Control of effects in the right-hand sides of a large ODE system of a block structure and optimization of sources in unseparated boundary conditions

In this paper, we investigate the problem of control of a complex object, described by a large ODE system of a block structure with unseparated boundary conditions between blocks. The controls in the right-hand sides of the equations and the values of the source parameters in the boundary conditions are to be optimized. We propose to apply the first order optimization methods for the numerical solution to the optimal control problem, using functional gradient formulas participating in the obtained necessary optimality conditions. Special schemes of the sweep method for the solution to the direct and conjugate boundary value problems, having a block structure, and unseparated non-local boundary conditions are offered. This method takes into account special features of ODE systems and boundary conditions, allows the transfer of boundary conditions for each block and each boundary condition in the block independent of each other. The obtained results of numerical experiments in solving the test problem and their analysis are given.