Matrix integro-differential Riccati equation for parabolic system

The problem of minimization of quadratic functional on solutions of a system of linear parabolic equations is under consideration. Controls enter simultaneously both right-hand parts of the equations and boundary conditions. For investigation of the stated optimization problem the method of Lagrange multipliers is used. Such approach makes it possible to obtain necessary conditions of optimality. Under these conditions the matrix integro-differential Riccati equation with partial derivatives was derived. © 2014 by Begell House Inc.