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 approximating \(u(\cdot)\) in the mean square. The algorithm in question should implement the tracking process in real time, i.e., should calculate an approximation of the input action realized till a time moment \(t\) not later than this time. Input data in the algorithm are the results of inaccurate measurements of 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 the 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 residual method well-known in the theory of ill-posed problems.
