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We consider the problem of dynamical reconstruction of input disturbances in a system of differential equations subject to the influence of an unknown disturbance. We present two algorithms for solving the problem that are robust to information noises and computational errors and are oriented to computer implementation. The algorithms operate under measurements (with errors) of phase states of the system at discrete times. [ABSTRACT FROM AUTHOR]

The problem of reconstructing a distributed input disturbance in a parabolic inclusion unsolved for the derivative is considered. A solution algorithm that is robust to information noises and computational errors is proposed. The algorithm combines methods of the theory of ill-posed problems and methods of feedback control theory. It reconstructs the unknown input disturbance from the solution of the inclusion measured inaccurately at sufficiently frequent discrete times. [ABSTRACT FROM AUTHOR]

A regularizing algorithm is presented for solving the problem of dynamic reconstruction of an unknown input in a nonlinear vector differential equation. The algorithm is stable under information noise and computational errors. [ABSTRACT FROM AUTHOR]

We consider the problem of reconstructing distributed inputs (disturbances) in linear parabolic equations. An algorithm for solving this problem is given. An upper bound for the convergence rate is established for the case in which the input is a function of bounded variation. The algorithm combines the optimal preset and positional control methods and permits reconstruction based on inaccurate measurements of solutions of the equations at discrete time instants. [ABSTRACT FROM AUTHOR]

We consider a differential equation of the Klein–Gordon type with an unknown input. The solution of this equation is assumed to be measured with some errors. We indicate a reconstruction algorithm whose input is formed by the feedback principle and serves as approximations to the unknown input of the original equation. [ABSTRACT FROM AUTHOR]

The problem of reconstructing an unknown disturbance of a nonlinear system of ordinary differential equations from inexact measurements of some of the state coordinates is considered. A solution algorithm robust to noises is proposed that combines constructions of dynamic inversion and guaranteed control theories. The algorithm consists of two blocks: one dynamically reconstructs the unmeasured coordinates and the other reconstructs the disturbance. [ABSTRACT FROM AUTHOR]

The dynamic reconstruction of input disturbances and unobserved state coordinates is considered. An algorithm based on the dynamic inversion theory is proposed, which is robust to observational and computational errors. [ABSTRACT FROM AUTHOR]

We consider the problem of dynamic reconstruction of a variable input of a nonlinear delay system on the basis of an inexact measurement of part of the phase vector. We present a solution algorithm on the basis of the method of auxiliary control models. [ABSTRACT FROM AUTHOR]

A dynamical inversion problem is considered. A regularizing solving algorithm oriented to a quite long time interval of system's functioning is designed. The algorithm is stable with respect to informational noises. [ABSTRACT FROM AUTHOR]

Discusses the reconstruction of input actions through measurements of a part of coordinates. Problem of robust reconstruction of variable inputs for a dynamical system by using results of inexact observations of its trajectory; Solution algorithms for a number of situations; Concepts of the theory of robust dynamic inversion; Statement of dynamic reconstruction problems.

Considers the problem of dynamic reconstruction of a variable input for a system governed by an abstract parabolic equation. Methods of the theory of positional differential games; Modification of an input reconstruction algorithm; Measurement accuracy parameter; Proof of theorem.