l-problem of moments for one-dimensional integro-differential equations with Erdélyi-Kober operators

Purpose: to investigate the possibility of statement of l-problem of moments for one-dimensional linear equations of three types, which contain Erdélyi-Kober differential and integral operators of fractional order. Methods: formulation of l-problem of moments for each type of investigated equations, analytical investigation and solution of problem formulated Results. Conditions derived that determine the possibility and solvability of the problem stated. In some cases an explicit solutions of l-problem of moments obtained. Conclusions. The possibility of statement of formulated l-problem of moments shown in cases that defined by conditions obtained in paper. Some analytical solutions of investigated problem obtained.

ABOUT ONE APPROACH TO MODELING OF OPTIMAL CONTROL OF MULTIDIMENSIONAL COMPOSITE LINEAR SYSTEMS

The approach to the synthesis of optimal control of multidimensional composite linear system based on solutions of optimal control problems for inclusion in its structure of partial linear systems with scalar controls is considered. Control tasks are reduced to the problem of moments in the L\ space for minimum functionals of the norm type, on minimum maximal Ноlder norms level (with indicators 2 and то) for the vector control composite system.

On the optimal control of the n-fold integrator

The optimal control problem n-fold integrator with arbitrary boundary conditions and functionals of type norms in spaces of Lq[t0; tf ], q = 1; 2;1 is considered. First, it is the problem of minimizing the total controling impulse, which boils down to L1- problem of moments; secondly, the problem of minimizing the maximum values of the control parameter (represented as L1-problem of moments), and, finally, it is the problem of minimizing ”generalized work control” (as L2-problem of moments). Solving problems is obtained by using the method of moments in the form of the maximum principle by N.N. Krasovsky. It is shown that optimal control in the first problem is approximated by a -impulsive control. Conditions for the existence of regular and singular solutions to this problem depending on the boundary conditions are also specified. The general solution of the second problem, which is the conditions for existence of regular and singular solutions and not equivalence with the mutual problem of time-optimal control is obtained. Examples of solution for the considered control tasks are given. In case of a quadratic functional general relations required for constructing a program optimal control were obtained.