Control problems for vector systems with deterministic uncertainty

A nonlinear control system with deterministic uncertain dynamics modeled by a differential inclusion in Rⁿ is considered. Two different kinds of problems are treated. The first consists in proving the existence of a state feedback control u=u(t,x) such that for every system dynamics f(t,x,u)∈F( t,x,u) any solution, defined on the time interval [0, 1], corresponding to an initial condition taken in a given ball centered at the origin, reaches at t=1 an assigned target, which is represented by a nonempty compact convex set in Rⁿ. The second problem is the following: given a nonlinear control system as a model, one searches for the existence of a state feedback control law u=u(t,x) such that for every choice of the dynamics f(t,x ,u) from F(t,x,u) the difference between any solution corresponding to this dynamics and any fixed solution of the model goes to zero as t→+∞