ISSN:
1573-2878
Keywords:
Parabolic differential equations
;
second boundary-value problems
;
time-delayed arguments
;
distributed optimal control problems
;
necessary and sufficient conditions
;
existence theory
;
algorithms
;
convergence of algorithms
;
Galerkin's scheme
;
lumped-parameter systems
Source:
Springer Online Journal Archives 1860-2000
Topics:
Mathematics
Notes:
Abstract In this paper, we consider a class of optimal control problems involving a second-order, linear parabolic partial differential equation with Neumann boundary conditions. The time-delayed arguments are assumed to appear in the boundary conditions. A necessary and sufficient condition for optimality is derived, and an iterative method for solving this optimal control problem is proposed. The convergence property of this iterative method is also investigated. On the basis of a finite-element Galerkin's scheme, we convert the original distributed optimal control problem into a sequence of approximate problems involving only lumped-parameter systems. A computational algorithm is then developed for each of these approximate problems. For illustration, a one-dimensional example is solved.
Type of Medium:
Electronic Resource
URL:
http://dx.doi.org/10.1007/BF00938951
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