Применение уравнения Гамильтона-Якоби-Беллмана (HJBЕ) для синтеза управляющих воздействий для нелинейных систем наталкивается, как правило, на сложности аналитического и вычислительного порядков. С другой стороны, использование уравнения HJBЕ дает возможность исследовать системы, параметры которых зависят от состояния (SDC) [1,2]. Для квадратичных функционалов качества в задаче стабилизации это позволяет осуществить переход от скалярного уравнения в частных производных (HJBE) к матричному уравнению типа Риккати с параметрами, зависящими от состояния (SDRE). Следует отметить, что использование метода SDRЕ для решения HJВЕ наталкивается на проблему неоднозначного представления нелинейной системы в форме SDC [2]. Отметим что, аналитического решения SDRE в общем случае получить невозможно. В работе используется метод синтеза гарантирующего управления нелинейным объектом, в качестве которого избран реактор на тяжелой воде.

In this paper we propose the scheme of diagnosing the problem situation of complex system development based on the analysis of structural properties of a cognitive-map-based model of the system development. It allows exploring different types of problem situations related to the interaction of active agents, the adverse effect of the environment and the structural features of the system. The distinctive feature of the proposed scheme is that the problem situation is considered in the whole. This is aimed to determine priorities for problem solving, depending on their causes.

Within a problem of control of dynamic plants under uncertainty are considered both classical methods of the theory of systems with variable structure, and their modern development in the form of the theory of new types of feedback. The exact structure of feedback in control variable structure systems is clari¯ed. Existence of two types of feedback is revealed: one classical feedback by the general regulation error, and another, new type, the coordinate- to-operational feedback. Thus feedback is responsible for a set of positive dynamical properties for control variable structure systems. Also the perspective directions of further development of the theory of new types of feedback are considered. In particular, methods of simultaneous control by families of dynamic plants are considered are considered.

Increasingly popular cognitive mapping of ill-structured socio-economic, manufacturing and other systems and situations carries risks for validity of end results. The problem of validity of expert estimates on prescribed normalized universal scales is raised. The main factor of risk is supposed to be the conceptual vagueness of expert knowledge on ill-structured systems and situations and knowledge of theoretical models for their cognitive mapping. An approach to analysis of expert estimation validity of variable values in cognitive mapping is proposed. In the approach the model of conceptual interpretation of a prescribed universal scale for an estimated variable is proposed. The model of conceptual interpretation enables to refine the influence of conceptual vagueness onto the expert estimation validity. Some results of empirical testing of the proposed approach operability in cognitive mapping are presented.