Control synthesis in a class of higher-order distributionsстатья
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Дата последнего поиска статьи во внешних источниках: 18 июля 2013 г.
Аннотация:The present paper deals with impulse control. Unlike other papers, here the controls are chosen
in the class of functions that admit first-order impulses (delta functions) as well as finitely many
higher derivatives of these functions (generalized impulses or higher-order impulses). In addition,
the control is sought in the form of positional strategies rather than open-loop solutions. The latter
leads to the use of a modified version of dynamic programming theory, which is adjusted for such
problems and based on the reduction of the original problem to another one problem considered in
the class of only first-order impulses. In this modification, instead of the Hamilton–Jacobi–Bellman
(HJB) equation, one uses variational inequalities of similar structure. However, solutions in the class
of higher-order distributions do not necessarily admit physical realization. In order to make such
solutions applicable, we suggest physically realizable approximations which converge to the exact
solutions. Thus, in the class of higher-order distributions, it becomes possible to bring a controllable
linear system from one given state to another in zero time. Then the physical realization of such a
solution permits one to solve the same problem in an arbitrarily small finite time, which leads to
the notion of physically realizable “fast” controls. We also indicate the possibility of numerically
solving the problem on the construction of reachability domains of linear systems in the considered
class of controls with higher-order impulses through methods of ellipsoidal calculus. This can be
achieved on the basis of the comparison principle for HJB-type equations and inequalities.