Abstract
We consider a finite horizon optimal control problem in Mayer form for a system governed by a semilinear state equation. We prove that, under suitable assumptions, the associated value function is differentiable along optimal trajectories. For this purpose we prove a backward uniqueness result for a class of abstract evolution equation of parabolic type.
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Cannarsa, P., Gozzi, F. (1992). On the smoothness of the value function along optimal trajectories. In: Zoléesio, J.P. (eds) Boundary Control and Boundary Variation. Lecture Notes in Control and Information Sciences, vol 178. Springer, Berlin, Heidelberg. https://doi.org/10.1007/BFb0006688
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DOI: https://doi.org/10.1007/BFb0006688
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