Algorithm to solve linear multipoint problems of control by the method of cascade decomposition

Proposed was a method to solve control problems for the nonstationary heterogeneous linear systems under conditions on the state and control functions at different time points. It consists of a phased transition from of the initial problem to the formula for the determination of some part of the functions of control and a problem similar to the previous one for a system with a smaller number of equations. The suggested method is a modification of the previous method of cascade decomposition, which solves problems using the projectors on the subspace. In the present paper, decomposition was carried out by solving the linear algebraic equations and replacing linearly the desired vector functions. The procedure of differentiation of certain functions was used to construct the controlled process.