On Solving the Optimal Control Problem

Abstract

We consider a solution of the optimal control problem for an adaptive multidirectional mirror antenna. With the Pontryagin maximum principle, we reduce the problem to solving a system of ordinary differential equations. The resulting system can be solved numerically using modern approaches such as the Runge–Kutta methods or hybrid evolutionary algorithms. Estimation of the state vector is performed by the maximum likelihood criterion with solving the generated Fokker–Planck–Kolmogorov stochastic differential equation. In this case, the posterior probability density function is associated with the normalized value of the energy flux density in the aperture of antenna feeders. We determine the ability to suppress interference with an adaptive multidirectional mirror antenna and give an example of solving the control problem.