On Viable Solutions for Uncertain Systems

One of the problems that arises in the theory of evolution and control under uncertainty is to specify the set of all the solutions to a differential inclusion that also satisfy a preassigned restriction on the state space variables (the "viability" constraint). The latter set of "viable" trajectories may be described by either a new differential inclusion whose right-hand side is formed with the aid of a contingent cone to the restriction map or by a variety of parametrized differential inclusions each of which has a relatively simple structure. The second approach is described here for a linear-convex differential inclusion with a convex valued restriction on the state space variables