Mathematical Problems in Engineering 
Volume 3 (1998), Issue 5, Pages 387-411
doi:10.1155/S1024123X97000616

Optimal boundary control of distributed systems involving dynamic boundary conditions

S. Kerbal1 and N. U. Ahmed2

 1Department of Mathematics and Statistics, University of Ottawa, 161 Louis Pasteur St., P.O. Box 450, Stn. A, Ottawa K1N 6N5, Ontario, Canada
2Department of Mathematics and Department of Electrical and Computer Engineering, University of Ottawa, 161 Louis Pasteur St., P.O. Box 450, Stn. A, Ottawa K1N 6N5, Ontario, Canada
Received 29 April 1997

Abstract

In this paper we consider Lagrange type control problem for systems involving dynamic boundary conditions that is, with boundary operators containing time derivatives. Assuming the existence of optimal controls, B-evolutions theory is used to present necessary conditions of optimality. The result is illustrated by an example from heat transfer problem and also an algorithm for computing optimal controls is presented.