Applied Mathematics > Vol.6 No.8, July 2015

Ivan G. Ivanov^1,2, Ivelin G. Ivanov², Nikolay C. Netov¹

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

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.

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

Ivanov, I. , Ivanov, I. and Netov, N. (2015) On the Iterative Solution to H_∞ Control Problems. Applied Mathematics, 6, 1263-1270. doi: 10.4236/am.2015.68119.