On an algorithm for dynamic reconstruction in systems with delay in control

We discuss a problem of the dynamic reconstruction of unknown input controls in nonlinear vector equations. A regularizing algorithm is proposed for reconstructing these controls simultaneously with the processes. The algorithm is stable with respect to informational noises and computational errors. © 2013 IFIP International Federation for Information Processing.German Sci. Found. (DFG) Eur. Sci. Found. (ESF);Natl. Inst. Res. Comput. Sci. Control France (INRIA);DFG Research Center MATHEON;Weierstrass Institute for Applied Analysis and Stochastics (WIAS);European Patent Offic

On a reconstruction algorithm for the trajectory and control in a delay system

We discuss a problem of the dynamic reconstruction of unmeasured coordinates of the phase vector and unknown controls in nonlinear vector equations with delay. A regularizing algorithm is proposed for the reconstruction of both controls and unmeasured coordinates simultaneously with the processes. The algorithm is stable with respect to information noises and computational errors. © 2013 Pleiades Publishing, Ltd

On an algorithm for dynamic reconstruction of the input

We consider the problem of dynamic reconstruction of the input in a system described by a vector differential equation and nonlinear in the state variable. We indicate an algorithm that is stable under information noises and computational errors and is aimed at infinite system operation time. The algorithm is based on the dynamic regularization method. © 2013 Pleiades Publishing, Ltd

The dynamical discrepancy method in problems of reconstructing unknown characteristics of a second-order system

This paper considers two problems of dynamical reconstruction of unknown characteristics of a system of nonlinear equations describing the process of innovation diffusion through inaccurate measurements of phase states. A dynamical variant for solving these problems is designed. The system is assumed to operate on a given finite time interval. The evolution of the system’s phase state, i.e., the solution of the system, is determined by an unknown input. A precise reconstruction of the real input (acting on the system) is, generally speaking, impossible due to inaccurate measurements. Therefore, some approximation to this input is constructed which provides an arbitrary smallness to the real input if the measurement errors and the step of incoming information are sufficiently small. Based on the dynamical version of the discrepancy method, two algorithms for solving the problems in question are specified. One of them is oriented to the case of measuring all coordinates of the phase vector, and the other, to the case of incomplete measurements. The algorithms suggested are stable with respect to informational noises and computational errors. Actually, they are special regularizing algorithms from the theory of dynamic inverse problems. © 2019 М.С. Близорукова

Modeling Earthquakes via Computer Programs

Modeling earthquakes plays an important role in investigation of different aspects of seismic risk. The paper continues previous studies and describes the user-friendly software destined for numerical simulation of lithosphere dynamics and seismicity by means of different modifications of the block model, which exploits the hierarchical block structure of the lithosphere. As a result, the model produces an earthquake catalog, and the programs give an opportunity to visualize it in different ways. The programs work in an interactive mode with a window interface. Numerical approximation of the Vrancea seismic region is considered as an example of application of the software. Parallel algorithms allowing to perform modeling dynamics of rather large structures are outlined

On reconstructing an unknown coordinate of a nonlinear system of differential equations

The paper discusses a method of auxiliary controlled models and the application of this method to solving problems of dynamical reconstruction of an unknown coordinate in a nonlinear system of differential equations. The solving algorithm, which is stable with respect to informational noises and computational errors, is presented. © AGH University of Science and Technology Press, Krakow 2014.Russian Academy of Sciences, RAS Russian Foundation for Basic Research, RFB

On one algorithm for reconstruction of an disturbance in a linear system of ordinary differential equations

The problem of reconstructing an unknown disturbance under measuring a part of phase coordinates of a system of linear differential equations is considered. Solving algorithm is designed. The algorithm is based on the combination of ideas from the theory of dynamical inversion and the theory of guaranteed control. The algorithm consists of two blocks: the block of dynamical reconstruction of unmeasured coordinates and the block of dynamical reconstruction of an input

On the application of control models technique to investigation of some ecological and economic problems

The paper discusses a method of auxiliary controlled models and the application of this method to solving some problems of identification and robust control for differential equations. The objects that the method is suggested to be used are two systems of nonlinear differential equations describing some ecological and economic processes. Two solving algorithms, which are stable with respect to informational noises and computational errors, are presented. The algorithms are tested by model examples