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A second order nonlinear differential equation is considered. An algorithm for reconstructing an input from inaccurate measurements of the solution at discrete times is designed. The algorithm based on the constructions of feedback control theory and theory of ill-posed problems is stable with respect to informational noises and computational errors. [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 input under measuring a phase coordinates of a Schlögl equation is considered. We propose a solving algorithm that is stable to perturbations and is based on the combination of ideas from the theory of dynamical inversion and the theory of guaranteed control. The convergence rate of the algorithm is obtained. [ABSTRACT FROM AUTHOR]

We consider the problem of dynamic reconstruction of unknown boundary disturbances in a parabolic equation. The disturbances are assumed to occur in the Neumann boundary condition. Based on the Osipov-Kryazhimskii dynamic regularization method, the problem is reduced to that of constructing a feedback control law for some auxiliary differential equation. We indicate an information-noise- and roundoff-error-robust algorithm for solving this problem. [ABSTRACT FROM AUTHOR]

We consider the feedback control problem for a nonlinear distributed equation with memory. An algorithm for solving this problem based on constructions of the theory of positional differential games is proposed under the assumption that the equation is subjected to an unknown dynamic disturbance. [ABSTRACT FROM AUTHOR]

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.