Existence, properties and trajectory specification of generalised multi-agent flocking

ABSTRACT

A class of flocking algorithms for second-order multi-agent networks with single virtual leaders are developed by including more weighting and navigating matrices in this paper. Flocking existence and properties under the generalised algorithms are investigated around control action boundedness, average trajectory, stability, controllability/observability and ultimate collision. Control significance and design principles of the algorithm matrices are summarised by means of Gronwall-type upper/lower bound inequalities. It is shown that multi-agent systems can form what we call the modified lattices such that flocking features in terms of convergence ratio, orientation, deformation, lattice scaling and subspace assignment can be manipulated with the algorithm matrices. Overall/local ultimate collisions due to dense initial aggregation and inadequate inter-agent distance evaluation are scrutinised. Moreover, by modelling the leader-average dynamics, the average transient/steady-state features of the multi-agent networks are expressed analytically and can be specified through the linear time-invariant (LTI) theory, say pole assignment, least quadratic regulation (LQR) and observer design. Numerical examples are included to verify the main results.

KEYWORDS:

• Multi-agent
• flocking
• stability
• controllability
• observability
• trajectory
• upper/lower bound
• ultimate collision

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. Let r(t) be a solution to (38(38) $$\begin{array}{c}\hfill \dot{u}\left(t\right)=g(t,u\left(t\right)),u\left(0\right)=m\left(0\right)\end{array}$$(38) ) on some time interval J. r(t) is the maximal (resp., minimal) solution to (38(38) $$\begin{array}{c}\hfill \dot{u}\left(t\right)=g(t,u\left(t\right)),u\left(0\right)=m\left(0\right)\end{array}$$(38) ) if u(t) ≤ r(t) (resp., u(t) ≥ r(t)) on J for every solution u(t) to (38(38) $$\begin{array}{c}\hfill \dot{u}\left(t\right)=g(t,u\left(t\right)),u\left(0\right)=m\left(0\right)\end{array}$$(38) ).

Additional information

Funding

This work was supported by the National Nature Science Foundation of China [grant number 61573001].