Robust stability analysis of formation control in local frames under time-varying delays and actuator faults. Issue 2 (January 2019)

• Record Type: Journal Article
• Authors: González, Antonio; Aranda, Miguel; López-Nicolás, Gonzalo; Sagüés, Carlos
• Is Part Of: Journal of the Franklin Institute. Volume 356:Issue 2(2019)
• Page Start: 1131
• Page End: 1153
• Publication Date: 2019-01
• Subjects: Science -- Periodicals; Technology -- Periodicals; Patents -- United States -- Periodicals; 505
• DOI: 10.1016/j.jfranklin.2018.06.020
• Languages: English
• ISSNs: 0016-0032

Abstract

Highlights: The paper addresses the stability analysis on coordinate-free formation control under time delays. The proposed approach extends other recent contributions by considering a more general framework. Time-varying delays, actuator faults and exponential stability with decay rate performance are also considered. Through a given algorithm and LMI, the maximum worst-case point-to-point delay can be obtained. Our method is less restrictive and applicable in a more general framework than previous works. Abstract: This paper investigates the robust stability of a multiagent system moving to a desired rigid formation in presence of unknown time-varying communication delays and actuator faults. Each agent uses relative position measurements to implement the proposed control method, which does not require common coordinate references. However, the presence of time delays in the measurements, which is inherent to the communication links between agents, has a negative impact in the control system performance leading, in some cases, to instability. Furthermore, the robust stability analysis becomes more complex if failures on actuators are taken into account. In addition, delays may be subject to time variations, depending on network load, availability of communication resources, dynamic routing protocols, or other environmental conditions. To cope with these problems, a sufficient condition based on Linear Matrix Inequalities (LMI) is provided to ensure the robust asymptotic convergence of the agents to the desired formation. This condition is valid for any arbitrarily fast time-varying delays and actuator faults, given a worst-case point-to-point delay. Finally, simulation results show the performance of the proposed approach.