Control and optimal response problems for quasilinear impulsive integrodifferential equations

In various real-world applications, there is a necessity given to steer processes in time. More and more it becomes acknowledged in science and engineering, that these processes exhibit discontinuities. Our paper on theory of control (especially, optimal control) and on theory of dynamical systems gives a contribution to this natural or technical fact. One of the central results of our paper is the Pontryagin maximum principle [L.S. Pontryagin, V.G. Boltyanskii, R.V. Gamkrelidze, E.F. Mishchenko, The Mathematical Theory of Optimal Processes, Interscience Publishers, John Wiley, New York, 1962] which is considered in sufficient form for the linear case of impulsive differential equations. The problem of controllability of boundary-value problems for quasilinear impulsive system of integrodifferential equations is investigated. The control consists of a piecewise continuous function part as well as impulses which act at a variable time. By studying the optimal control of response, we give a first inclusion of an objective function. By this pioneering contribution, we invite to future research in the wide field of optimal control with impulses and in modern challenging applications. 2005 Elsevier B.V. All rights reserved.