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.
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Communicated by G. Leitmann
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Wong, K.H. Optimal control computation for parabolic systems with boundary conditions involving time delays. J Optim Theory Appl 53, 475–507 (1987). https://doi.org/10.1007/BF00938951
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DOI: https://doi.org/10.1007/BF00938951