On solving a linear control problem

The problem of a linear regulator is considered. There is a system of linear differential equations with a quadratic control quality criterion. The method of dynamic programming is applied to the solution of the considered linear problem. As is known, the main difficulty in applying this method is to integrate partial differential equations. In this problem, the obtained optimal control function depends on the solution of the Riccati equation. In [1], conditions were obtained under which there is a solution to such optimal control problems with a quadratic quality criterion. These conditions were obtained along with formulas for minimizing control and for optimal trajectory. But all these statements depended on the ability to solve the matrix Riccati equation under certain boundary conditions given at some time point. To construct a solution to the problem under consideration, a system of 2 n adjoint differential equations is constructed. After splitting the transition matrix of this system into block ones, it is possible to express the state of the system at the time instant t through the state variable and the adjoint variable at the final time instant t 1. A feature of this work is that an example is given, where the solution of the Riccati equation, which determines the optimal solution of the problem, was obtained explicitly

Generalized differential transformation method for solving two-interval Weber equation subject to transmission conditions

The main goal of this study is to adapt the classical differential transformation method to solve new types of boundary value problems. The advantage of this method lies in its simplicity, since there is no need for discretization, perturbation or linearization of the differential equation being solved. It is an efficient technique for obtaining series solution for both linear and nonlinear differential equations and differs from the classical Taylor’s series method, which requires the calculation of the values of higher derivatives of given function. It is known that the differential transformation method is designed for solving single interval problems and it is not clear how to apply it to many-interval problems. In this paper we have adapted the classical differential transformation method for solving boundary value problems for two-interval differential equations. To substantiate the proposed new technique, a boundary value problem was solved for the Weber equation given on two non-intersecting segments with a common end, on which the left and right solutions were connected by two additional transmission conditions

Short-term prediction of ionospheric parameters based on auto-correlation analysis

A prediction method based on a simple auto-regressive model has been developed for short-term prediction of ionospheric characteristics. The method determines the auto-correlation function for the hourly values of the parameter of interest, using the time series from the previous 25 days. The resulting weighting coefficients can then be used to forecast future values of the parameter. The method has been applied to predict f0F2 up to 24 h ahead for stations Uppsala, Slough, Poitiers and Sofia. Error statistics are presente

Short-term prediction of ionospheric parameters based on auto-correlation analysis

A prediction method based on a simple auto-regressive model has been developed for short-term prediction of ionospheric characteristics. The method determines the auto-correlation function for the hourly values of the parameter of interest, using the time series from the previous 25 days. The resulting weighting coefficients can then be used to forecast future values of the parameter. The method has been applied to predict f0F2 up to 24 h ahead for stations Uppsala, Slough, Poitiers and Sofia. Error statistics are presente