Hakkı Ulaş Ünal

Comparison of PI controllers designed for the delay model of TCP/AQM networks

One of the major problems of communication networks is congestion. In order to address this problem in TCP/IP networks, Active Queue Management (AQM) scheme is recommended. AQM aims to minimize the congestion by regulating the average queue size at the routers. To improve upon AQM, recently, several feedback control approaches were proposed. Among these approaches, PI controllers are gaining attention because of their simplicity and ease of implementation. In this paper, by utilizing the fluid-flow model of TCP networks, we study the PI controllers designed for TCP/AQM. We compare these controllers by first analyzing their robustness and fragility. Then, we implement these controllers in ns-2 platform and conduct simulation experiments to compare their performances in terms of queue length. Taken together, our results provide a guideline for choosing a PI controller for AQM given specific performance requirements.

Stable H∞ controller design for systems with multiple input/output time-delays

Abstract The stable H ∞ controller design problem is considered for multi-input–multi-output systems with multiple input/output time-delays. An algorithm is presented to solve this problem. The algorithm makes use of the small-gain theorem and the structure of the H ∞ controller for the class of systems under consideration.

Prediction of partial synchronization in delay-coupled nonlinear oscillators, with application to Hindmarsh–Rose neurons

The full synchronization of coupled nonlinear oscillators has been widely studied. In this paper we investigate conditions for which partial synchronization of time-delayed diffusively coupled systems arises. The coupling configuration of the systems is described by a directed graph. As a novel quantitative result we first give necessary and sufficient conditions for the presence of forward invariant sets characterized by partially synchronous motion. These conditions can easily be checked from the eigenvalues and eigenvectors of the graph Laplacian. Second, we perform stability analysis of the synchronized equilibria in a (gain,delay) parameter space. For this analysis the coupled nonlinear systems are linearized around the synchronized equilibria and then the resulting characteristic function is factorized. By such a factorization, it is shown that the relation between the behaviour of different agents at the zero of the characteristic function depends on the structure of the eigenvectors of the weighted Laplacian matrix. By determining the structure of the solutions in the unstable manifold, combined with the characterization of invariant sets, we predict which partially synchronous regimes occur and estimate the corresponding coupling gain and delay values. We apply the obtained results to networks of coupled Hindmarsh–Rose neurons and verify the occurrence of the expected partially synchronous regimes by using a numerical simulation. We also make a comparison with an existing approach based on Lyapunov functionals.

Utilization of non-causal uncertainty blocks in the robust flow controller design problem for data-communication networks

Robust flow controller design problem for data-communication networks with multiple uncertain time-delays is considered. A recent result on the validity of the small gain theorem for systems with non-causal subsystems is first extended for application to this problem. Then, using this extension, a robust flow controller design approach is proposed. Simulations are performed to illustrate the performance improvement obtained by using the proposed approach.

Strong Stabilization of Time-Delay Systems

Abstract Stable controllers are required due to modelling imperfections and for better performance achievements. As is well known, a stable stabilizing controller for a given real-rational plant exists if and only if the plant staisfies the so-called parity interlacing property. In this paper, a recent result, which proves that this condition is also necessary for infinite-dimensional plants is first presented. The condition is also sufficient if the plant satisfies certain additional properties. This result is then applied to time-delay systems. Two examples are considered. For the first example it is shown that it is not possible to design a stable stabilizing controller. For the second example it is shown that there exists a stable controller which stabilizes the plant and the design of such a controller is demonstrated.

Performance level and stability margins of an optimal ℋ∞ flow controller

Flow controllers are needed to avoid congestion in different types of networks. The dynamics of such networks, however, can usually be represented by infinite-dimensional models, which are either based on partial-differential equations or delay-differential equations. An optimal ℋ∞ flow controller design approach has recently been proposed for networks whose dynamics involve multiple and uncertain time-varying time delays. In the present paper, performance level and stability margins of controllers designed by this approach are analyzed. It is shown that, by choosing certain controller design parameters large, stability margins can be improved; while choosing them small improves performance levels. Therefore, there is a clear trade-off between robustness and performance.

Further remarks on delay dynamics in Oregonator models

Motivated by the fact that molecules reacting through some biological channels may need some time-lag due transcription and translation processes, this note is devoted to the study of stability properties of a delayed Oregonator model. In this work, we consider an Oregonator based model consisting of two different delays, which origin the time needed to reach the chemical equilibrium and regeneration of certain chemical variable used as a negative feedback. Positive equilibrium points as well as the stability of solutions in their neighborhood are investigated. Furthermore, Hopf bifurcation points and their crossing frequencies are further discussed.

Evaluating and Approximating FIR Filters: An Approach Based on Functions of Matrices

Most of the controllers designed for systems with timedelays involve finite impulse response (FIR) filters in their structure, in particular prediction based controllers for systems with input/output delays. We present theory, algorithms and software to evaluate the frequency response, to approximate the filters by stable linear timeinvariant systems and to compute their induced L2 gain. The approach is based on the theory of functions of matrices. In the approach pole zero cancelations in frequency domain representations are explicitly taken into account.

Characterization and Computation of Partial Synchronization Manifolds for Diffusive Delay-Coupled Systems

Sometimes a network of dynamical systems shows a form of incomplete synchronization, characterized by synchronization of some but not all of its component systems. This type of incomplete synchronization is called partial synchronization or cluster synchronization. Partial synchronization is associated with the existence of partial synchronization manifolds, which are linear invariant subspaces of

Prediction of partially synchronous regimes of delay-coupled nonlinear oscillators

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