Aitziber Ibáñez is a PhD student at Universidad Autónoma de Madrid (UAM). She finished her Bachelor’s degree in Mathematics at the University of the Basque Country (UPV/EHU) in June 2009. She studied Master’s degree in Computational Engineering and Intelligent Systems, also in (UPV/EHU). Currently, she is working on her PhD in the area of Control Theory, under the joint supervision of Professor Enrique Zuazua.

“My current research interests are related to the turnpike property in control problems and the study of driving problems in collective motion models.”

Education

• Internship (Jun 2014 – Aug 2014), BCAM – Basque Center for Applied Mathematics, Bilbao, Spain.
• Master degree in Computational Engineering and Intelligent Systems (2013-2014), University of the Basque Country (UPV/EHU), Spain.
• Bachelor’s Degree in Mathematics (2008-2013), University of the Basque Country (UPV/EHU), Spain.

PhD Thesis

Optimal control and turnpike properties of the Lotka–Volterra model

Advisor: Prof. Enrique Zuazua – Universidad Autónoma de Madrid and DeustoTech – University of Deusto – Bilbao, Spain
Description:
My thesis has two main research lines: the turnpike property in control problems and the study of driving problems in collective motion models.
Regarding the first topic, the turnpike property has been applied to the Lotka-Volterra model, studying the problem both analytically and numerically. In particular, a variant of the classic single shooting method was implemented, using the turnpike property of the problem. Results show the efficiency of the combined use of the classical method with the turnpike property [1].

With respect to the second line mentioned before, in the recent work [2], we propose to solve the guidance problem from a novel viewpoint, based on the use of repulsive forces, in what we have called a ”move away from me” strategy.

A “guidance by repulsion” model is presented, describing the behaviour of two agents, a driver and an evader. The guide follows the guided but cannot be arbitrarily close to it, while the evader tries to move away from the driver beyond a short distance. The key point of the guidance maneuver is that the driver can display a circumvention motion around the evader, in such a way that the trajectory of the evader is modified due to the repulsion that the driver exerts on the evader. With this model, we show that the evader can be guided to any target on the plane or to follow a sufficiently smooth path by adjusting a single parameter which controls the driver’s behaviour, activating or deactivating the circumvention mode and selecting the clockwise/counterclockwise direction of the circumvention motion. We propose different open loop strategies to drive the evader from any given point to another assuming that both switching the control and keeping the circumvention mode active have a cost. Finally, we develop a feedback law which prevents the excessive use of the circumvention mode and gives rise to a significant reduction of the cost.