Publication Date
6-1-2024
Abstract
In the first approximation, when changes are small, most real-world systems are described by linear dynamical equations. If we know the initial state of the system, and we know its dynamics, then we can, in principle, predict the system's state many moments ahead. In practice, however, we usually know both the initial state and the coefficients of the system's dynamics with some uncertainty. Frequently, we encounter interval uncertainty, when for each parameter, we only know its range, but we have no information about the probability of different values from this range. In such situations, we want to know the range of possible values of the following states. It turns out that we can feasible predict the future state one moment ahead, but predicting two moments ahead is already NP-hard -- meaning that (unless P = NP), no feasible algorithm can preform these predictions for all possible linear dynamical systems under interval uncertainty.
Comments
Technical Report: UTEP-CS-24-27