Control Systems with Constraints and Uncertain Initial Conditions

AMS subject classification: 49N55, 93B52, 93C15, 93C10, 26E25.

We study the problem of finding a control such that all solutions of a control systems, starting from a given set of initial conditions, satisfy a given constraint. This problem is an extension of the well-known Viability Problem when the initial condition is a set. The present paper is mainly a survey of results recently obtained by the authors, but some new results with proofs are also included.