Algorithms for Controlling Dynamic Systems under Uncertainty. Part 1

The paper considers the control of dynamic systems (DS) in situations with a high level of uncertainty caused by disturbances acting on the DS and interference in information channels during operation. 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 these control problems is that they are single events. In these conditions, the synthesis of positional control of dynamic systems is considered based on the minimax approach — worst-case design. The mathematical model of processes is characterized by disturbances and measurement errors known with a precision up to sets. 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 N. N. Krasovsky’s control concepts under information deficiency and A. A. Krasovsky’s concepts of building self-organizing systems. The “principle of a guaranteed result” was chosen to synthesize DS control. A control problem is solved in two stages in incomplete information. At the first stage, the state vector estimation problem is solved. The paper considers several implementations of estimation algorithms. It also proposes a minimax filtration algorithm based on the use of three filters (minimax filter (MMF), Kalman filter (KF), and guaranteeing filter (GF)) which can increase the estimation accuracy and make the proposed minimax filtration algorithm adaptable. The author discusses the implementation of the proposed algorithm and considers examples. The second part of the paper solves the control problem.