Browsing by Subject "Dynamical systems"
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Item Open Access Adaptive control design for nonlinear systems via successive approximations(ASME, 2017) Babaei, N.; Salamcı, M. U.; Karakurt, Ahmet HakanThe paper presents an approach to the Model Reference Adaptive Control (MRAC) design for nonlinear dynamical systems. A nonlinear reference system is considered such that its response is designed to be stable via Successive Approximation Approach (SAA). Having designed the stable reference model through the SAA, MRAC is then formulated for nonlinear plant dynamics with a new adaptation rule to guarantee the convergence of the nonlinear plant response to that of the response of the nonlinear reference model. The proposed design methodology is illustrated with examples for different case studies.Item Open Access Approximate analytic solutions to non-symmetric stance trajectories of the passive Spring-Loaded Inverted Pendulum with damping(Springer Netherlands, 2010) Saranlı U.; Arslan, Ö.; Ankaralı, M. M.; Morgül, Ö.This paper introduces an accurate yet analytically simple approximation to the stance dynamics of the Spring-Loaded Inverted Pendulum (SLIP) model in the presence of non-negligible damping and non-symmetric stance trajectories. Since the SLIP model has long been established as an accurate descriptive model for running behaviors, its careful analysis is instrumental in the design of successful locomotion controllers. Unfortunately, none of the existing analytic methods in the literature explicitly take damping into account, resulting in degraded predictive accuracy when they are used for dissipative runners. We show that the methods we propose not only yield average predictive errors below 2% in the presence of significant damping, but also outperform existing alternatives to approximate the trajectories of a lossless model. Finally, we exploit both the predictive performance and analytic simplicity of our approximations in the design of a gait-level running controller, demonstrating their practical utility and performance benefits. © 2010 Springer Science+Business Media B.V.Item Open Access A beam search algorithm to optimize robustness under random machine breakdowns and processing time variability(Institute of Industrial Engineers, 2007) Gören, S.; Sabuncuoğlu, İhsanThe vast majority of the machine scheduling research assumes complete information about the scheduling problem and a static environment in which scheduling systems operate. In practice, however, scheduling systems are subject to considerable uncertainty in dynamic environments. The ability to cope with the uncertainty in scheduling process is becoming increasingly important in today's highly dynamic and competitive business environments. In the literature, two approaches have appeared as the effective way: reactive and proactive scheduling. The objective in reactive scheduling is to revise schedules as necessary, while proactive scheduling attempts to incorporate future disruptions when generating schedules. In this paper we take a proactive scheduling approach to solve a machine scheduling problem with two sources of uncertainty: processing time variability and machine breakdowns. We define two robustness measures and develop a heuristic based on beam search methodology to optimize them. The computational results show that the proposed algorithms perform significantly better than a number of heuristics available in the literature.Item Open Access The classical SIR model in epidemiology(Romanian Mathematical Society, 2020) Gheondea, AurelianThis is a survey note in which we describe the classical SIR model in mathematical epidemiology, a bit of qualitative analysis, its Euler discretisation, and some simulations.Item Open Access Combined component swapping modularity for a VCT engine controller(ASME, 2010) Çakmakcı, Melih; Ulsoy, A.G.The use of bi-directional communication provides additional design freedom which can be used to maximize the swapping modularity of networked smart components. In this paper, application of a design method for combined swapping modularity of two or more system components is discussed. Development of measures for combined swapping modularity is important to be able to analyze more realistic engineering cases. The combined modularity problem is a more difficult problem compared to the individual component swapping modularity problem. First, two approaches (simultaneous and sequential) for combining component swapping modularity of two or more components are presented. Then these combined modularity approaches are used to design controllers which maximize the component-swapping modularity of the Variable Camshaft Timing (VCT) component (i.e. actuator and sensor) and the Exhaust Gas Oxygen (EGO) sensor for an internal combustion engine. Copyright © 2009 by ASME.Item Open Access A connection management protocol for promoting cooperation in Peer-to-Peer networks(Elsevier BV, 2008-02-05) Karakaya, M.; Körpeoǧlu, I.; Ulusoy, ÖzgürThe existence of a high degree of free riding in Peer-to-Peer (P2P) networks is an important threat that should be addressed while designing P2P protocols. In this paper we propose a connection-based solution that will help to reduce the free riding effects on a P2P network and discourage free riding. Our solution includes a novel P2P connection type and an adaptive connection management protocol that dynamically establishes and adapts a P2P network topology considering the contributions of peers. The aim of the protocol is to bring contributing peers closer to each other on the adapted topology and to push the free riders away from the contributors. In this way contribution is promoted and free riding is discouraged. Unlike some other proposals against free riding, our solution does not require any permanent identification of peers or a security infrastructure for maintaining a global reputation system. It is shown through simulation experiments that there is a significant improvement in performance for contributing peers in a network that applies our protocol. © 2007 Elsevier B.V. All rights reserved.Item Open Access Effective drifts in dynamical systems with multiplicative noise: a review of recent progress(Institute of Physics Publishing, 2016) Volpe, G.; Wehr, J.Noisy dynamical models are employed to describe a wide range of phenomena. Since exact modeling of these phenomena requires access to their microscopic dynamics, whose time scales are typically much shorter than the observable time scales, there is often need to resort to effective mathematical models such as stochastic