Browsing by Subject "Time delay systems"
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Item Open Access Analysis of a gene regulatory network model with time delay using the secant condition(IEEE, 2016-10-04) Ahsen, M. E.; Özbay, Hitay; Nicolescu, Silviu-IulianA cyclic model for gene regulatory networks with time delayed negative feedback is analyzed using an extension of the so-called secant condition, which is originally developed for systems without time delays. It is shown that suf cient conditions obtained earlier for delay-independent local stability can be further improved for homogenous networks to obtain delay-dependent necessary and suf cient conditions, which are expressed in terms of the parameters of the Hill-type nonlinearity.Item Open Access Analysis of an extended gene regulatory network model with time delay(Institute of Applied Mathematics of Baku State University, 2023) Özturk, Dilan; Özbay, HitayThis paper is concerned with the analysis of an extended gene regulatory network model with time delayed negative feedback. An extended model amounts to considering the unmodeled dynamics in the earlier Gene regulatory network (GRN) designs. Stability analysis of the extended model is further investigated with different design parameters. A local stability condition is derived for a model of extended GRN with time delay. Several numerical examples are given to illustrate the stability characteristics of the delayed extended GRN model and the results are compared with the benchmark homogeneous gene regulatory network.Item Open Access Delay margin optimization for systems with ınternal delayed feedback(Elsevier, 2021-07-16) Özbay, HitayIn this brief paper, controller design for delay margin optimization is considered for systems with internal feedback delays (systems with delays in the state variables). Similar to existing results on delay margin optimization for finite dimensional systems with I/O delays, it is shown that the problem considered can be solved by using Nevanlinna-Pick interpolation involving non-minimum phase zeros of the plant.Item Open Access Essays on gene regulatory network models and their stability analysis(Bilkent University, 2023-07) Şener, Dilan ÖztürkGene expression is one of the core areas in comprehending and assessing how biological cells work. Gene regulatory networks (GRNs), representing the intri-cate mechanism between genes and their regulatory modules, are instrumental in controlling gene expression and cell functions. These models shed light on how transcription factors interact with their regulatory modules within a cell. Despite the multitude of studies focusing on the analysis and enhancement of GRNs, there is still room for contributions. This thesis investigates a novel framework inspired by the gene networks constructed using synthetic biology, and presents stability analyses of the nonlinear infinite dimensional dynamical system models arising in this framework. In the first part of the thesis, we extend a previously studied benchmark GRN model including time delay, and present an analysis of the extended frame-work. We utilize unmodeled dynamics and possibly ignored interactions, including higher-order dynamics, in our system design. The stability of the extended system is analyzed by considering various nonlinearity functions and design pa-rameters, and the results are compared with those of the benchmark original model. In the second part, we employ an extension of a gene network model using a multiplicative perturbation of the dynamical system. Each cascaded subsystem in this extended framework has an additional block, including a multiplicative term with a high-pass filter, and the effect of additional parameters on the robustness and delay margin of the system is investigated. Experiments with various design parameters yield that the stability characteristics of GRNs can be improved using the model pertaining to the extension under specific perturbations. Finally, the third part covers the analysis of nonlinear dynamics and chaos in GRNs, particularly focusing on the two-gene original and extended gene net-works. Chaotic dynamics depend strongly on the inclusion of time delays, but the circuit motifs that show chaos differ when both original and extended models are considered. Our results suggest that for a particular higher-order extension of the gene network, it is possible to observe the chaotic dynamics in a two-gene system without adding any self-inhibition. This finding can be explained as a result of the modification of the original benchmark model induced by unmodeled dynamics. We argue that regulatory gene circuit models with additional parameters demonstrate non-periodic dynamics much more easily.Item Open Access Explicit adaptive time-delay compensation for bilateral teleoperation(IEEE, 2015) Abidi, K.; Yıldız, Yıldıray; Körpe, Bekir EmreThis paper proposes a control framework that addresses the destabilizing effect of communication time-delays and system uncertainties in telerobotics, in the presence of force-feedback. Force feedback is necessary to obtain transparency, which is providing the human operator as close a feel as possible of the environment where the slave robot is operating. Achieving stability and providing transparency are conflicting goals. This is the major reason why currently a very few, if at all, fully operational force feedback teleoperation devices exist except for research environments. The proposed framework handles system uncertainty with adaptation and communication time delays with explicit delay compensation. The technology that allows this explicit adaptive time-delay compensation is inspired by MIT's Adaptive Posicast Controller.Item Open Access Extension of an Anti-windup Scheme for Systems with Time Delay and Integral Action(Elsevier B.V., 2018) Öztürk, D.; Özbay, HitayThis study extends a recent anti-windup scheme by using Smith predictor based controller approach and by redesigning the transfer functions within the anti-windup structure. We present simulation studies for a system including time delay and integrator to illustrate that our extended structure successfully accomplish accurate tracking under the saturation nonlinearity.Item Open Access On dwell time minimization for switched delay systems: free-weighting matrices method(IEEE, 2014) Koru, A. T.; Delibaşı, A.; Özbay, HitayIn this paper, we present a quasi-convex minimization method to calculate an upper bound of dwell-time for stability of switched delay systems. Piecewise Lyapunov-Krasovskii functionals are introduced and the upper bound for the derivative of Lyapunov functionals are estimated by free weighting matrices method to investigate non-switching stability of each candidate subsystems. Then, a sufficient condition for dwell-time is derived to guarantee the asymptotic stability of the switched delay system. Once these conditions are represented by a set of linear matrix inequalities (LMIs), dwell time optimization problem can be formulated as a standard quasi-convex optimization problem. Numerical examples are given to illustrate improvements over previously obtained dwell-time bounds.Item Open Access Robust adaptive posicast controller(IFAC, 2015) Yıldız, Yıldıray; Annaswamy, A.Adaptive Posicast Controller that is robust to delay-mismatch is introduced in this paper. Inspired from a recent result on guaranteed delay margins in adaptive control, the original adaptive laws of the above mentioned controller are modified using projection to compensate the uncertainty in the input delay. It is conjectured and shown in simulations that even though the assumed upper bound for the delay value is exceeded, Adaptive Posicast Controller with projection algorithm keeps all the system signals bounded.Item Open Access Stable and robust controller synthesis for unstable time delay systems via ınterpolation and approximation(Elsevier B.V., 2018) Yücesoy, V.; Özbay, HitayIn this paper, we study the robust stabilization of a class of single input single output (SISO) unstable time delay systems by stable and finite dimensional controllers through finite dimensional approximation of infinite dimensional parts of the plant. The plant of interest is assumed to have finitely many non-minimum phase zeros but is allowed to have infinitely many unstable poles in the open right half plane. Conservatism of the proposed methods is illustrated by numerical examples for which infinite dimensional strongly stabilizing controllers are derived in the literature.