Application of the mini-batch adaptive method of random search (MAMRS) in problems of optimal in mean control of the trajectory pencils

Abstract

Abstract The article discusses the application of one of the new methods of constrained optimization to solve the problem of finding optimal control of a pencil of trajectories of nonlinear deterministic systems emanating from a given set of initial states. The structure of a feedback system is proposed, which contains a model of a control object, a measurement system model, a state observer that generates an estimate of the state vector from incoming measurements, and a regulator. The quality of control is assessed by the value of the average value of the functional determined on individual trajectories. Unknown control laws for the object model and the state observer are found in the form of expansions in terms of orthonormal systems of basic functions defined on the set of admissible states of the dynamic system. The problem of controlling a pencil of trajectories is reduced to the problem of parametric optimization, which is solved using a mini-batch adaptive random search method. A step-by-step algorithm for solving the problem is proposed, which is demonstrated by solving the problem of tracking various coordinates of a dynamical system according to the measurement results. The influence of the mini-batch size on the achieved tracking accuracy is investigated.