Abstract
We consider a general optimal control problem for a distributed parameter described by a semilinear parabolic equation. We show that the Hamiltonian is invariant over optimally controlled trajectories, and that it vanishes when the terminal time is free. The method is that of approximation of the original control system by a sequence of “smoothed” control systems
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Fattorini, H.O. (1994). Invariance of the Hamiltonian in Control Problems for Semilinear Parabolic Distributed Parameter Systems. In: Desch, W., Kappel, F., Kunisch, K. (eds) Control and Estimation of Distributed Parameter Systems: Nonlinear Phenomena. ISNM International Series of Numerical Mathematics, vol 118. Birkhäuser, Basel. https://doi.org/10.1007/978-3-0348-8530-0_7
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DOI: https://doi.org/10.1007/978-3-0348-8530-0_7
Publisher Name: Birkhäuser, Basel
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Online ISBN: 978-3-0348-8530-0
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