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Existence of minimizers for optical flow based optimal control problems under mild regularity assumptions. (English) Zbl 1451.49041

Summary: Optimal control problems governed by a transport equation are investigated that are motivated by optical flow problems. The control is given by the velocity field, corresponding to the optical flow, while the state corresponds to the brightness of image points. The problem is studied in the setting of spatially BV-regular vector fields under very low regularity requirements. Existing stability results for the control-to-state operator are improved and based on this the existence of minimizers for several classes of optimal control problems is proved under mild assumptions on the admissible sets.

MSC:

49Q22 Optimal transportation
49N60 Regularity of solutions in optimal control
78M30 Variational methods applied to problems in optics and electromagnetic theory
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