Invariance of the Approximately Reachable Set under Nonlinear Perturbations.

摘要

Consider a linear control system of the form: first derivative of x with respect to time = Ax + B(u). The approximately reachable set is the closure (in the state space X) of K(sub o) := x(T) : u is a member of the set U (sub ad). The authors consider perturbation by a nonlinearity giving: first derivative of x with respect to time = Ax + F(x) + B(u) and ask when the corresponding K-bar(sub F) is the same as K-bar(sub o). The concern is to reduce this to an analysis of the relation to K(sub o) of K(sub g), obtained from an affine perturbation: first derivative of x with respect to time = Ax + g + B(u), for g is a member of the set G.