Strong stability of linear parabolic time-optimal control problems
ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 1.

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.

Reçu le :
Accepté le :
DOI : 10.1051/cocv/2017079
Classification : 49K20, 49K40, 58J70
Mots-clés : Time-optimal control, weak invariance, strong stability, optimality conditions, perturbation analysis
Bonifacius, Lucas 1 ; Pieper, Konstantin 1

1 
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Bonifacius, Lucas; Pieper, Konstantin. Strong stability of linear parabolic time-optimal control problems. ESAIM: Control, Optimisation and Calculus of Variations, Tome 25 (2019), article no. 1. doi : 10.1051/cocv/2017079. http://www.numdam.org/articles/10.1051/cocv/2017079/

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