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In this paper, we consider the problem of tracking a solution of a reference parabolic equation by a solution of another equation. A stable algorithm based on the extremal shift method is proposed for this problem. The algorithm is designed to work on a sufficiently large time interval where both equations operate.
In this paper, we discuss a method of auxiliary controlled models and its application to solving some robust control problems for a system described by differential equations. As an illustration, a system of nonlinear differential equations of the fourth order is used. A solution algorithm, which is stable with respect to informational noise and computational errors, is presented. The algorithm is...
In the paper, the problem of source function reconstruction in a differential equation of the parabolic type is investigated. Using the semigroup representation of trajectories of dynamical systems, we build a finite-step iterative procedure for solving this problem. The algorithm originates from the theory of closed-loop control (the method of extremal shift). At every step of the algorithm, the...
A problem of guaranteed control is under discussion. This problem consists in the attainment of a given target set by a phase trajectory of a system described by an equation with time delay. An uncontrolled disturbance (along with a control) is assumed to act upon the system. An algorithm for solving the problem in the case when information on a phase trajectory is incomplete (measurements of a 'part'...
We study the problem of identification of an input to a linear finite-dimensional system. We assume that the input has a feedback form, which is related to a problem often encountered in fault detection. The method we use is to embed the identification problem in a class of inverse problems of dynamics for controlled systems. Two algorithms for identification of a feedback matrix based on the method...
A problem of reconstruction of a non-observable control input for a system with a time delay is analyzed within the framework of the dynamical input reconstruction approach (see Kryazhimskii and Osipov, 1987; Osipov and Kryazhimskii, 1995; Osipov et al., 1991). In (Maksimov, 1987; 1988) methods of dynamical input reconstruction were described for delay systems with fully observable states. The present...
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