Pointwise observation of the state given by parabolic system with boundary condition involving multiple time delays

• Main Author: Kowalewski Adam
• Format: Article
• Language: English
• Published: Polish Academy of Sciences 2016-06-01
• Series: Archives of Control Sciences
• Subjects: distributed control; parabolic system; time delays; pointwise observation
• Online Access: http://www.degruyter.com/view/j/acsc.2016.26.issue-2/acsc-2016-0011/acsc-2016-0011.xml?format=INT

Various optimization problems for linear parabolic systems with multiple constant time delays are considered. In this paper, we consider an optimal distributed control problem for a linear parabolic system in which multiple constant time delays appear in the Neumann boundary condition. Sufficient conditions for the existence of a unique solution of the parabolic equation with the Neumann boundary condition involving multiple time delays are proved. The time horizon T is fixed. Making use of the Lions scheme [13], necessary and sufficient conditions of optimality for the Neumann problem with the quadratic cost function with pointwise observation of the state and constrained control are derived.