ANALYSIS OF THE PROBLEM OF OPTIMAL CONTROL OF A SECOND-ORDER OBJECT IN THE PRESENCE OF RANDOM DISTURBANCES

Key words. Optimal control, L.S. Pontryagin's maximum principle, method of synthesizing variables, double aperiodic link, random disturbances.

Abstract

The article discusses the theoretical and practical aspects of analyzing the problem of optimal control of a second-order object in the presence of random disturbances in the form of "white" Gaussian noise. The problem of optimal control for an object described by the model of a double aperiodic link is considered, in the presence of asymmetric restrictions on the control action, with fixed ends of the trajectory of the change in the vector of phase coordinates, a fixed time interval of control and a functional of the type "minimum fuel consumption". The mathematical apparatus of the theory of optimal control is used (the maximum principle of L.S. Pontryagin and the method of synthesizing variables). The study of the existence of a solution to the optimal control problem for given initial data using the analytical and graphical method is carried out. Analytical dependences for calculating the parameters of the optimal control function are given. The obtained results of the analysis of the optimal control problem can be used in the development of algorithmic support for automatic control systems for technological objects and processes that ensure the synthesis of optimal control actions in real time.