Some aspects of reachability for parabolic boundary control problems with control constraints
- 114 Downloads
A class of one-dimensional parabolic optimal boundary control problems is considered. The discussion includes Neumann, Robin, and Dirichlet boundary conditions. The reachability of a given target state in final time is discussed under box constraints on the control. As a mathematical tool, related exponential moment problems are investigated. Moreover, based on a detailed study of the adjoint state, a technique is presented to find the location and the number of the switching points of optimal bang-bang controls. Numerical examples illustrate this procedure.
Unable to display preview. Download preview PDF.
- 5.Fattorini, H.O.: The time–optimal control problem for boundary control of the heat equation. In: Russell, D. (ed.) Calculus of Variations and Control Theory, pp. 305–320. Academic Press, New York (1976) Google Scholar
- 10.Gruver, W.A., Sachs, E.W.: Algorithmic Methods in Optimal Control. Pitman, London (1980) Google Scholar
- 16.Morozov, V.A.: Methods for Solving Incorrectly Posed Problems. Springer, New York (1984) Google Scholar
- 17.Russell, D.L.: A unified boundary controllability theory for hyperbolic and parabolic partial differential equations. Stud. Appl. Math. LII, 189–211 (1973) Google Scholar
- 19.Schäfer, U.: A fixed point theorem based on Miranda. Fixed Point Theory Appl. Article ID 78706, 6 p. (2007) Google Scholar