Abstract
In the paper we consider the one model of dynamic system under conditions of indeterminacy – linear controllable differential inclusions. For the informational model of the control system the minimax control problem for ensemble trajectories is researched. This control problem is study with a methods nonsmooth and multi-value analysis. The necessary and sufficient conditions of optimality are obtained.
Highlights
Effective control of complex technical objects and processes is impossible without taking into account factors such as incomplete information on external parameters and inaccuracy of the initial a priori data of the system
The control problems in conditions of limited information of various types lead to the so-called information models of control systems
Known methods for studying a information models of control systems are developed taking into account the degree of limited information regarding external parameters and the initial state of the system
Summary
Effective control of complex technical objects and processes is impossible without taking into account factors such as incomplete information on external parameters and inaccuracy of the initial a priori data of the system. A more common situation is when a priori data on the initial state of the system and the parameters of external influences are minimal, i.e. there are no statistical descriptions of them, and information is limited to setting only the set of possible values of unknown parameters In such cases, we can say that the consideration model represents a control system in conditions of uncertainty. Models of decision making under conditions of incomplete information on the initial data and external parameters of the system lead to optimization problems with such criteria [1] In studies of such models control system, methods of nonsmoth analysis and the theory of differential inclusions are of great importance. Among the urgent tasks for such systems, it is worth noting such tasks as the dependence of the set of trajectories on the parameters and initial data, the controllability conditions of the ensemble of trajectories, and the optimization of the control of the ensemble of trajectories according to given criteria [8–11]
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