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Numerical investigation of the optimal measurement for a semilinear descriptor system with the Showalter-Sidorov condition: algorithm and computational experiment. (English) Zbl 1459.49017

Summary: The article deals with the problem of optimal measurement for a semilinear descriptor system with a distinguished linear part and a nonlinear term unsolved with respect to the derivative of the unknown vector function with the Showalter-Sidorov initial condition. Basing on the methods of the theory of optimal control we found sufficient conditions for the existence of solutions of the optimal measurement problem – the problem of recovering a dynamically distorted signal from a measuring device. An algorithm for finding a numerical solution uses the methods of decomposition, penalty and the Ritz method as well. The algorithm is based on the representation of the measurement components by polynomials of a given degree, which allows reducing the optimal control problem to a computer programming problem with respect to the unknown coefficients of the polynomials. As an example of a sensor we consider FitzHugh-Nagumo oscilloscope described by a nonlinear descriptor system. Computational experiments for the considered sensor model are presented.

MSC:

49M27 Decomposition methods

References:

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