Synchronization in a population of oscillators

Nowadays a lot of interest in Systems Theory is directed to problems in which separate systems are coupled to each other. We study the dynamics of a population of uniformly all-to-all coupled limit cycle oscillators. The oscillators are permitted to possess different natural frequencies. Our greatest interest goes out to the synchronization of such populations consisting of finitely many oscillators. This synchronized behaviour is only present if the strength of the interactions supersedes some threshold value. We try to obtain some stability properties of this behaviour

Vehicle platoons through ring coupling

In this paper, a novel strategy for the control of a string of vehicles is designed. The vehicles are coupled in a unidirectional ring at the interaction level: each vehicle is influenced by the position of its immediate forward neighbor; the first vehicle in the platoon is influenced by the position of the last vehicle. Through these interactions a cooperative behavior emerges and a platoon of vehicles moving at a constant velocity with constant inter-vehicle spacings is formed. This contrasts with more traditional control schemes where an independent leader vehicle is followed by the remaining vehicles. For this control structure, stability properties are established. The concept of string stability of a platoon is discussed and applied to the ring interconnection. Design rules are presented, showing how an appropriate choice of parameter values leads to a constant spacing or constant time headway policy. Furthermore, the scheme has a characteristic property: it maintains the platoon structure when subject to malfunctioning vehicles

Vehicle platoons with ring coupling

We design a control strategy for platoons of identical vehicles. It is assumed that each vehicle measures the distance with its immediate forward neighbor. The lead vehicle in the platoon only receives information on the position of the last vehicle in the platoon. The resulting behavior of the system is a platoon of vehicles moving at a constant velocity with constant distance between pairs of consecutive vehicles. For a class of identical controllers this solution is asymptotically stable for sufficiently small coupling strength. The concept of string stability of a platoon is discussed and applied to the proposed interconnection. Simulations show the system is well-behaved with respect to string stability. To improve the behavior, integral action is added between the first and last vehicle of the platoon. The resulting behavior is determined and its stability properties are discussed

Consensus over ring networks as a quadratic optimal control problem

This paper presents the consensus problem in the framework of optimal control. Our aim is to synchronize a set of identical linear systems. We propose a cost which penalizes mutual differences between the states of these systems. The feedback matrix resulting from this linear quadratic control problem represents the interconnection network which synchronizes the systems. In general the interconnection structure is of the all-to-all type. We show that it is possible to devise an LQR problem in which the cost results in an interconnection structure representing ring coupling. Care has to be taken that the effect of the feedback control is restricted to synchronizing the systems, i.e. when the systems are synchronized, the feedback control signal is required to be equal to zero

A novel strategy for exploration with multiple robots

The present paper develops a novel strategy for the exploration of an unknown environment with a multi-robot system. Contrary to most exploration problems, the topographical properties of the space need not be mapped. The algorithm we propose is inspired by methods used for complete coverage of an area, where all free space has to be physically covered by all robots. In the present paper it is required that the entire free space is covered by the sensors of the robots, with a certainty of 100%. This weaker requirement enables us to scan more space in less time, compared to complete coverage algorithms. Moreover the shape of the robot formation adjusts itself to situations where obstacles, narrow spaces, etc. have to be passed. Communication between the robots is restricted to line-of-sight and to a maximum interdistance between robots. A direct application of the algorithm is mine field clearance

Stability of phase locking in a ring of unidirectionally coupled oscillators

In this paper we discuss the behavior of a finite group of phase oscillators unidirectionally coupled in a ring. The dynamics is described by the Kuramoto model. In the case of identical oscillators, all phase locking solutions are obtained explicitly, together with their stability properties. For nonidentical oscillators it is proven that there exist phase locking solutions for sufficiently strong coupling. An algorithm for obtaining all phase locking solutions is given. These solutions can be subdivided into classes, the stability properties of each of which are established separately. The stability results are extended to interconnections belonging to a class of odd functions. Finally, a connection with the field of active antenna arrays is made, generalizing some results earlier obtained in this field