Abstract:
The problem of tracking an unknown input action $u(\cdot)$ in a system of nonlinear ordinary differential equations is considered. Its essence consists in the construction of an algorithm for calculating some function that approximates $u(\cdot)$ in the mean square. The algorithm in question should implement the tracking process in real time, i.e., it should calculate an approximation of the input action realized up to a time moment $t$, not later than this time. The input data to the algorithm are the results of inaccurate measurements of the system's phase state at discrete times. As a consequence of this feature of the problem, the exact tracking of $u(\cdot)$ is impossible. Therefore, we construct an algorithm of approximate tracking based on a controlled model. The model control obtained by the feedback principle taking into account current phase states is formed on the basis of an appropriate modification of the dynamic discrepancy method well-known in the theory of ill-posed problems.
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