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3 International Journal of Applied Mathematics and Computer Science

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Input reconstruction by feedback control for the Schlögl and FitzHugh–Nagumo equations

Maksimov Vyacheslav, Trlötzsch Fredi

International Journal of Applied Mathematics and Computer Science

2020

Vol. 30, no. 1

5--22

Dynamical reconstruction of unknown time-varying controls from inexact measurements of the state function is investigated for a semilinear parabolic equation with memory. This system includes as particular cases the Schlögl model and the FitzHugh–Nagumo equations. A numerical method is suggested that is based on techniques of feedback control. An error analysis is performed. Numerical examples confirm the theoretical predictions.

Input reconstruction by means of system inversion: A geometric approach to fault detection and isolation in nonlinear systems

Edelmayer A., Bokor J., Szabo Z., Szigeti F.

International Journal of Applied Mathematics and Computer Science

2004

Vol. 14, no 2

189-199

In this paper the classical detection filter design problem is considered as an input reconstruction problem. Input reconstruction is viewed as a dynamic inversion problem. This approach is based on the existence of the left inverse and arrives at detector architectures whose outputs are the fault signals while the inputs are the measured system inputs and outputs and possibly their time derivatives. The paper gives a brief summary of the properties and existence of the inverse for linear and nonlinear multivariable systems. A view of the inversion-based input reconstruction with special emphasis on the aspects of fault detection and isolation by using invariant subspaces and the results of classical geometrical systems theory is provided. The applicability of the idea to fault reconstruction is demonstrated through examples.

Robust Dynamic Input Reconstruction for Delay Systems

Kappel F., Maksimov V.

International Journal of Applied Mathematics and Computer Science

2000

Vol. 10, no 2

283-307

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 paper provides an input reconstruction algorithm for partially observable systems. The algorithm is robust to the observation perturbations.