| 1. |
- Briat, Corentin, et al.
(författare)
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A conservation-law-based modular fluid-flow model for network congestion modeling
- 2012
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Ingår i: 2012 Proceedings - IEEE INFOCOM. - : IEEE Computer Society. - 9781467307758 ; , s. 2050-2058
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Konferensbidrag (refereegranskat)abstract
- A modular fluid-flow model for network congestion analysis and control is proposed. The model is derived from an information conservation law stating that the information is either in transit, lost or received. Mathematical models of network elements such as queues, users, and transmission channels, and network description variables, including sending/ acknowledgement rates and delays, are inferred from this law and obtained by applying this principle locally. The modularity of the devised model makes it sufficiently generic to describe any network topology, and appealing for building simulators. Previous models in the literature are often not capable of capturing the transient behavior of the network precisely, making the resulting analysis inaccurate in practice. Those models can be recovered from exact reduction or approximation of this new model. An important aspect of this particular modeling approach is the introduction of new tight building blocks that implement mechanisms ignored by the existing ones, notably at the queue and user levels. Comparisons with packet-level simulations corroborate the proposed model.
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| 2. |
- Briat, Corentin, et al.
(författare)
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An axiomatic fluid-flow model for congestion control analysis
- 2011
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Ingår i: 2011 50th IEEE Conference on Decision and Control andEuropean Control Conference (CDC-ECC). ; , s. 3122-3129
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Konferensbidrag (refereegranskat)abstract
- An axiomatic model for congestion control isderived. The proposed four axioms serve as a basis for theconstruction of models for the network elements. It is shownthat, under some assumptions, some models of the literature canbe recovered. A single-buffer/multiple-users topology is finallyderived and studied for illustration.
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| 3. |
- Briat, Corentin
(författare)
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Convergence and Equivalence Results for the Jensen's Inequality-Application to Time-Delay and Sampled-Data Systems
- 2011
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Ingår i: IEEE Transactions on Automatic Control. - 0018-9286 .- 1558-2523. ; 56:7, s. 1660-1665
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Tidskriftsartikel (refereegranskat)abstract
- The Jensen's inequality plays a crucial role in the analysis of time-delay and sampled-data systems. Its conservatism is studied through the use of the Gruss Inequality. It has been reported in the literature that fragmentation (or partitioning) schemes allow to empirically improve the results. We prove here that the Jensen's gap can be made arbitrarily small provided that the order of uniform fragmentation is chosen sufficiently large. Nonuniform fragmentation schemes are also shown to speed up the convergence in certain cases. Finally, a family of bounds is characterized and a comparison with other bounds of the literature is provided. It is shown that the other bounds are equivalent to Jensen's and that they exhibit interesting well-posedness and linearity properties which can be exploited to obtain better numerical results.
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| 4. |
- Briat, Corentin, et al.
(författare)
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Convex Dwell-Time Characterizations for Uncertain Linear Impulsive Systems
- 2012
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Ingår i: IEEE Transactions on Automatic Control. - 0018-9286 .- 1558-2523. ; 57:12, s. 3241-3246
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Tidskriftsartikel (refereegranskat)abstract
- New sufficient conditions for the characterization of dwell-times for linear impulsive systems are proposed and shown to coincide with continuous decrease conditions of a certain class of looped-functionals, a recently introduced type of functionals suitable for the analysis of hybrid systems. This approach allows to consider Lyapunov functions that evolve nonmonotonically along the flow of the system in a new way, broadening then the admissible class of systems which may be analyzed. As a byproduct, the particular structure of the obtained conditions makes the method is easily extendable to uncertain systems by exploiting some convexity properties. Several examples illustrate the approach.
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| 5. |
- Briat, Corentin, et al.
(författare)
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Design of LPV observers for LPV time-delay systems : an algebraic approach
- 2011
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Ingår i: International Journal of Control. - : Informa UK Limited. - 0020-7179 .- 1366-5820. ; 84:9, s. 1533-1542
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Tidskriftsartikel (refereegranskat)abstract
- The design of reduced order observer for linear parameter varying (LPV) time-delay systems is addressed. Necessary conditions guaranteeing critical structural properties for the observation error dynamics are first provided through nonlinear algebraic matrix equalities. An explicit parametrisation of the family of observers fulfilling these necessary conditions is then derived. Finally, an approach based on linear matrix inequalities is provided and used to select a suitable observer within this family, according to some criterion; e.g. maximisation of the delay margin or guaranteed suboptimal L(2)-gain. Examples from the literature illustrate the efficiency of the approach.
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| 6. |
- Briat, Corentin, et al.
