@article {2022,
	title = {A Gradient Flow Equation for Optimal Control Problems With End-point Cost},
	year = {2022},
	month = {2022/07/07},
	abstract = {In this paper, we consider a control system of the form $\dot x = F(x)u$, linear in the control variable u. Given a fixed starting point, we study a finite-horizon optimal control problem, where we want to minimize a weighted sum of an end-point cost and the squared 2-norm of the control. This functional induces a gradient flow on the Hilbert space of admissible controls, and we prove a convergence result by means of the Lojasiewicz-Simon inequality. Finally, we show that, if we let the weight of the end-point cost tend to infinity, the resulting family of functionals is Γ-convergent, and it turns out that the limiting problem consists in joining the starting point and a minimizer of the end-point cost with a horizontal length-minimizer path.},
	isbn = {1573-8698},
	url = {https://doi.org/10.1007/s10883-022-09604-2},
	author = {Alessandro Scagliotti}
}
