Consensus and synchronization of complex networks via proportional-integral coupling

Burbano, Daniel; Bernardo, Mario di

doi:10.1109/iscas.2014.6865505

Cited by 13 publications

(5 citation statements)

References 12 publications

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“…The compact form in (26) reveals the dissipative nature of the closed loop when using the Hamiltonian function (27) where I is the Luré-type integral function in (25). In (27) we used the Bregman distance of U (θ) and I(λ) to θ * and λ * , respectively, to construct an incremental Hamiltonian function as in [11]. Next we show some properties related to this integral function.…”

Section: Local Asymptotic Stabilitymentioning

confidence: 99%

“…As alternatives to decentralized integral control (9) or centralized AGC (11), distributed secondary integral controllers have been proposed that average the integral actions among the generation units through a communication network between the controllers. Different distributed secondary integral approaches have been proposed on the basis of continuous-time consensus averaging with all-to-all [21,22,23,24] or nearestneighbor [25,26,27] communication. These distributed secondary control approaches can be merged with the tertiary optimization layer, based on the economic dispatch criterion (6) that all marginal utilities must be identical.…”

Section: Distributed Secondary Controllersmentioning

confidence: 99%

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Gather-and-broadcast frequency control in power systems

2017

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We propose a novel frequency control approach in between centralized and distributed architectures, that is a continuous-time feedback control version of the dual decomposition optimization method. Specifically, a convex combination of the frequency measurements is centrally aggregated, followed by an integral control and a broadcast signal, which is then optimally allocated at local generation units. We show that our gather-and-broadcast control architecture comprises many previously proposed strategies as special cases. We prove local asymptotic stability of the closed-loop equilibria of the considered power system model, which is a nonlinear differential-algebraic system that includes traditional generators, frequency-responsive devices, as well as passive loads, where the sources are already equipped with primary droop control. Our feedback control is designed such that the closed-loop equilibria of the power system solve the optimal economic dispatch problem.

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Section: Local Asymptotic Stabilitymentioning

confidence: 99%

Section: Distributed Secondary Controllersmentioning

confidence: 99%

Gather-and-broadcast frequency control in power systems

2017

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“…Yating Wang et al (2010) investigated the first-and secondorder consensus problem using the Linear Matrix Inequality (LMI) technique. The consensus problem of a homogeneous system for a complex network using the PI control technique is proposed in Burbano and di Bernardo (2014). Saboori and Khorasani (2014) introduced the consensus problems with H ' and weighted H ' bounds for a homogeneous team of linear time-invariant (LTI) MAS with switching topology and directed communication network graph.…”

Section: Introductionmentioning

confidence: 99%

Fixed time steps discrete-time sliding mode consensus protocols for two degree of freedom helicopter systems

Patel

Mehta

2021

Transactions of the Institute of Measurement and Control

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This paper presents analysis of number of steps required for the consensus in a leader-following discrete multi-agent system (DMAS) with discrete-time sliding mode protocols designed by Gao’s reaching law and power rate reaching laws. The DMAS is configured for communication with a fixed, undirected graph topology having one leader and other agents as followers. The sufficient condition for global stability is established using the Lyapunov function in both the cases. The efficacy of both the protocols is compared in simulation for number of steps required for the consensus of a homogeneous multiple two degree of freedom helicopter systems where the pitch angle and its velocity and yaw angle and its velocity are used for consensus. The simulation results reveal that the consensus performance due to protocol with power rate reaching law outperforms the protocol with Gao’s reaching law.

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“…The resulting dynamic coupling strategy is a proportional-integral (PI) or a proportional-derivative (PD) law that has been shown to be effective in improving the network synchronization performance. 7 From a control theoretic viewpoint, 34 the approach can be seen as the deployment of distributed PI or PD controllers over a network of interest. 8 The use of PI couplings has been proposed in the literature for achieving consensus in networks of identical nodes with linear dynamics.…”

Section: Introductionmentioning

confidence: 99%

“…The resulting dynamic coupling strategy is shown to be effective in improving the network synchronization performance. 7…”

mentioning

confidence: 99%

Synchronization and local convergence analysis of networks with dynamic diffusive coupling

Lombana

Bernardo

2016

Chaos: An Interdisciplinary Journal of Nonlinear Science

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In this paper, we address the problem of achieving synchronization in networks of nonlinear units coupled by dynamic diffusive terms. We present two types of couplings consisting of a static linear term, corresponding to the diffusive coupling, and a dynamic term which can be either the integral or the derivative of the sum of the mismatches between the states of neighbouring agents. The resulting dynamic coupling strategy is a distributed proportional-integral (PI) or a proportional-derivative (PD) law that is shown to be effective in improving the network synchronization performance, for example, when the dynamics at nodes are nonidentical. We assess the stability of the network by extending the classical Master Stability Function approach to the case where the links are dynamic ones of PI/PD type. We validate our approach via a set of representative examples including networks of chaotic Lorenz and networks of nonlinear mechanical systems.

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Consensus and synchronization of complex networks via proportional-integral coupling

Cited by 13 publications

References 12 publications

Gather-and-broadcast frequency control in power systems

Gather-and-broadcast frequency control in power systems

Fixed time steps discrete-time sliding mode consensus protocols for two degree of freedom helicopter systems

Synchronization and local convergence analysis of networks with dynamic diffusive coupling

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