On Performance of Time-Delay Linear Consensus Networks with Directed Interconnection Topologies

Dezfulian, Shima; Ghaedsharaf, Yaser; Motee, Nader

doi:10.23919/acc.2018.8430769

Cited by 11 publications

(6 citation statements)

References 23 publications

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“…For these simulations, we choose nominal values for each parameter; K = 1, χ = 1, and ε = 1. Considering each agent's difference from the average as an output, similar to [33], we adopt the square of the H 2 -norm of the system as a cost performance metric…”

Section: Simulationsmentioning

confidence: 99%

Distributed Dynamic Event-Triggered Coordination with a Designable Minimum Inter-Event Time

Berneburg

Nowzari

2019

2019 American Control Conference (ACC)

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This paper revisits the classical multi-agent average consensus problem for which many different event-triggered control strategies have been proposed over the last decade. Many of the earliest versions of these works conclude asymptotic stability without proving that Zeno behavior, or deadlocks, do not occur along the trajectories of the system. More recent works that resolve this issue either: (i) propose the use of a dwelltime that forces inter-event times to be lower-bounded away from zero but sacrifice asymptotic convergence in exchange for practical convergence (or convergence to a neighborhood); (ii) guarantee non-Zeno behaviors and asymptotic convergence but do not provide a positive minimum inter-event time guarantee; or (iii) are not fully distributed. Additionally, the overwhelming majority of these works provide no form of robustness analysis. Instead, this work for the first time presents a fully distributed, robust, dynamic event-triggered algorithm, for general directed communication networks, for which a desired positive minimum inter-event time can be chosen by each agent in a distributed fashion. Simulations illustrate our results.

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Section: Simulationsmentioning

confidence: 99%

Distributed Dynamic Event-Triggered Coordination with a Designable Minimum Inter-Event Time

Berneburg

Nowzari

2019

2019 American Control Conference (ACC)

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“…Condition (30) ensures stability of the closed-loop network (27). Since the problem given by ( 28)-( 31) is combinatorial, the exact solution must be found by an exhaustive search and appraising ρss(L + L F ; τ ) for all possible k i=1 |Ec| i cases.…”

Section: Improving Performance By Adding New Feedback Loopsmentioning

confidence: 99%

“…Lemma 5.1: For a stable linear consensus network (27) with output matrix C with property C1n = 0n, the spectral function Fig. 2: The relative error of f with respect to f1.…”

Section: A Cost Function Approximation and Sdp Relaxationmentioning

confidence: 99%

“…Theorem 5.6: Adding a new link e with weight (e) to network (27) will retain stability of the network if and only if (e) < ws(L; e), (50) where ws(L; e) = τ re π 2 Mn − τ L −1 .…”

Section: B Greedy Algorithmsmentioning

confidence: 99%

“…These assumptions allow us to quantify performance explicitly using closed-form formulae. Relaxing these assumptions to include networks with nonuniform time delays and/or directed coupling graphs are challenging and require separate investigations, which may not lend themselves to analytic performance evaluation and prevent us from devising low time-complexity algorithms [27], [28]. Since time-delay is intrinsic to all networked control systems, devising efficient and scalable algorithms for analysis and design of networked systems with higherorder dynamics and time-delay will remain an active research area, for many years to come.…”

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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