Convergence of a strong variational algorithm for relaxed controls involving a distributed optimal control problem of parabolic type 1

In this paper, we consider a class of Optimal Control problems involving first boundary value problems of parabolic type. A strong variational algorithm has been obtained for solving this class of optimal control problems in a paper by the author and D. W. Reid. It was also shown that any L∞ accumulation points of control sequences generated by the algorithm satisfy a necessary condition for optimality. Since such accumulation points need not exist, it is shown in this paper that control sequences generated by the algorithm always have accumulation points in the sense of control measure, and these accumulation points satisfy a necessary condition for optimality for the corresponding relaxed control problem.     

A control parametrization algorithm for optimal control problems involving linear systems and linear 1

Computational schemes based on control parametrization techniques are known to be very efficient for solving optimal control problems. However, the convergence result is only available for the case in which the dynamic system is linear and without the terminal equality and inequality constraints. This paper is to improve this convergence result by allowing the presence of the linear terminal inequality. For illustration, an example arising in the study of optimally one-sided heating of a metal slab in a furnace is considered.     

On the boundary value problem in a dihedral angle for normally hyperbolic systems of first order

Some structural properties as well as a general three-dimensional boundary value problem for normally hyperbolic systems of partial differential equations of first order are studied. A condition is given which enables one to reduce the system under consideration to a first-order system with the spliced principal part. It is shown that the initial problem is correct in a certain class of functions if some conditions are fulfilled.     

Distributed control for cooperative systems involving parabolic operators with an infinite number of variables

^** Email: serraghm{at}yahoo.com The optimal control for cooperative systems involving parabolicoperators with an infinite number of variables is considered.First the existence and uniqueness of the states are proved;then the necessary and sufficient condition for the controlto be optimal is obtained by a set of inequalities. The controlin our problems is of distributed type and is allowed to bein the Hilbert space (L²(0, T, L²()))ⁿ.