ state feedback control, Information Sciences, 222, 472-485, 2013). However, the crucial point of their method is to find an initial point, which ensuring the convergence of the method. We will show one example where Wu and Luo’s method is not effective and it converges to an indefinite solution. Three effective methods for computing the stabilizing solution to the considered equation are investigated. Computer realizations of the presented methods are numerically compared on the computational platforms MATLAB and SCILAB.