Synchronization of Linear Time-Varying Multi-Agent Systems with Heterogeneous Time-Varying Disturbances Using Integral Controller

Kim, Jae-Yong; Yang, Jongwook; Shim, Hyungbo; Kim, Jung-Su

doi:10.5302/j.icros.2012.18.7.622

Cited by 3 publications

(2 citation statements)

References 8 publications

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“…(1) The weak concept of synchronization, practical synchronization, has been used in the discussion of chaotic systems [6,14,16,[37][38][39] and the first-order linear consensus model [29]. In fact, natural frequency ν j for the Kuramoto dynamics (1.1) is a function of t, the complete synchronization may not emerge as observed in [22,23].…”

Section: Definition 11 ([24]mentioning

confidence: 99%

Emergence of synchronous behaviors for the Schrödinger–Lohe model with frustration

Kim

2019

Nonlinearity

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We introduce the Schrödinger-Lohe model (S-L) with interaction frustration which is a toy model for quantum synchronization, and study its emergent collective dynamics. Our proposed model might not capture quantum entanglement which is one of genuine quantum phenomenon as it is, however it exhibits collective synchronous behaviors and can be reduced to the Kuramoto model with frustration in the case of spatial homogeneity and unit mass. For the emergent dynamics of the model, we present two sufficient frameworks leading to the complete and practical synchronizations for identical and non-identical oscillators, respectively, in terms of frustration function, system parameters and initial data. When the frustration functions admit real diagonal perturbations, complete synchronization emerges for identical ensemble with some class of initial data, in contrast, for non-identical ensemble, we can expect practical synchronization in which the diameter for wave functions can be controlled by tuning the coupling strength. For purely imaginary valued frustrations, we analytically show that complete or practical synchronization cannot occur for generic initial data. This illustrates that the S-L model exhibits some interesting dynamic patterns different from the Kuramoto synchronization. We provide several numerical examples which manifest periodic behaviors, reminiscent of the Kuramoto model with cosine coupling.

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Section: Definition 11 ([24]mentioning

confidence: 99%

Emergence of synchronous behaviors for the Schrödinger–Lohe model with frustration

Kim

2019

Nonlinearity

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“…(1) The concept of practical synchronization has been used in the control and network community in [4,17,22,23], and it has been used in the study of the dynamics of Kuramoto oscillators with intrinsic dynamics [10,11] and finite dimensional Lohe model [5].…”

Section: Introductionmentioning

confidence: 99%

Practical quantum synchronization for the Schrödinger–Lohe system

Choi

Cho

2016

J. Phys. A: Math. Theor.

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We present a practical synchronization method for the Schrödinger-Lohe (S-L) system distinct potentials. The S-L model describes the spatial-temporal evolution of the wave functions of quantum Lohe oscillators on a network with Lohe couplings. When the potential effects are ignored, complete wave function synchronization (CWFS) can emerge in the sense that the L 2 -distance between wave functions exponentially approaches zero for a class of initial wave functions. In contrast, when the Lohe oscillators are under the effect of potential forces, CWFS cannot occur. In this study, we employ a weaker concept of quantum synchronization for discussing the asymptotic collective behavior of the S-L model. This concept leads to 'practical synchronization' of the S-L model. In practical synchronization, the L 2 -distance between wave functions can be upper bounded by the inverse power of the square root of the coupling strength; as the coupling strength increases. Thus, the L 2 -discrepancy between wave functions arbitrarily decreases as the coupling strength increases. We present a sufficient analytical framework for this practical synchronization, which is a generalization of the earlier result in (

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Discrete-Time State Feedback Algorithm for State Consensus of Uncertain Homogeneous Multi-Agent Systems

Yoon¹,

Kim

Back

2013

Journal of Institute of Control, Robotics and Systems

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This paper presents a consensus algorithm for uMAS (uncertain Multi-Agent Systems). Unlike previous results in which only nominal models for agents are considered, it is assumed that the uncertain agent model belongs to a known polytope set. In the middle of deriving the proposed algorithm, a convex set is found which includes all uncertainties in the problem using convexity of the polytope set. This set plays an important role in designing the consensus algorithm for uMAS. Based on the set, a consensus condition for uMAS is proposed and the corresponding consensus design problem is solved using LMI (Linear Matrix Inequality). Simulation result shows that the proposed consensus algorithm successfully leads to consensus of the state of uMAS.

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Synchronization of Linear Time-Varying Multi-Agent Systems with Heterogeneous Time-Varying Disturbances Using Integral Controller

Cited by 3 publications

References 8 publications

Emergence of synchronous behaviors for the Schrödinger–Lohe model with frustration

Emergence of synchronous behaviors for the Schrödinger–Lohe model with frustration

Practical quantum synchronization for the Schrödinger–Lohe system

Discrete-Time State Feedback Algorithm for State Consensus of Uncertain Homogeneous Multi-Agent Systems

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