Successive approximation method for quasilinear impulsive differential equations with control

Abstract We introduce a technique to define successive approximations to solutions of the control problem with implulse actions on surfaces where μ is a small positive parameter, ζ i + θ i + μτ i ( x (ζ i ), μ), x ϵ R n and Δ x (θ) := x (θ+) − x (θ). A sequence of piecewise continuous functions with discontinuities of the first kind that converges to a solution of the above problem is constructed.