TY - JOUR
T1 - A Gradient Flow Equation for Optimal Control Problems With End-point Cost
Y1 - 2022
A1 - Alessandro Scagliotti
AB - 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.
SN - 1573-8698
UR - https://doi.org/10.1007/s10883-022-09604-2
JO - Journal of Dynamical and Control Systems
ER -