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.


49N05 Linear optimal control problems
49N90 Applications of optimal control and differential games
93C35 Multivariable systems, multidimensional control systems