On finite-dimensional parametrizations of attainability sets
Nonlinear finite-dimensional, continuous-time control systems are considered. Under the assumption that there is only a scalar control function, a formal definition of the attainable sets is given. Next, a method of finite-dimensional parametrization of the attainable sets is proposed. It should be stressed that the parametrization is universal, i.e., the same for all attainable sets of a fixed dimension. Moreover, it is shown, that an upper estimate on the number of switchings sufficient to bring the control system to an arbitrary reachable state at a prescribed time is finite and depends on the dimensionality of the state space. Several remarks and comments on the properties of the attainable sets are also given. Similar problems have been considered in the paper [\textit{A. A. Agrachev} and \textit{S. A. Vakhrameev}, Sov. Math., Dokl. 30, 620-624 (1984); translation from Dokl. Akad. Nauk SSSR 279, No. 2, 265-269 (1984)].
scientific article; zbMATH DE number 932142