Integral equation in the theory of optimal speed of linear systems with constraints

Abstract

We propose a method for solving the optimal speed problem for linear ordinary differential
equations with curve conditions from given sets in the presence of phase and integral constraints,
as well as holonomic connections. In contrast to the known methods of solving the problem of
optimal performance, a new approach to the problem of performance in the form of the principle
of immersion is developed. The immersion principle is based on the study of solvability and the
construction of a General solution of the integral equation.
The main results are:
– necessary and sufficient conditions for the existence of a solution of one class of integral equation
and the construction of its General solution;
– selection of all sets of controls, each element of which translates the trajectory of the system
from any initial state to any desired final state for linear systems;
– the proposed immersion principle allows reducing the initial boundary value problem of optimal
performance with restrictions to a special initial problem of optimal control;
– necessary and sufficient conditions for the existence of acceptable management;
– an algorithm for solving the optimal performance problem with constraints for linear systems
of any order has been developed.
The results obtained are solutions to current problems in the theory of optimal performance with
restrictions that have numerous applications.

A new metho d is develop ed for solving the problem of optimal p erformance of linear systems with

b oundary conditions, in the presence of phase, integral constraints and holonomic connections. A
General theory of b oundary value problems of optimal p erformance has b een develop ed that has
numerous applications in the natural Sciences, technology, and Economics.
The principal difference b etween the prop osed metho d and the known metho ds is that the initial
problem is immersed in the manageability problem with controls from functional spaces, and then
reduced to the initial optimal control problem.