Effect of network structure on the stability margin of large vehicle formation with distributed control

He, Hao; Barooah, Prabir; Veerman, J. J. P.

doi:10.1109/cdc.2010.5717528

Cited by 18 publications

(28 citation statements)

References 15 publications

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“…The eigenvalues of the grounded Laplacian characterize the variance in the equilibrium values for noisy instances of such dynamics, and determine the rate of convergence to steady state [12], [13]. Optimization algorithms have been developed to select "leader nodes" in the network in order to minimize the steady-state variance or to maximize the rate of convergence [13], [14], [15], [16], and various works have studied the effects of the location of such leaders in distributed control and consensus dynamics [17], [18], [19], [20], [21].…”

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confidence: 99%

On the Smallest Eigenvalue of Grounded Laplacian Matrices

Pirani

Sundaram

2015

IEEE Trans. Automat. Contr.

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We provide bounds on the smallest eigenvalue of grounded Laplacian matrices (which are obtained by removing certain rows and columns of the Laplacian matrix of a given graph). The gap between our upper and lower bounds depends on the ratio of the smallest and largest components of the eigenvector corresponding to the smallest eigenvalue of the grounded Laplacian. We provide a graph-theoretic bound on this ratio, and subsequently obtain a tight characterization of the smallest eigenvalue for certain classes of graphs. Specifically, for Erdos-Renyi random graphs, we show that when a (sufficiently small) set S of rows and columns is removed from the Laplacian, and the probability p of adding an edge is sufficiently large, the smallest eigenvalue of the grounded Laplacian asymptotically almost surely approaches |S|p.We also show that for random d-regular graphs with a single row and column removed, the smallest eigenvalue is Θ( d n ). Our bounds have applications to the study of the convergence rate in consensus dynamics with stubborn or leader nodes.

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confidence: 99%

On the Smallest Eigenvalue of Grounded Laplacian Matrices

Pirani

Sundaram

2015

IEEE Trans. Automat. Contr.

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“…The result for the symmetric bidirectional architecture follows from Theorem 4 in [42] in a straightforward manner and is therefore omitted.…”

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confidence: 99%

Stability and robustness of large platoons of vehicles with double‐integrator models and nearest neighbor interaction

Barooah

2012

Intl J Robust & Nonlinear

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113

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We study the stability and robustness of a large platoon of vehicles, where each vehicle is modeled as a double integrator, for two decentralized control architectures: predecessor following and symmetric bidirectional. In the predecessor-following architecture, the control action on each agent only depends on the information from its immediate front neighbor, whereas in the symmetric bidirectional architecture, it depends equally on the information from both its immediate front neighbor and back neighbor. We prove asymptotic stability of the formation for a class of nonlinear controllers with sector nonlinearity, with the linear controller as a special case. We show that the convergence rate of the predecessor-following architecture is much faster than that of the symmetric bidirectional architecture. However, the predecessor-following architecture suffers high algebraic growth of initial errors. We also establish scaling laws (with N ) of certain H 1 norms of the formation that measure its robustness to external disturbances for the linear case. It is shown that the robustness performance grows geometrically in N for predecessor-following architecture but only polynomially in N for symmetric-bidirectional architecture. Extensive numerical simulations are conducted to verify the predictions for the linear case and empirically estimate the corresponding performance metrics for a saturation-type nonlinear controller. On the basis of the analytical and numerical results, it is seen that the symmetric bidirectional architecture outperforms the predecessor-following architecture in all measures of performance. Within the predecessor-following architecture, the nonlinear controller is seen to perform better in general than the linear one. A number of design guidelines are provided on the basis of these conclusions. motivations for automated platooning is to achieve higher highway capacity by making cars move with a small inter-vehicle separation, there is a need to study the constant spacing policy. It was shown in [11,14,15] that, with constant spacing policy, the leader's information need to be broadcasted to the following vehicles to assure string stability. Nevertheless, the inevitable time delay and package drop in broadcasting the leader's information will cause string instability [16]. This leads to the study of decentralized control architecture, that is, each vehicle can only use measurements of relative position and/or velocity with respect to its nearest neighbors.Two decentralized control architectures that are commonly examined are predecessor-following and bidirectional architectures. In the predecessor-following architecture, the control action on each vehicle only depends on the relative information from its immediate predecessor, that is, the vehicle in front of it. In the bidirectional architecture, the control depends on the relative information from both its immediate predecessor and follower. Within the bidirectional architecture, the most commonly analyzed case is the symmetric bidirectional arch...

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“…Theorem 4: Consider a k-nearest neighbor platoon P(n, k) with dynamics (17). If there exist at least |R| = n 2k+1 reference vehicles, then there exists an arrangement of the reference vehicles satisfying ||G|| ∞ ≤ 1.…”

Section: Proposition 1 ( [21])mentioning

confidence: 99%

Graph Theoretic Approach to the Robustness of $k$ -Nearest Neighbor Vehicle Platoons

Pirani

Hashemi

Simpson-Porco

et al. 2017

IEEE Trans. Intell. Transport. Syst.

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We consider a graph theoretic approach to the performance and robustness of a platoon of vehicles, where each vehicle communicates with its k-nearest neighbors. In particular, we quantify the platoon's stability margin, robustness to disturbances (in terms of system H ∞ norm), and maximum delay tolerance via graph-theoretic notions such as nodal degrees and (grounded) Laplacian matrix eigenvalues. Our results show that there is a trade-off between robustness to time delay and robustness to disturbances.Both first-order dynamics (reference velocity tracking) and second-order dynamics (controlling intervehicular distance) are analyzed in this direction. Theoretical contributions are confirmed via simulation results.

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Effect of network structure on the stability margin of large vehicle formation with distributed control

Cited by 18 publications

References 15 publications

On the Smallest Eigenvalue of Grounded Laplacian Matrices

On the Smallest Eigenvalue of Grounded Laplacian Matrices

Stability and robustness of large platoons of vehicles with double‐integrator models and nearest neighbor interaction

Graph Theoretic Approach to the Robustness of $k$ -Nearest Neighbor Vehicle Platoons

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