Asymptotic analysis of an optimal control problem connected to the human locomotion

The article is devoted to the analysis of two optimal control problems. We first consider a model proposed by Arechavaleta et al. (see) describing the goal-oriented locomotion, for which the control on the derivative of the curvature ¿¿ along the trajectory is supposed bounded. Necessary conditions on optimal trajectories are given. We then investigate an extension of this model obtained by removing the boundedness assumption on ¿¿. In this framework several properties of the optimal trajectories are detected and in particular we determine an asymptotic behavior of the initial value of the associated covector with respect to the final point.