Successive approximation method for quasilinear impulsive differential equations with control Original Research Article

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, ζi + θi + μτi(x(ζi), μ), x ϵ Rn and Δx(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.