Network coordination and synchronization in a noisy environment with time delays

Hunt, David; Szymanski, Boleslaw K.; Korniss, G.

doi:10.1103/physreve.86.056114

Cited by 26 publications

(45 citation statements)

References 76 publications

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“…This subset is depicted in Figure 7 along with S. One can verify that s * cot(s * ) = s2 is invertible for s2 ∈ [0.1, 0.9] and it can be expressed as s * (s2). For s1, s2 ∈ S, we choose the following class of rational functions f (s1, s2) = As 2 (s1) s 2 1 + Bs 2 (s1) s1 − s * (s2) (26) in which the enumerators Figure 11 depicts the exact function f (s1, 0.5) and the rational approximationf (s1, 0.5) for s1 ∈ S together with the associated relative error. The relative error function…”

Section: Approximation Formulas For Riskmentioning

confidence: 99%

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Risk of Collision and Detachment in Vehicle Platooning: Time-Delay–Induced Limitations and Tradeoffs

Somarakis¹,

Ghaedsharaf

Motee

2020

IEEE Trans. Automat. Contr.

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We quantify the value-at-risk of inter-vehicle collision and detachment for a class of platoons, which are governed by secondorder dynamics in presence of communication time-delay and exogenous stochastic noise. Closed-form expressions for the risk measures are obtained as functions of Laplacian eigen-spectrum as well as their fine explicit approximations using rational polynomial functions. We quantify several hard limits and fundamental trade-offs among the risk measures, network connectivity, communication time-delay, and statistics of exogenous stochastic noise. Simultaneous presence of stochastic noise and time delay in a platoon imposes some idiosyncratic behavior risk of collision and detachment, for instance, weakening (improving) network connectivity may result in lower (higher) levels of risk. Furthermore, a thorough risk analysis is conducted for networks with specific graph topology. We support our theoretical findings via multiple simulations.

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Section: Approximation Formulas For Riskmentioning

confidence: 99%

“…In the final step, we utilize approximation (26) and arrive at a tight approximation of the risk measureR…”

Section: Approximation Formulas For Riskmentioning

confidence: 99%

Risk of Collision and Detachment in Vehicle Platooning: Time-Delay–Induced Limitations and Tradeoffs

Somarakis¹,

Ghaedsharaf

Motee

2020

IEEE Trans. Automat. Contr.

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“…, n , substituting λi from equation (24) into the equation (23) yields identity (22). The lower bound of the coherency for the case that C = Mn was found using numerical analysis in [24], [25]. We found the fundamental limit for general output matrix C and studied uniqueness of the limit using convex analysis.…”

Section: Optimal and Robust Topologies Wrt Time-delaymentioning

confidence: 99%

Performance Improvement in Noisy Linear Consensus Networks With Time-Delay

Ghaedsharaf

Siami

Somarakis

et al. 2019

IEEE Trans. Automat. Contr.

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We analyze performance of a class of time-delay first-order consensus networks from a graph topological perspective and present methods to improve it. The performance is measured by network's square of H 2 -norm and it is shown that it is a convex function of Laplacian eigenvalues and the coupling weights of the underlying graph of the network. First, we propose a tight convex, but simple, approximation of the performance measure in order to achieve lower complexity in our design problems by eliminating the need for eigen-decomposition. The effect of time-delay reincarnates itself in the form of non-monotonicity, which results in nonintuitive behaviors of the performance as a function of graph topology. Next, we present three methods to improve the performance by growing, re-weighting, or sparsifying the underlying graph of the network. It is shown that our suggested algorithms provide near-optimal solutions with lower complexity with respect to existing methods in literature.performance measure for network synthesis, (iii) low time complexity algorithms to design state feedback controllers for performance enhancement of time-delay linear consensus networks. In section III, we express the H2-norm performance of a time-delay linear consensus network in terms of its Laplacian spectrum. Furthermore, we prove that this performance measure is convex with respect to coupling weights and Laplacian spectrum, and in addition, it is an increasing function of time-delay. In section IV, we discuss topologies with optimal performance. Furthermore, we quantify a sharp lower bound on the best achievable performance for a network with a fixed timedelay. In presence of time-delay, the H2-norm performance of firstorder consensus network is not monotone decreasing with respect to connectivity, which impose challenges in design of the optimal network as increasing connectivity may deteriorate the performance. Then, we present methods to improve the performance measure. We categorize these procedures as growing, reweighting, and sparsification. Although the H2-norm performance is a convex function of Laplacian eigenvalues, direct use of this spectral function in our network design problems requires eigen-decomposition, which adds to time complexity of our design procedures. To overcome this, our key idea is to calculate an approximation function of the performance measure that spares us eigen-decomposition of the Laplacian matrix. In section V, we tackle the combinatorial problem of improving the non-monotone performance measure of the time-delay network by adding new interconnection links. Our time-complexity analysis of our proposed algorithm to grow a time-delay network shows that it can be done in O(n 3 + mn 2 + kn 2 ) arithmetic operations, where n is number of nodes, m is number of rows of the output matrix C and k is maximum number of new interconnections. Section VI discusses reweighting of the coupling weights as an approach to improve the performance measure. This design problem can be cast as a semidefinite programming (SD...

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“…For the state-space system given by (13) and (26), the square of H 2 norm of the system is also defined by (17), in which B and M are given by (18) and (19), Z is expressed by…”

Section: B Vertex Variancementioning

confidence: 99%

Biharmonic Distance and Performance of Second-Order Consensus Networks with Stochastic Disturbances

Yang

Zhang

et al. 2018

2018 Annual American Control Conference (ACC)

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We study second order consensus dynamics with random additive disturbances. We investigate three different performance measures: the steady-state variance of pairwise differences between vertex states, the steady-state variance of the deviation of each vertex state from the average, and the total steady-state variance of the system. We show that these performance measures are closely related to the biharmonic distance; the square of the biharmonic distance plays similar role in the system performance as resistance distances plays in the performance of first-order noisy consensus dynamics. We further define the new concepts of biharmonic Kirchhoff index and vertex centrality based on the biharmonic distance. Finally, we derive analytical results for the performance measures and concepts for complete graphs, star graphs, cycles, and paths, and we use this analysis to compare the asymptotic behavior of the steady-variance in first-and second-order systems.

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Network coordination and synchronization in a noisy environment with time delays

Cited by 26 publications

References 76 publications

Risk of Collision and Detachment in Vehicle Platooning: Time-Delay–Induced Limitations and Tradeoffs

Risk of Collision and Detachment in Vehicle Platooning: Time-Delay–Induced Limitations and Tradeoffs

Performance Improvement in Noisy Linear Consensus Networks With Time-Delay

Biharmonic Distance and Performance of Second-Order Consensus Networks with Stochastic Disturbances

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