%0 Journal Article
%@ 1873-5649
%A Heymann, V.I.
%A Kryazhimskiy, A.V.
%D 1996
%F iiasa:4687
%I Elsevier
%J Applied Mathematics and Computation
%N 2
%P 137-151
%R 10.1016/0096-3003(96)00004-5
%T On finite-dimensional parametrizations of attainability sets
%U https://pure.iiasa.ac.at/id/eprint/4687/
%V 78
%X The attainability set is defined to be a finite-dimensional integral-type image of the set of all absolutely continuous scalar functions of time whose derivatives take values in a given interval. For a class of control systems with scalar controls restricted to the above interval (the class comprises, in particular, some bilinear systems), the attainability set has the traditional meaning. A method of finite-dimensional parametrization of the attainability set is described. The parametrization is universal, i.e., the same for all attainability sets of a fixed dimension. For the case of control systems, the result provides an upper estimate on the number of switchings sufficient to bring the system to an arbitrary reachable state at a prescribed time.