Kalinin, A. I. An asymptotic solution of a singularly perturbed problem of optimum speed. (Russian, English) Zbl 1102.49020 Zh. Vychisl. Mat. Mat. Fiz. 45, No. 11, 1963-1968 (2005); translation in Comput. Math. Math. Phys. 45, No. 11, 1888-1892 (2005). The task of optimum speed for a linear singularly perturbed system with multivariate controls is considered. The multivariate controls are limited on the Euclidean norm. For build-up approximate (in asymptotic sense) solution of this task the two nonperturbed tasks of optimum control of smaller dimension are resolved. Reviewer: Evgenij Nechaev (Moskva) MSC: 49N05 Linear optimal control problems 49N90 Applications of optimal control and differential games 93C35 Multivariable systems, multidimensional control systems Keywords:optimum speed; linear singularly perturbed system; multivariate control; Euclidean norm; optimum control PDF BibTeX XML Cite \textit{A. I. Kalinin}, Zh. Vychisl. Mat. Mat. Fiz. 45, No. 11, 1963--1968 (2005; Zbl 1102.49020); translation in Comput. Math. Math. Phys. 45, No. 11, 1888--1892 (2005) OpenURL