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**Asymptotic attainability. Transl. from an orig. Russian manuscript.**
*(English)*
Zbl 0859.93002

Mathematics and its Applications (Dordrecht). 383. Dordrecht: Kluwer Academic Publishers. xiv, 322 p. (1997).

In this monograph, questions of extensions and relaxations are considered. These questions arise in many applied problems in connection with the operation of perturbations. Asymptotic behaviour of the attainability sets for different kinds of dynamical control systems with integral constraints are considered. The prediction of random events is also discussed. Special attention is paid to finite additive measure with the property of weak absolute continuity. Nonlinear control problems with impulse control are discussed.

Regularizations of extremal problems on the basis of well-posed extensions are considered. The general problem of the asymptotic optimization in a preordered topological space is investigated. Moreover, the asymptotic nonsensitivity property of the optimization problem under some restricted perturbations is analyzed. Several remarks and comments on the asymptotic attainability under perturbation are presented. Connections with classical control theory are explained and discussed.

Regularizations of extremal problems on the basis of well-posed extensions are considered. The general problem of the asymptotic optimization in a preordered topological space is investigated. Moreover, the asymptotic nonsensitivity property of the optimization problem under some restricted perturbations is analyzed. Several remarks and comments on the asymptotic attainability under perturbation are presented. Connections with classical control theory are explained and discussed.

Reviewer: J.Klamka (Katowice)

### MSC:

93-02 | Research exposition (monographs, survey articles) pertaining to systems and control theory |

93B05 | Controllability |

93C05 | Linear systems in control theory |

93B03 | Attainable sets, reachability |