We consider an optimal boundary control problem for a linear parabolic system in which time delays appear in the integral form with k ∈ (0,c) in the state equation and with h ∈ (0,b) in the Neumann boundary condition.
Sufficient conditions for the existence of a unique solution for such parabolic system are presented. The performance functionals have quadratic form. The time horizon T is fixed. Finally, we impose some constraints on the boundary control. Making use of Lion's framework necessary and sufficient conditions of optimality are derived for a linear quadratic problem.
A simple example of application is also provided.
Current 2019 2018 2017 2016 2015 2014 2013 2012 2011 2010 2009 2008 2007 2006 2005 2004 2003 2002 2001 2000 1999 1998 1997 1996
