The problem of reconstructing an unknown disturbance in a nonlinear system consisting of a combination of differential and algebraic equations is considered. Two cases are discussed. In the first case, the disturbance occurs in the system linearly, and in the second case, nonlinearly. In the case of linearity, the problem has two specific features. First, it is assumed that only part of phase coordinates of the system (namely, the coordinates described by the differential equation) is inaccurately measured at discrete times. Second, it is only known about the disturbance acting on the system that it is an element of the space of square integrable functions; i.e., it can be unbounded. These assumptions imply the impossibility of exact reconstruction. Taking into account this peculiarity, we construct a solving algorithm, which is stable with respect to information noises and computational errors. This algorithm is based on a combination of elements of the theory of ill-posed problems and the extremal shift method well known in the theory of positional differential games. A similar algorithm is designed for the general case in which the disturbance occurs in the system nonlinearly.
Maksimov et al. (Sat,) studied this question.