Computability of the Avoidance Set and of the Set-Valued Identification Problem

In some practical situations, we need to find the avoidance set, i.e., the set of all initial states for which the system never goes into the forbidden region. Algorithms are known for computing the avoidance set in several practically important cases. In this paper, we consider a general case, and we show that, in some reasonable sense, the corresponding general problem is always algorithmically solvable. A similar algorithm is possible for another general system-related problem: the problem of describing the set of all possible states which are consistent with the available measurement results. 1 Formulation of the Problem In control, we usually deal with robots (or other controlled devices) whose states s are described by tuples of real numbers s = (s1 . . . , sd). The dynamics of such devices is usually described by a system of differential equations