(författare)
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Dynamic equations on time-scale : Application to stability analysis and stabilization of aperiodic sampled-data systems
- 2011
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Ingår i: IFAC Proc. Vol. (IFAC-PapersOnline). - 9783902661937 ; , s. 11374-11379
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Konferensbidrag (refereegranskat)abstract
- The stability analysis of systems with aperiodic sampling is analyzed in the framework of dynamic equations on time-scales. Lyapunov theory is used, with sample-period-dependent and independent Lyapunov functions, to obtain stability conditions expressed in terms of parameter dependent matrix inequalities. The examples illustrate the efficiency of the approach which is able to recover, for some systems, the theoretical results for the periodic sampling case even in the aperiodic case. It is also shown that some systems may have admissible varying sampling periods located in disjoint sets. Finally, stabilization results via switching statefeedback are provided; both robust and sampling-period-dependent controllers are considered. It is shown that the latter ones, using the information on the sampling period, can improve stability properties. Stabilization examples illustrate the effectiveness of the approach.
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| 7. |
- Briat, Corentin, et al.
(författare)
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H ∞ bounded resilient state-feedback design for linear continuous-time systems -a robust control approach
- 2011
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Ingår i: IFAC Proceedings Volumes. - 9783902661937 ; , s. 9307-9312
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Konferensbidrag (refereegranskat)abstract
- The quadratic stabilization of LTI systems by bounded resilient state-feedback controllers is addressed. The controllers are guaranteed to be non-fragile with respect to either uniform or nonuniform maximal implementation errors. The design of resilient controller relies on an LMI problem while boundedness of the coefficients (a NP-Hard problem) can be guaranteed by solving a nonconvex problem involving a BMI. The latter problem is solved using proposed locally convergent iterative LMI algorithms. Finally, an example is considered in order to illustrate the effectiveness of the approach.
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| 8. |
- Briat, Corentin, et al.
(författare)
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Impact of Queueing Delay Estimation Error on Equilibrium and Its Stability
- 2011
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Ingår i: NETWORKING 2011, PT II. - Berlin, Heidelberg : Springer Berlin Heidelberg. - 9783642207983 ; , s. 356-367
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Konferensbidrag (refereegranskat)abstract
- Delay-based transmission control protocols need to separate round-trip time (RTT) measurements into their constituting parts: the propagation and the queueing delays. We consider two means for this; the first is to take the propagation delay as the minimum observed RTT value, and the second is to measure the queueing delay at the routers and feed it back to the sources. We choose FAST-TCP as a representative delay-based transmission control protocol for analysis and study the impact of delay knowledge errors on its performance. We have shown that while the first method destroys fairness and the uniqueness of the equilibrium, the stability of the protocol can easily be obtained through tuning the protocol terms appropriately. Even though the second technique is shown to preserve fairness and uniqueness of the equilibrium point, we have presented that unavoidable oscillations can occur around the equilibrium point.
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| 9. |
- Briat, Corentin, et al.
(författare)
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Memory-resilient gain-scheduled state-feedback control of uncertain LTI/LPV systems with time-varying delays
- 2010
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Ingår i: Systems & control letters (Print). - : Elsevier BV. - 0167-6911 .- 1872-7956. ; 59:8, s. 451-459
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Tidskriftsartikel (refereegranskat)abstract
- The stabilization of uncertain LTI/LPV time-delay systems with time-varying delays by state-feedback controllers is addressed. Compared to other works in the literature, the proposed approach allows for the synthesis of resilient controllers with respect to uncertainties on the implemented delay. It is emphasized that such controllers unify memoryless and exact-memory controllers usually considered in the literature. The solutions to the stability and stabilization problems are expressed in terms of LMIs which allow us to check the stability of the closed-loop system for a given bound on the knowledge error and even optimize the uncertainty radius under some performance constraints; in this paper, the H-infinity performance measure is considered. The interest of the approach is finally illustrated through several examples.
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| 10. |
- Briat, Corentin, et al.
(författare)
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Nonlinear state-dependent delay modeling and stability analysis of internet congestion control
- 2010
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Ingår i: 49TH IEEE CONFERENCE ON DECISION AND CONTROL (CDC). - 9781424477463 ; , s. 1484-1491
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Konferensbidrag (refereegranskat)abstract
- It is shown that the queuing delay involved in the congestion control algorithm is state-dependent and does not depend on the current time. Then, using an accurate formulation for buffers, networks with arbitrary topologies can be built. At equilibrium, our model reduces to the widely used setup by Paganini et al. Using this model, the delay-derivative is analyzed and it is proved that the delay time-derivative does not exceed one for the considered topologies. It is then shown that the considered congestion control algorithm globally stabilizes a delay-free single buffer network. Finally, using a specific linearization result for systems with state-dependent delays from Cooke and Huang, we show the local stability of the single bottleneck network.
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