@ARTICLE{Klamka_Jerzy_Exact_2020, author={Klamka, Jerzy and Avetisyan, Ara S. and Khurshudyan, Asatur Zh.}, volume={vol. 30}, number={No 1}, journal={Archives of Control Sciences}, pages={177-193}, howpublished={online}, year={2020}, publisher={Committee of Automatic Control and Robotics PAS}, abstract={In this paper, we study the constrained exact and approximate controllability of traveling wave solutions of Korteweg-de Vries (third order) and Boussinesq (fourth order) semi-linear equations using the Green’s function approach. Control is carried out by a moving external source. Representing the general solution of those equations in terms of the Frasca’s short time expansion, system of constraints on the distributed control is derived for both types of controllability. Due to the possibility of explicit solution provided by the heuristic method, the controllability analysis becomes straightforward. Numerical analysis confirms theoretical derivations.}, type={Article}, title={Exact and approximate distributed controllability of processes described by KdV and Boussinesq equations: The Green’s function approach}, URL={http://czasopisma.pan.pl/Content/115854/PDF/ACS-2020-1-9.pdf}, doi={10.24425/acs.2020.132591}, keywords={KdV equation, Boussinesq equation, Frasca’s method, short time expansion, traveling wave, heuristic method, distributed control, constrained controllability}, }