Abstract
We study an approximation of the boundary control problem for the heat equation over a finite horizon. Our goal is to obtain an approximation of the value function and of the corresponding “locally optimal” trajectories. We examine here a time discretization also proving some a priori estimates of convergence for the value function of the time-discrete problem. Some hints are also given for the construction of a fully discrete scheme.
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Briani, A., Falcone, M. (1998). A Priori Estimates for the Approximation of a Parabolic Boundary Control Problem. In: Desch, W., Kappel, F., Kunisch, K. (eds) Control and Estimation of Distributed Parameter Systems. International Series of Numerical Mathematics, vol 126. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8849-3_4
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DOI: https://doi.org/10.1007/978-3-0348-8849-3_4
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