Convergence of the spline method for solving the optimal dynamic measurement problem

The problem of optimal dynamic measurement consists in finding the dynamically distorted input signal by observing the output signal. This problem is solved as an optimal control problem to minimize the difference between the values obtained from the output data and the model values obtained in the course of a computational experiment. It was shown earlier that this problem has a unique solution. For a complex form of the input signal, various numerical methods can be used to find the optimal dynamic measurement. This article suggests to use the spline method in order to solve this problem. Namely, we present the algorithm of this method and show that the solution obtained by the spline method converges to the exact solution of this problem.