Abstract
AbstractThis article describes the task of monitoring the behavior of dynamical objects. The mathematical model is described by a system of nonlinear ODEs depending on control and tracking signals. It is proposed to formalize the monitoring task as a task that controls a pencil of trajectories corresponding to a set of possible initial states. The cost functional represents the control quality of an individual trajectory versus control signal and the square of the tracking error. Optimal control can be obtained from the condition of the minimum of the average functional over the entire pencil of trajectories. In the selection of control structures, known results were used to ensure the internal stability and the desired quality of the transition process. A new adaptive random mini-batch search method is used to calculate the unknown control law parameters in a selected structure. It belongs to the zero-order optimization methods and is a modification of the adaptive random search method using the idea of the mini-batch gradient optimization algorithm used in machine learning. The results of solving the tracking problem of various coordinates of a chaotic process obtained by parametric optimization are presented.KeywordsThe mini-batch optimization methodThe adaptive random search methodZero order optimization methodsThe tracking problem
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