Nonlinear Consensus Protocols With Applications to Quantized Communication and Actuation

Wei, Jieqiang; Yi, Xinlei; Johansson, Karl Henrik

doi:10.1109/tcns.2018.2860461

Cited by 24 publications

(18 citation statements)

References 29 publications

(27 reference statements)

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“…Thus the 2-norm distance of Krasovskii solutions from consensus is, asymptotically, at most N/2. The assumptions that L be symmetric and the interaction graph be undirected can be lifted: recently, [50] has proved the same convergence property for more general functions q and weaker connectivity. Namely, q only needs to be nondecreasing and the graph can be directed and only needs to have a globally reachable node 4 .…”

Section: Quantized States Dynamicsmentioning

confidence: 95%

Discontinuities, Generalized Solutions, and (Dis)agreement in Opinion Dynamics

Ceragioli¹,

Frasca²

2018

Control Subject to Computational and Communication Constraints

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Section: Quantized States Dynamicsmentioning

confidence: 95%

Discontinuities, Generalized Solutions, and (Dis)agreement in Opinion Dynamics

Ceragioli¹,

Frasca²

2018

Control Subject to Computational and Communication Constraints

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“…Instead, papers like [12,22,20,25,29] have considered other possible quantizations of (1): in [12,22] all states are quantized in the right-hand side, while in [20,25] distances between couples of states are seen through the quantizer. In these papers convergence to consensus is proved under appropriate but generally mild assumptions [38].…”

mentioning

confidence: 99%

Consensus and Disagreement: The Role of Quantized Behaviors in Opinion Dynamics

Ceragioli¹,

Frasca²

2018

SIAM J. Control Optim.

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Abstract. This paper deals with continuous-time opinion dynamics that feature the interplay of continuous opinions and discrete behaviours. In our model, the opinion of one individual is only influenced by the behaviours of fellow individuals. The key technical difficulty in the study of these dynamics is that the right-hand sides of the equations are discontinuous and thus their solutions must be intended in some generalized sense: in our analysis, we consider both Carathéodory and Krasovskii solutions. We first prove existence and completeness of Carathéodory solutions from every initial condition and we highlight a pathological behavior of Carathéodory solutions, which can converge to points that are not (Carathéodory) equilibria. Notably, such points can be arbitrarily far from consensus and indeed simulations show that convergence to non-consensus configurations is common. In order to cope with these pathological attractors, we study Krasovskii solutions. We give an estimate of the asymptotic distance of all Krasovskii solutions from consensus and we prove its tightness by an example of equilibrium such that this distance is quadratic in the number of agents. This fact implies that quantization can drastically destroy consensus. However, consensus is guaranteed in some special cases, for instance when the communication among the individuals is described by either a complete or a complete bipartite graph.

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“…This proves the positions of the agents are not interchangeable. Second, noticing that B is the (in-degree) Laplacian of the directed ring graph which is strongly connected, then by Theorem 6 in [19], β converges to consensus 2π n 1.…”

Section: Resultsmentioning

confidence: 99%

Cooperative decentralised circumnavigation with application to algal bloom tracking

Fonseca

Wei

Johansson

et al. 2019

2019 IEEE/RSJ International Conference on Intelligent Robots and Systems (IROS)

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Harmful algal blooms occur frequently and deteriorate water quality. A reliable method is proposed in this paper to track algal blooms using a set of autonomous surface robots. A satellite image indicates the existence and initial location of the algal bloom for the deployment of the robot system. The algal bloom area is approximated by a circle with time varying location and size. This circle is estimated and circumnavigated by the robots which are able to locally sense its boundary. A multi-agent control algorithm is proposed for the continuous monitoring of the dynamic evolution of the algal bloom. Such algorithm comprises of a decentralised least squares estimation of the target and a controller for circumnavigation. We prove the convergence of the robots to the circle and in equally spaced positions around it. Simulation results with data provided by the SINMOD ocean model are used to illustrate the theoretical results.

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Nonlinear Consensus Protocols With Applications to Quantized Communication and Actuation

Cited by 24 publications

References 29 publications

Discontinuities, Generalized Solutions, and (Dis)agreement in Opinion Dynamics

Discontinuities, Generalized Solutions, and (Dis)agreement in Opinion Dynamics

Consensus and Disagreement: The Role of Quantized Behaviors in Opinion Dynamics

Cooperative decentralised circumnavigation with application to algal bloom tracking

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