| Issue |
ESAIM: COCV
Volume 25, 2019
|
|
|---|---|---|
| Article Number | 1 | |
| Number of page(s) | 35 | |
| DOI | https://doi.org/10.1051/cocv/2017079 | |
| Published online | 14 March 2019 | |
Strong stability of linear parabolic time-optimal control problems★
1
Fakultät für Mathematik, Technische Universität München, Germany.
2
Department of Scientific Computing, Florida State University,
Tallahassee,
FL
32304, USA.
** Corresponding author: lucas.bonifacius@ma.tum.de
Received:
23
December
2016
Accepted:
11
December
2017
Sufficient conditions for strong stability of a class of linear time-optimal control problems with general convex terminal set are derived. Strong stability in turn guarantees qualified optimality conditions. The theory is based on a characterization of weak invariance of the target set under the controlled equation. An appropriate strengthening of the resulting Hamiltonian condition ensures strong stability and yields a priori bounds on the size of multipliers, independent of, e.g., the initial point or the running cost. In particular, the results are applied to the control of the heat equation into an L2-ball around a desired state.
Mathematics Subject Classification: 49K20 / 49K40 / 58J70
Key words: Time-optimal control / weak invariance / strong stability / optimality conditions / perturbation analysis
The authors gratefully acknowledge support from the International Research Training Group IGDK, funded by the German Science Foundation (DFG) and the Austrian Science Fund (FWF). The second author also acknowledges funding by the US Department of Energy Office of Science grant DE-SC0016591 and by the US Air Force Office of Scientific Research grant FA9550-15-1-0001.
© EDP Sciences, SMAI 2019
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