Метод сетевого оператора для синтеза робастной системы управления спуском космического аппарата на Луну

Рассмотрена задача синтеза оптимальной системы управления. Осуществлен поиск многомерной функции управления, зависящей от координат пространства состояния и гарантирующей оптимальное управление на множестве объектов из разных начальных условий. Представлен численный пример синтеза оптимальной системы управления спуском космического аппарата на Луну в условиях неопределенности.

A METHOD OF NETWORK OPERATOR FOR ROBUST CONTROL SYSTEM SYNTHESIS OF SPACE SATELLITE LANDING ON THE MOON

The problem of optimal control system synthesis is considered. We search for a multi-dimensional function of control that depends on coordinates of objects' state. This function should guarantee optimal control for set of objects that start from different initial conditions. The space of functions is very huge, and it leads to computational complexity while using evolutional algorithms. The paper applies a method of network operator that is more effective for control synthesis problems. Mathematical expressions are presented as integer matrices. In mathematical expressions we consider functions of one or two arguments. A network operator matrix is upper triangular and describes the structure of directed graph, that sets the order of calculations over arguments of the mathematical expression. The search is performed using genetic algorithm based on the principle of small basic solution variations. A set of possible solutions is given by basic solution and ordered sets of vectors of variations. Genetic operations are performed over the sets of small variation vectors. A numerical example for the optimal control system synthesis of space satellite landing on the Moon under uncertainty is given.