Differential inequalities in multi-agent coordination and opinion dynamics modeling

Proskurnikov, Anton V.; Cao, Ming

doi:10.1016/j.automatica.2017.07.065

Cited by 19 publications

(15 citation statements)

References 39 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…Theorem 3 thus requires some tools that are principally different from usual contraction analysis [44], [45]; its proof is actually based on the seminal idea of the solution's ordering originally used to study undelayed typesymmetric algorithms in [28] (a similar yet slightly different technique was employed in [27], [38]). As shown in our previous works [41], [60], averaging inequalities, which are beyond the scope of this paper, have numerous applications in multi-agent control and social dynamics modeling.…”

Section: A Comparison To Alternative Criteriamentioning

confidence: 96%

“…In particular, Theorem 1 is not valid for the inequalities and estimates like (13) cannot be established for them (in fact, consensus in (18) requires strong connectivity of the persistent graph G ∞ [59], [60]). Theorem 3 thus requires some tools that are principally different from usual contraction analysis [44], [45]; its proof is actually based on the seminal idea of the solution's ordering originally used to study undelayed typesymmetric algorithms in [28] (a similar yet slightly different technique was employed in [27], [38]).…”

Section: A Comparison To Alternative Criteriamentioning

confidence: 99%

See 1 more Smart Citation

Delay Robustness of Consensus Algorithms: Beyond The Uniform Connectivity (Extended Version)

Proskurnikov,

Calafiore

2021

Preprint

Self Cite

View full text Add to dashboard Cite

Consensus of autonomous agents is a benchmark problem in multi-agent control. In this paper, we consider continuous-time averaging consensus policies (or Laplacian flows) and their discrete-time counterparts over time-varying graphs in presence of unknown but bounded communication delays. It is known that consensus is established (no matter how large the delays are) if the graph is periodically, or uniformly quasi-strongly connected (UQSC). The UQSC condition is often believed to be the weakest sufficient condition under which consensus can be proved. We show that the UQSC condition can actually be substantially relaxed and replaced by a condition that we call aperiodic quasi-strong connectivity (AQSC), which, in some sense, proves to be very close to the necessary condition of integral connectivity. Furthermore, in some special situations such as undirected or type-symmetric graph, we find a necessary and sufficient condition for consensus in presence of bounded delay; the relevant results have been previously proved only in the undelayed case. The consensus criteria established in this paper generalize a number of results known in the literature.

show abstract

Section: A Comparison To Alternative Criteriamentioning

confidence: 96%

Section: A Comparison To Alternative Criteriamentioning

confidence: 99%

Delay Robustness of Consensus Algorithms: Beyond The Uniform Connectivity (Extended Version)

Proskurnikov,

Calafiore

2021

Preprint

Self Cite

View full text Add to dashboard Cite

show abstract

“…We start with consensus algorithms, based on the principle of iterative averaging (similar dynamics appear in the literature under different names, e.g. local voting [Amelina et al, 2015, Vergados et al, 2018, Laplacian flows [Bullo, 2018, Proskurnikov andCao, 2017a] or rendezvous algorithm [Lin et al, 2007a]).…”

Section: Consensus Via Iterative Averagingmentioning

confidence: 99%

“…For the detailed analysis of Altafini models over static and time-varying graphs the reader is referred to , Meng et al, 2016, Xia et al, 2016, Proskurnikov and Cao, 2017a, Proskurnikov and Cao, 2017b, Liu et al, 2017.…”

Section: Balance and Negativementioning

confidence: 99%

Evolution of clusters in large-scale dynamical networks

Proskurnikov

Granichin

2018

CAP

Self Cite

View full text Add to dashboard Cite

Recent tremendous progress in electronics, complexity theory and network science provides new opportunities for intellectual control of complex large-scale systems operating in turbulent environment via networks of interconnected miniature devices, serving as actuators, sensors and data processors. Actual dynamics of the resulting control systems are too sophisticated to be examined controlled by traditional methods, which primarily deal with ordinary differential equations. However, their complexity can be dramatically reduced by fast processes, organizing the elementary units of the system (called agents) into relatively small number of clusters. The clusters emerge and deteriorate in response to changes in the environment, and the processes of their formation and destruction are very short in time. During the periods of the clusters’ existence, the system’s dynamics is essentially low-dimensional due to synchronization between the agents in each cluster. An enormously complicated system is thus reduced to a finite-dimensional model with time-varying structure of the state vector. The low-dimensionality of the reduced model allows to control it by using classical methods, e.g. model-predictive or adaptive control. This philosophy of complex systems control is illustrated on an experimental setup, called the “airplane with feathers”. The wings of this airplane are equipped with arrays of microsensors, microcomputers, and microactuators (“feathers”). The feathers self-organize into clusters by using a multi-agent consensus protocol; the aim of this coordination is to reduce the perturbing forces, affecting the airplane in a turbulent flow.

show abstract

“…The most recent results from [32] allow non-instantaneous forms of the latter property, for instance, the action of group S on group S c may be responded after some limited amount of time. It is remarkable that some conditions of reciprocity imply consensus not only in the ODE system (1), but also in the system of associated differential inequalities [33]…”

Section: Introductionmentioning

confidence: 99%

New Results on Delay Robustness of Consensus Algorithms

Proskurnikov¹,

Calafiore²

2020

Preprint

Self Cite

View full text Add to dashboard Cite

Consensus of autonomous agents is a benchmark problem in cooperative control. In this paper, we consider standard continuous-time averaging consensus policies (or Laplacian flows) over time-varying graphs and focus on robustness of consensus against communication delays. Such a robustness has been proved under the assumption of uniform quasi-strong connectivity of the graph. It is known, however, that the uniform connectivity is not necessary for consensus. For instance, in the case of undirected graph and undelayed communication consensus requires a much weaker condition of integral connectivity. In this paper, we show that the latter results remain valid in presence of unknown but bounded communication delays, furthermore, the condition of undirected graph can be substantially relaxed and replaced by the conditions of non-instantaneous type-symmetry. Furthermore, consensus can be proved for any feasible solution of the delay differential inequalities associated to the consensus algorithm. Such inequalities naturally arise in problems of containment control, distributed optimization and models of social dynamics.

show abstract

Differential inequalities in multi-agent coordination and opinion dynamics modeling

Cited by 19 publications

References 39 publications

Delay Robustness of Consensus Algorithms: Beyond The Uniform Connectivity (Extended Version)

Delay Robustness of Consensus Algorithms: Beyond The Uniform Connectivity (Extended Version)

Evolution of clusters in large-scale dynamical networks

New Results on Delay Robustness of Consensus Algorithms

Contact Info

Product

Resources

About