An Emerging Dynamics Approach for Synchronization of Linear Heterogeneous Agents Interconnected Over Switching Topologies

Adhikari, Bikash; Morărescu, Irinel-Constantin; Panteley, Elena

doi:10.1109/lcsys.2020.2999406

Cited by 11 publications

(4 citation statements)

References 17 publications

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“…This two-time scale modeling approach provides insights into the emergent behavior of the network. Similarly, in [12], singularperturbation techniques are applied to study interconnected A. Lazri is with L2S, CNRS, Univ Paris-Saclay, France (e-mail: anes.lazri@centralesupelec.fr) E. Panteley and A. Loría are with L2S, CNRS, (e-mail: {elena.panteley,antonio.loria}@cnrs.fr).…”

Section: Introductionmentioning

confidence: 99%

Analysis and Control of Multi-timescale Modular Directed Heterogeneous Networks

Lazri,

Panteley,

Loría

2024

IEEE Trans. Control Netw. Syst.

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We examine the collective behavior of largescale networks of heterogeneous nonlinear systems with directed weighted interconnections, and containing a spanning tree. We consider networks that are composed of groups of densely interconnected nodes, called modules, that are in turn sparsely interconnected. Such networks are called modular. The modules represent sub-networks wherein consensus may be rapidly achieved, while synchronization among modules occurs at a lower pace. Furthermore, relying on the framework of [1], we identify an underlying dynamics that corresponds to a weighted average of the nodes' respective states. This average dynamics evolves on a yet slower time-scale. Such triple time-scale make modular networks are amenable to be analyzed via singular-perturbations theory. We show that if the nodes' dynamics are semi-passive and the average dynamics is globally asymptotically stable, so is the entire network. In the case that the average dynamics is not globally asymptotically stable we show how our main analysis statement can be used for network control, via the addition of control nodes, in order to globally asymptotically stabilize the network.

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Section: Introductionmentioning

confidence: 99%

Analysis and Control of Multi-timescale Modular Directed Heterogeneous Networks

Lazri,

Panteley,

Loría

2024

IEEE Trans. Control Netw. Syst.

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“…Finally, the relevant conditions in the form of linear matrix inequalities are deduced, proving the stability of the system; however, many issues are still open for future research, such as considering uncertainties in the parameters of agents and the quantization effects. Adhikari et al [11] proposed a dynamical model-based tool to approximate synchronous behavior in large networks of interconnected linear systems with exchange topology and linear coupling. Zhang et al [12] designed a local fault estimation observer for the output estimation error of each agent for the distributed fault estimation problem of multi-agent systems with switched topologies.…”

Section: Introductionmentioning

confidence: 99%

AUV Formation Coordination Control Based on Transformed Topology under Time-Varying Delay and Communication Interruption

Zhang

Chen

et al. 2022

JMSE

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Aiming at the control problem of autonomous underwater vehicle (AUV) pilot-following formation with communication delay and communication interruption, a controller based on feedback linearization and the PD control method is designed in this paper. Firstly, the nonlinear, strongly coupled vehicle model is transformed into a second-order model via the feedback linearization method, and then the formation coordination controller is designed based on consistency theory and the PD control method. The Markov random jump process is used to simulate the formation topology in the event of communication interruption. The condition of stable convergence of the AUV pilot-following formation is analyzed in the presence of time-varying delay and Markov transformation topology. A Lyapunov–Krasovskii equation is established, and linear matrix inequality (LMI) is used to solve the problem of communication interruption and communication delay. The boundary conditions of error convergence of the control system are obtained. Finally, the effectiveness of the formation coordination controller based on the second-order integral model under the unstable conditions of underwater acoustic communication is verified by simulation.

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“…This is specifically the case for networks of linear systems, in which case complexity hardly appears and the focus turns towards relaxing the various conditions pertaining to the nature of the interconnections. These may be linear [4]; nonlinear [6,7]; time-varying [8,9]; switching [10,11] or even state dependent [12,13]. Other topology aspects, such as whether the graph is directed [14] or the interconnections are signed [15], may also alter consensus.…”

Section: Introductionmentioning

confidence: 99%

Singular-Perturbations-Based Analysis of Dynamic Consensus in Directed Networks of Heterogeneous Nonlinear Systems

Maghenem¹,

Panteley²,

Lorı́a³

2022

Preprint

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We analyze networked heterogeneous nonlinear systems, with diffusive coupling and interconnected over a generic static directed graph. Due to the network's hetereogeneity, complete synchronization is impossible, in general, but an emergent dynamics arises. This may be characterized by two dynamical systems evolving in two time-scales. The first, "slow", corresponds to the dynamics of the network on the synchronization manifold. The second, "fast", corresponds to that of the synchronization errors. We present a framework to analyse the emergent dynamics based on the behavior of the slow dynamics. Firstly, we give conditions under which if the slow dynamics admits a globally asymptotically stable equilibrium, so does the networked systems. Secondly, we give conditions under which, if the slow dynamics admits an asymptotically stable orbit and a single unstable equilibrium point, there exists a unique periodic orbit that is almost-globally asymptotically stable. The emergent behavior is thus clear, the systems asymptotically synchronize in frequency and, in the limit, as the coupling strength grows, the emergent dynamics approaches that of the slow system. Our analysis is established using singularperturbations theory. In that regard, we contribute with original statements on stability of disconnected invariant sets and limit cycles.

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An Emerging Dynamics Approach for Synchronization of Linear Heterogeneous Agents Interconnected Over Switching Topologies

Cited by 11 publications

References 17 publications

Analysis and Control of Multi-timescale Modular Directed Heterogeneous Networks

Analysis and Control of Multi-timescale Modular Directed Heterogeneous Networks

AUV Formation Coordination Control Based on Transformed Topology under Time-Varying Delay and Communication Interruption

Singular-Perturbations-Based Analysis of Dynamic Consensus in Directed Networks of Heterogeneous Nonlinear Systems

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