Consensus Problems with Distributed Delays, with Application to Traffic Flow Models

Michiels, Wim; Morărescu, Irinel-Constantin; Niculescu, Silviu–Iulian

doi:10.1137/060671425

Cited by 120 publications

(71 citation statements)

References 18 publications

Supporting

Mentioning

Contrasting

Order By: Relevance

“…We show that consensus can be achieved regardless of the presence of the delays, provided that the network has a directed spanning tree. This result is in contrast to the case of processing delays (1.4), where consensus is not possible for large values of the delay [7,8]. Furthermore, we calculate the consensus value explicitly, and show that it depends on the initial history of the agents over a time interval as well as on the details of the network structure.…”

Section: Introductionmentioning

confidence: 72%

The consensus problem in networks with transmission delays

Atay

2013

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

We study discrete- and continuous-time consensus problems on networks in the presence of distributed time delays. We focus on information transmission delays, as opposed to information processing delays, so that each node of the network compares its current state with the past states of its neighbours. We consider directed and weighted networks where the connection structure is described by a normalized Laplacian matrix and show that consensus is achieved if and only if the underlying graph contains a directed spanning tree. This statement holds independently of the transmission delays, which is in contrast to the case of processing delays. Furthermore, we calculate the consensus value explicitly, and show that it is determined by the history of the system over an interval of time, unlike the case of processing delays where the consensus value depends only on the initial state of the system at time zero. This provides the consensus algorithm with improved robustness against noise.

show abstract

Section: Introductionmentioning

confidence: 72%

The consensus problem in networks with transmission delays

Atay

2013

Phil. Trans. R. Soc. A.

View full text Add to dashboard Cite

show abstract

“…The influence of discrete fixed delays on the consensus and synchronization of coupled subsystems is considered in [8], [5], [7]. However, as pointed out in several studies [3], [1], [4], the behavior of interconnected systems is often more accurately reflected by considering distributed delays affecting their interactions. This paper focuses on the synchronization problem in networks of identical oscillators with couplings affected by distributed delays.…”

Section: Introductionmentioning

confidence: 99%

Synchronization of coupled nonlinear oscillators with shifted gamma-distributed delays

Morărescu

Michiels

Jungers

2013

2013 American Control Conference

Self Cite

View full text Add to dashboard Cite

Abstract-We derive conditions for the synchronization of coupled nonlinear oscillators affected by distributed delays in the interconnections. The distributed delays are characterized by a gamma-distribution kernel with a gap. The approach is based on the stability analysis of synchronized equilibria in the (delays,gain) parameter space and the characterization of the structure of the emanating solutions at the bifurcations. The results are applied to networks of coupled Lorenz system. In particular it is shown that, independently of the network topology, for sufficiently large coupling gains the distribution of the delay has a stabilizing effect on the stability of the synchronized equilibrium.

show abstract

“…More applications include chemical reactors [26], plate rolling [35], milling processes [24] and burned gas recirculation in an engine [6]. Complex model structures with time delays can also be obtained in multi-agent systems with internal communication delays [38], traffic flow models [31], and distributed communication networks [45]. In all these above applications, time delays are inherent parts of the dynamical properties that cannot be neglected.…”

Section: Introductionmentioning

confidence: 99%

Reduced modelling and fixed‐order control of delay systems applied to a heat exchanger

Michiels

Hilhorst

Pipeleers

et al. 2017

IET Control Theory & Applications

Self Cite

View full text Add to dashboard Cite

This paper presents an integrated approach for designing low-order multi-objective controllers for linear time-delay systems, combining recently developed methods for reduction of delay systems and fixed-order control design, respectively. First, as a benchmark problem for process control applications, a model of an experimental heat transfer setup is discussed in detail, which serves to motivate the adopted combination of model reduction and control technique. The former corresponds to a Krylov based reduction procedure, which is generalized to multiple-input-multiple-output systems with state, input and output delays, and allows the adaptive construction of an accurate low-order linear time-invariant approximation of the original linear time-delay system. Concerning the latter, a fixed-order controller is synthesized for the delay-free approximation, exploiting a recently proposed linear matrix inequality based framework for fixed-order controller design, and validated on the original linear time-delay system. In this way, the systematic overall design procedure, which is grounded in convex optimization, complements approaches based on directly optimizing stability and performance measures as a function of the controller parameters, which may lead to highly nonconvex and even non-smooth optimization problems. The successful design of a fixed-order multi-H 2 controller is validated on the benchmark problem, confirming the potential of the adopted approach for realistic industrial applications. IntroductionWe consider continuous-time models for control systems, described in terms of delay differential equations of the form(1) i = 1, . . . , my, where x(t) ∈ R n is the state, u i (t) ∈ R, i = 1, . . . , mu are the inputs, and y i (t) ∈ R, i = 1, . . . , my correspond to the outputs at time t. The quantities τ i , i = 1, . . . , mx, µ i , i = 1, . . . , mu and ν i , i = 1, . . . , my represent time-delays in the system's state, inputs and outputs, respectively, where the largest state delay is denoted by τmax = max i∈{1,...,mx} τ i . The inputs u i and outputs y i are grouped in vectors as follows:where we assume that the number of scalar inputs does not exceed the dimension of the system state, i.e., mu ≤ n. Without loss of generality, the input u and output y are subdivided asto distinguish between exogenous inputs u 1 and control inputs u 2 on the one hand, and regulated outputs y 1 and measured outputs y 2 on the other hand. The targeted class of delay systems described by (1) results from the physics based modeling of complex interconnections of components, where time-delay elements naturally appear in modeling propagation phenomena. The latter are due to the fact that the transfer of material, energy and information is mostly not instantaneous. For this class of systems, the experimental heat-transfer setup described in Section 3 serves as a benchmark problem for the control design. An analogous model has been derived in [25] for a greenhouse. More applications include chemical reactors [26], plate...

show abstract

Consensus Problems with Distributed Delays, with Application to Traffic Flow Models

Cited by 120 publications

References 18 publications

The consensus problem in networks with transmission delays

The consensus problem in networks with transmission delays

Synchronization of coupled nonlinear oscillators with shifted gamma-distributed delays

Reduced modelling and fixed‐order control of delay systems applied to a heat exchanger

Contact Info

Product

Resources

About