Pseudospectral Method for Finding Optimal Control of Trajectory Bundles Based on Multi-Agent Optimization Algorithms

A class of problems of optimal control of nonlinear continuous deterministic systems under conditions of uncertainty is considered. To solve the problem, a numerical algorithm for finding the optimal control is formed, in which the parameterization of the control law is used, which depends on time and a set of coordinates of the state vector available for measurement. This approach is based on the approximation of the control law by a series using a system of basis functions with unknown coefficients. The search for unknown coefficients in the expansion of the control law is implemented using multi-agent optimization methods: a hybrid multi-agent interpolation search algorithm and a multi-agent algorithm based on the use of linear controllers for controlling the movement of agents. A software has been developed and two model examples and an applied problem of stabilizing a satellite with the help of engines installed on it have been solved.