2014/01/24 by Abdul Basit Memon, Memon, Abdul Basit, Erik I. Verriest +1
Computer Science · Engineering · #Distributed Control Multi-Agent Systems #FOS: Electrical engineering #FOS: Mathematics #Optimization and Control (math.OC) #Robotic Locomotion and Control #Systems and Control (eess.SY) #electronic engineering #information engineering
paper · pdf · doi:10.48550/arxiv.1401.6220
openalex publication_date 2014/01/24 · openalex created_date 2025/10/10 · openalex updated_date 2026/08/01
This paper considers the optimal control problem of connecting two periodic trajectories with maximal persistence. A maximally persistent trajectory is close to the periodic type in the sense that the norm of the image of this trajectory under the operator defining the periodic type is minimal among all trajectories. A solution is obtained in this paper for the case when the two trajectories have the same period but it turns out to be only piecewise continuous and so an alternate norm is employed to obtain a continuous connection. The case when the two trajectories have different but rational periods is also solved. The problem of connecting periodic trajectories is of interest because of the observation that the operating points of many biological and artificial systems are limit cycles and so there is a need for a unified optimal framework of connections between different operating points. This paper is a first step towards that goal.