The mini-batch adaptive method of random search (MAMRS) for parameters optimization in the tracking control problem

Abstract

Abstract The tracking control problem for nonlinear dynamic system linear in control and signal tracked is considered. It is proposed to formalize the tracking problem as a problem of controlling a bunch of trajectories emanating from a given set of possible initial states. The quality of a single trajectory control is described by the value of the integral criterion, which depends on the square of the tracking error and the intensity of the control used. The control is sought from the condition of the minimum value of the average criterion defined on the set of the bunch trajectories. When choosing a control structure, the well-known result was used that provides internal stability and the desired quality of the output control. The unknown parameters of the control law within the selected structure are found using the new mini-batch adaptive method of random search (MAMRS). This new optimization algorithm combines the ideas of the adaptive random search and stochastic gradient descent methods. The examples of solving the tracking problem as a result of parametric optimization of controlling a bunch of trajectories are presented.