Algorithms for Controlling Dynamic Systems under Uncertainty. Part 2

Abstract

The paper considers the problems of synthesizing positional control of dynamic systems (DS) in situations with a high level of uncertainty caused both by disturbances acting on the DS and interference in information channels. Uncertainty results from the action of various external disturbing factors, uncontrolled changes in the object properties, and equipment failures and malfunctions. A peculiar feature of the considered problems is that they are single events. In these information conditions, the synthesis of positional control of dynamic systems is considered based on the minimax approach worst-case design. Therefore, the mathematical model of processes is characterized by disturbances and measurement errors known with a precision up to sets, and the DS state vector is known with a precision up to membership in the information set as a result of solving the estimation problem. The proposed approach combines control concepts under information deficiency proposed by N. N. Krasovsky, A. B. Kurzhansky, and V. M. Kuntsevich with A. A. Krasovsky’s concepts of building selforganizing systems. The "principle of a guaranteed result" was chosen to synthesize DS control. A key distinction between the guaranteed and stochastic approach is the use of uncertainty sets of disturbances, interference, and the system state vector in DS control. The first part of the article solves the problem of estimating the state vector and, as a result, constructs an information set, to which the system state vector is guaranteed to belong. The second part of the article solves the control problem taking into account control restrictions, when the system operation quality is assessed by the belonging of the object’s state vector to a given set, which may depend on time. The tasks of stabilization, tracking, and terminal control can be set here. The control problem is also solved based on the guaranteed approach when specifying the requirements for the system in the form of a quadratic functional. The paper also considers the use of the Lyapunov function for control synthesis. The solution of estimation and control problems is reduced to extremal problems with linear and quadratic objective functions under restrictions in the form of systems of linear inequalities. The paper provides their examples.