differential equations (SDEs). In particular, here we consider effective SDEs describing the behavior of systems in the limits when natural time scales become very small. In the presence of multiplicative noise (i.e. noise whose intensity depends upon the system's state), an additional drift term, called noise-induced drift or effective drift, appears. The nature of this noise-induced drift has been recently the subject of a growing number of theoretical and experimental studies. Here, we provide an extensive review of the state of the art in this field. After an introduction, we discuss a minimal model of how multiplicative noise affects the evolution of a system. Next, we consider several case studies with a focus on recent experiments: the Brownian motion of a microscopic particle in thermal equilibrium with a heat bath in the presence of a diffusion gradient; the limiting behavior of a system driven by a colored noise modulated by a multiplicative feedback; and the behavior of an autonomous agent subject to sensorial delay in a noisy environment. This allows us to present the experimental results, as well as mathematical methods and numerical techniques, that can be employed to study a wide range of systems. At the end we give an application-oriented overview of future projects involving noise-induced drifts, including both theory and experiment.Item Open Access Intelligent controlling microbubble radial oscillations by using Slave-Master Feedback control(Elsevier Inc., 2014) Behnia, S.; Yahyavi, M.; Mobadersani F.Dynamics of acoustically driven microbubbles in ultrasonic fields are known to be complex and uncontrollable phenomena indicative of a highly active nonlinear as well as chaotic behavior. In this paper, a method based on Slave-Master Feedback (SMF) to suppress unstable radial oscillations of contrast agents is presented. In the proposed control process, the encapsulated microbubbles as the slave system is coupled with a dynamical system as the master, so that the output of the coupled system is able to produce a stable oscillation. A great virtue of this control technique is its flexibility. In comparison with existing techniques, the present dynamical chaos control method does not need to know more than one variable. The numerical results show its strong impact on reducing the chaotic oscillations to regular ones. © 2014 Elsevier Inc. All rights reserved.Item Open Access Lattice dynamics and elastic properties of lanthanum monopnictides(2008) Gökoǧlu G.; Erkişi, A.In this study, first principles calculation results of the second order elastic constants and lattice dynamics of two lanthanum monopnictides, LaN and LaBi, which crystallize in rock-salt structure (B1 phase), are presented. Calculations were based on plane wave basis sets and pseudopotential methods in the framework of Density Functional Theory (DFT) with generalized gradient approximation. Elastic constants are calculated by tetragonal and orthorhombic distortions on cubic structure. Phonon dispersion spectra was constructed in the linear response approach of the Density Functional Perturbation Theory (DFPT). The complete phonon softening with negative frequencies and large elastic anisotropy were observed for LaN single crystal as a sign of the structural instability. The phonon dispersion curve for LaBi is typical for lanthanum monopnictides and does not show any anomalous physical property. The calculated structural quantities for both LaN and LaBi systems agree well with the available experimental and theoretical data. © 2008 Elsevier Ltd. All rights reserved.Item Open Access A Mathematical Model for Cholesterol Biosynthesis under Nicotine Exposure(Elsevier B.V., 2016) Gölgeli, M.; Özbay, HitayIn this paper, a mathematical model is considered for analyzing the impact of nicotine exposure to cholesterol biosynthesis. The dynamical model is nonlinear. Its equilibrium points are computed and conditions are provided under which a unique locally stable positive equilibrium exists. Moreover, effect of internal time delays on local stability is also investigated.Item Open Access Model based anticontrol of chaos(IEEE, 2003) Morgül, ÖmerWe will consider model based anticontrol of chaotic systems. We consider both continuous and discrete time cases. We first assume that the systems to be controlled are linear and time invariant. Under controllability assumption, we transform these systems into some canonical forms. We assume the existence of chaotic systems which has similar forms. Then by using appropriate inputs, we match the dynamics of the systems to be controlled and the model chaotic systems.Item Open Access A new model of cell dynamics in Acute Myeloid Leukemia involving distributed delays(2012) Avila, J. L.; Bonnet, C.; Clairambault, J.; Özbay, Hitay; Niculescu, S. I.; Merhi, F.; Tang, R.; Marie, J. P.In this paper we propose a refined model for the dynamical cell behavior in Acute Myeloid Leukemia (AML) compared to (Özbay et al, 2012) and (Adimy et al, 2008).We separate the cell growth phase into a sequence of several sub-compartments. Then, with the help of the method of characteristics, we show that the overall dynamical system of equations can be reduced to two coupled nonlinear equations with four internal sub-systems involving distributed delays. © 2012 IFAC.Item Open Access Nonlinear laser lithography for indefinitely large-area nanostructuring with femtosecond pulses(Nature publishing group, 2013) Öktem, B.; Pavlov, I.; Ilday, S.; Kalaycıoǧlu, H.; Rybak, A.; Yavaş, S.; Erdoǧan, M.; Ilday F. Ö.Dynamical systems based on the interplay of nonlinear feedback mechanisms are ubiquitous in nature. Well-understood examples from photonics include mode locking and a broad class of fractal optics, including self-similarity. In addition to the fundamental interest in such systems, fascinating technical functionalities that are difficult or even impossible to achieve with linear systems can emerge naturally from them if the right control tools can be applied. Here, we demonstrate a method that exploits positive nonlocal feedback to initiate, and negative local feedback to regulate, the growth of ultrafast laser-induced metal-oxide nanostructures with unprecedented uniformity, at high speed, low cost and on non-planar or flexible surfaces. The nonlocal nature of the feedback allows us to stitch the nanostructures seamlessly, enabling coverage of indefinitely large areas with subnanometre uniformity in periodicity. We demonstrate our approach through the fabrication of titanium dioxide and tungsten oxide nanostructures, but it can also be extended to a large variety of other materials.