On finite-time consensus objectives in time-varying interconnected discrete linear dynamic systems under internal and external delays

Manuel De La Sen,Santiago Alonso-Quesada

doi:10.1177/1687814018784840

Abstract

This article formulates the properties of achievable consensus of linear interconnected discrete systems with multiple internal and external point delays. The formulation is stated in an algebraic generic context as the ability of achievement of (a non-necessarily zero) finite-time common error between the various subsystems. The consensus signals are generically defined so that they can be, in general, distinct of the output or state components. However, the consensus signals of all the interconnected subsystems have the same dimension for coherency reasons. A particular attention is paid to the case of weak interconnection couplings in both the open-loop case and the closed-loop one under, in general, linear output feedback. Some further extensions are given related to consensus over intervals and related to consensus of positive interconnected systems.

Highlights

The so-called ‘‘consensus objective’’ between a set of agents integrated in networked multi-agent systems is of usefulness in relevant problems like formation flight of unmanned air vehicles, clusters of satellites, selforganization, auto-matched highway systems, congestion control in communication networks, and others.[1]
To fix some ideas for consensus objectives in the Control Theory context, we identify the following: (1) the states of the interconnected subsystems of the whole dynamic system as the agents of a multiagent network disposal; (2) the synthesized control law leading to reach zero values of the errors between the consensus signals as the consensus protocol
The control sequences leading to the achievement of the consensus objectives are characterized explicitly via a so-called consensus Gramian which is defined to characterize the consensus achievement

Summary

Introduction

The so-called ‘‘consensus objective’’ between a set of agents integrated in networked multi-agent systems is of usefulness in relevant problems like formation flight of unmanned air vehicles, clusters of satellites, selforganization, auto-matched highway systems, congestion control in communication networks, and others.[1]. The consensus objective is stated for discrete systems as follows in the most general case: (1) a finitetime deterministic objective in a discrete time-varying linear control system; (2) the error between the various relevant candidate signals for consensus is neither necessarily zero nor identical to any non-zero prefixed value for each pair of compared signals; (3) the various signal candidates for the consensus achievement are not necessarily state or output components of the various subsystems in the interconnected structure; (4) the discrete system can be subject to internal and external commensurate delays; and (5) the problem treatment is based on algebraic tools.

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Conclusion