Discontinuities and hysteresis in quantized average consensus

Ceragioli, Francesca; Persis, Claudio De; Frasca, Paolo

doi:10.1016/j.automatica.2011.06.020

Cited by 279 publications

(213 citation statements)

References 13 publications

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“…The poor perfomance of the dynamics in terms of approaching consensus explains the scarcity 1 of known results about (2). 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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confidence: 99%

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

Ceragioli¹,

Frasca²

2018

SIAM J. Control Optim.

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“…By introducing the HamiltonianH(i, ρ, ∆(Ṽ ), ∂ ρṼ , t) given in (12), the first equation is proven. To prove (13), observe that the optimal control is the minimizer in the computation of the extended Hamiltonian.…”

Section: Lemma 21mentioning

confidence: 99%

“…There are several physical and natural phenomena in which hysteresis occurs such as in filtration through porous media, phase tran-sition, superconductivity, shape memory and communication delay (see [12,27] for more details).…”

Section: Related Literaturementioning

confidence: 99%

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Game Theoretic Decentralized Feedback Controls in Markov Jump Processes

Bagagiolo

Bauso

Maggistro

et al. 2017

J Optim Theory Appl

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This paper studies a decentralized routing problem over a network, using the paradigm of mean-field games with large number of players. Building on a state space extension technique, we turn the problem into an optimal control one for each single player. The main contribution is an explicit expression of the optimal decentralized control which guarantees the convergence both to local and global equilibrium points. Furthermore, we study the stability of the system also in the presence of a delay which we model using an hysteresis operator. As a result of the hysteresis, we prove existence of multiple equilibrium points and analyze convergence conditions. The stability of the system is illustrated via numerical studies .

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“…The uniform quantizer and logarithmic quantizer [11] are among the most popular choices for designing such controllers with quantized information. Moreover, the paper [12] has discussed Krasowskii solutions and hysteretic quantizers in connection with continuous-time average consensus algorithms under quantized measurements.…”

Section: Introductionmentioning

confidence: 99%

Control of one-dimensional guided formations using coarsely quantized information

Persis

Liu

Cao

2010

49th IEEE Conference on Decision and Control (CDC)

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Abstract-Motivated by applications of platoon formations, the paper studies the problem of guiding mobile agents in a onedimensional formation to their desired relative positions. Only coarsely quantized information is used which is communicated from a guidance system that monitors in real time the agents' motions. The desired relative positions are defined by the given distance constraints between the agents under which the overall formation is rigid in shape and thus admits locally a unique realization. It is firstly shown that even when the guidance system can only transmit at most four bits of information to each agent, it is still possible to design control laws to guide the agents to their desired positions. We further delineate the thin set of initial conditions for which the proposed control law may fail using the example of a three-agent formation. Tools from non-smooth analysis are utilized for the convergence analysis.

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Discontinuities and hysteresis in quantized average consensus

Cited by 279 publications

References 13 publications

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

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

Game Theoretic Decentralized Feedback Controls in Markov Jump Processes

Control of one-dimensional guided formations using coarsely quantized information

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