On the reconstruction of an unknown input of a system of differential equations

We study the problem of dynamic reconstruction of an unknown input acting on a system of ordinary differential equations nonlinear in the state variables and linear in the control. We consider the case of the absence of instantaneous constraints; i.e., we assume that the unknown perturbation can be unbounded, being a function summable with the square of the Euclidean norm. Taking this fact into account, we construct an algorithm for solving this problem that is resistant to information interferences and computational errors. The algorithm is based on a combination of constructions from the theory of ill-posed problems with the extremal shift method known in positional differential games. The algorithm is focused on the case of “continuous” measurement of the states of the system.