<p>For a system of nonlinear differential equations with the Gerasimov–Caputo fractional derivative, the problem of reconstruction an unknown input is considered. The input is unknown in advance as well as a trajectory of the system, but the information about its position is available for inaccurate online measurements. A reconstruction algorithm for solving this problem in the uniform norm is proposed. It is based on the Tikhonov regularization method and the Krasovskii extremal aiming method, which provide the stability of the algorithm with respect to informational noises and computational errors. A numerical example illustrating the application of the developed technique on a specific fractional order system is provided.</p>

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ONLINE SOLUTION ALGORITHM FOR AN INPUT RECONSTRUCTION PROBLEM IN THE UNIFORM NORM FOR A FRACTIONAL ORDER SYSTEM

  • Platon G. Surkov

摘要

For a system of nonlinear differential equations with the Gerasimov–Caputo fractional derivative, the problem of reconstruction an unknown input is considered. The input is unknown in advance as well as a trajectory of the system, but the information about its position is available for inaccurate online measurements. A reconstruction algorithm for solving this problem in the uniform norm is proposed. It is based on the Tikhonov regularization method and the Krasovskii extremal aiming method, which provide the stability of the algorithm with respect to informational noises and computational errors. A numerical example illustrating the application of the developed technique on a specific fractional order system is provided.