Abstract
Various optimization problems associated with the optimal control of distributed-parameter systems with time delays appearing in the boundary conditions have been studied recently in Refs. [1]÷[7] and [11], [12]. In this paper, we consider an optimal boundary control problem for a linear parabolic system in which constant time delays appear in the equation and in the boundary condition simultaneously. Sufficient conditions for the existence of a unique solution of the parabolic delay equation with the Neumann boundary condition involving a time delay are proved. The performance functional has the quadratic form. The time horizon T is fixed. Finally, we impose some constraints on the control. Making use of the Lions scheme
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Kowalewski, A. (1990). Optimality conditions for a parabolic time delay system. In: Bensoussan, A., Lions, J.L. (eds) Analysis and Optimization of Systes. Lecture Notes in Control and Information Sciences, vol 144. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0120040
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DOI: https://doi.org/10.1007/BFb0120040
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