Interplay between performance and communication delay in noisy linear consensus networks

Ghaedsharaf, Yaser; Siami, Milad; Somarakis, Christoforos; Motee, Nader

doi:10.1109/ecc.2016.7810536

Cited by 18 publications

(25 citation statements)

References 20 publications

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“…The current manuscript extends results of [29]- [31] and presents a consistent story on how to analyze and improve the performance of noisy linear consensus networks subject to time-delay. In [29], we studied properties of the first-order consensus network's H2-norm in the presence of time-delay, and in [30], [31], we offered growing and sparsification algorithms to enhance the H2-norm of the network. This manuscript extends results of [29]- [31] to the general output matrix and provides detailed proofs and explanation for all theorems and lemmas.…”

Section: Introductionsupporting

confidence: 63%

“…L2 always results in performance improvement, i.e., ρss(L2; 0) ≤ ρss(L1; 0) and path graph has the worst performance among all unweighted graphs. In conclusion, in time-delay linear consensus networks, higher connectivity does not necessarily imply better H2-norm performance [29].…”

Section: Theorem 42mentioning

confidence: 88%

“…subject to: (29), (30), (32), (33) In spite of smoothness of the cost function in (34), the structure of the cost function is not appealing since we cannot cast it as an SDP with linear objective function and constraints or solve it using existing and standard solvers or toolboxes. Moreover, if we want to write a solver for the problem using the conventional methods, e.g., interior-point or subgradient methods, we have to find eigenvalues and eigenvectors of L + L F for each step of minimizing the performance function; which significantly increases complexity in terms of both time and details of solver.…”

Section: A Cost Function Approximation and Sdp Relaxationmentioning

confidence: 99%

“…In [29], we studied properties of the first-order consensus network's H2-norm in the presence of time-delay, and in [30], [31], we offered growing and sparsification algorithms to enhance the H2-norm of the network. This manuscript extends results of [29]- [31] to the general output matrix and provides detailed proofs and explanation for all theorems and lemmas. Furthermore, Theorems 4.2, 4.3, 4.4, which relate the performance measure to known graph topologies are new additions to this manuscripts.…”

Section: Introductionmentioning

confidence: 99%

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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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Section: Introductionsupporting

confidence: 63%

Section: Theorem 42mentioning

confidence: 88%

Section: A Cost Function Approximation and Sdp Relaxationmentioning

confidence: 99%

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Performance Improvement in Noisy Linear Consensus Networks With Time-Delay

Ghaedsharaf

Siami

Somarakis

et al. 2019

IEEE Trans. Automat. Contr.

Self Cite

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“…The H2-norm has been recently utilized as a measure of performance and coherency for linear consensus networks (see [1], [14], [15], [16], [8] and references therein). One of the main advantages of using H2-norm is its elegant representation in terms of Laplacian spectrum that makes development of tractable and scalable network design algorithms possible [17].…”

Section: Introductionmentioning

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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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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