Browsing by Subject "Stabilization"
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Item Open Access Analysis and design of switching and fuzzy systems(Bilkent University, 2002-09) Akgül, MuratIn this thesis we consider the controller design problems for switching and fuzzy systems. In switching systems, the system dynamics and/or control input take dierent forms in different parts of the underlying state space. In fuzzy systems, the system dynamics and/or control input consist of certain logical expressions. From this point of view, it is reasonable to expect certain similarities between these systems. We show that under certain conditions, a switching system may be converted into an equivalent fuzzy system. While the changes in the system variables in a switching system may be abrupt, such changes are typically smooth in a fuzzy system. Therefore obtaining such an equivalent fuzzy system may inherit the stability properties of the original switching system while smoothing the system dynamics. Motivated from this idea we propose various switching strategies for certain classes of nonlinear systems and provide some stability results. Due to the dificulties in designing such switching rules for nonlinear systems, most of the results are developed for certain specific type of systems. Due to the logical structure, obtaining rigorous stability results are very difficult for fuzzy systems. We propose a fuzzy controller design method and prove a stability result under certain conditions. The proposed method may also be applied to function approximation. We also consider a different stabilization method, namely phase portrait matching, in which the main aim is to choose the control input appropriately so that the dynamics of the closed-loop system is close to a given desired dynamics. If this is achieved, then the phase portrait of the closed-loop system will also be close to a desired phase portrait. We propose various schemes to achieve this task.Item Open Access Decentralized strong stabilization problem(IEEE, 1992-06) Özgüler, A. Bülent; Ünyelioğlu, Konur A.In the decentralized strong stabilization problem for linear time-invariant finite-dimensional systems, the objective is to stabilize a given plant using a stable decentralized controller. A solvability condition for this problem is given in terms of a parity interlacing property which is to be satisfied among the real unstable poles and real unstable decentralized blocking zeros of the plant. The problem of synthesizing decentralized stabilizing controllers with minimum number of unstable poles is also solved.Item Open Access Dynamic output feedback stabilization of switched linear systems with delay via a trajectory based approach(Elsevier, 2018) Ahmed, Saeed; Mazenc, F.; Özbay, HitayA new technique is proposed to construct observers and to achieve output feedback stabilization of a class of continuous-time switched linear systems with a time-varying delay in the output. The delay is a piecewise continuous bounded function of time and no constraint is imposed on the delay derivative. For stability analysis, an extension of a recent trajectory based approach is used; this is fundamentally different from classical Lyapunov function based methods. A stability condition is given in terms of the upper bound on the time-varying delay to ensure global uniform exponential stability of the switched feedback system. The main result applies in cases where some of the subsystems of the switched system are not stabilizable and not detectable.Item Open Access Encapsulation of vanillin/cyclodextrin inclusion complex in electrospun polyvinyl alcohol (PVA) nanowebs: prolonged shelf-life and high temperature stability of vanillin(2012-08) Kayaci, F.; Uyar, TamerWe produced functional nanowebs, containing vanillin, having prolonged shelf-life and high temperature stability facilitated by cyclodextrin (CD) inclusion complexation. Polyvinyl alcohol (PVA) nanowebs incorporating vanillin/cyclodextrin inclusion complex (vanillin/CD-IC) were produced via electrospinning technique. The vanillin/CD-IC was prepared with three types of CDs; α-CD, β-CD and γ-CD to find out the most favourable CD type for the stabilization of vanillin. PVA/vanillin/CD-IC nanofibres, having fibre diameters around ∼200 nm, were successfully electrospun from aqueous mixture of PVA and vanillin/CD-IC. Our results indicated that vanillin with enhanced durability and high temperature stability was achieved for PVA/vanillin/CD-IC nanowebs due to complexation of vanillin with CD, whereas the PVA nanofibres without CD-IC could not effectively preserve the vanillin. Additionally, we observed that PVA/vanillin/γ-CD-IC nanoweb was more effective for the stabilization and slow release of vanillin suggesting that the strength of interaction between vanillin and the γ-CD cavity is stronger when compared to α-CD and β-CD. © 2012 Elsevier Ltd. All rights reserved.Item Open Access An Evaluation of the Turkish stabilization and liberalization policies since 1980, in the light of Southern Cone experience(Bilkent University, 1989) Çakal, RecepPurpose of this study is to compare the stabilization and liberalization policies implemented in the Southern Cone countries and Turkey. It investigates these policies in a comparative way, and evaluates the Turkish stabilization and liberalization policies in the light of the failure of the Southern Cone reform policies. Policies that were implemented show close similarities in all countries with slight differences, Argentina and Uruguay, for example, opened their capital account before liberalizing their trade. So was the outcomes of the reform policies. All countries initially were able to eliminate external imbalances, to moderate high rates of inflation, and also to achieve high rates of growth compared to prereform periods. However,the shift in stabilization policies in the form of using the exchange rate determination policy (tablita) as an anti-inflationary tool created inconsistencies and undermined the credibility of reform policies in the Southern Cone. Comparing with the Southern Cone, developments aftermath of the reform policies were in favor of Turkey in some aspects. The most obvious one was the higher performance in exports. Nevertheless, in some other aspects,developments resemble to the Southern Cone, such as unsustained monetary and fiscal restrictions and consequently, reemerged high rates of inflation was the common characteristic in all countries. In conclusion, at present, Turkey is at the edge of the success or failure in terms of reform policies that were implemented since 1980, and the success could be realized if corrective actions are taken immediately.Item Open Access Finite time estimation through a continuous-discrete observer(John Wiley and Sons, 2018) Mazenc, F.; Ahmed, S.; Malisoff, M.We study two broad classes of nonlinear time-varying continuous-time systems with outputs. For the first class, we build an observer in the case where a state dependent disturbance affects the linear approximation. When the disturbances are the zero functions, our observer provides exact values of the state at all times larger than a suitable finite time, and it provides an approximate estimate when there are nonzero disturbances, so our observers are called finite time observers. We use this construction, which is of interest for its own sake, to design a globally exponentially stabilizing dynamic output feedback for a family of nonlinear systems whose outputs are only available on some finite time intervals. Our simulations illustrate the efficacy of our methods.Item Open Access Fixed order controller design via parametric methods(Bilkent University, 2003) Saadaoui, KarimIn this thesis, the problem of parameterizing stabilizing fixed-order controllers for linear time-invariant single-input single-output systems is studied. Using a generalization of the Hermite-Biehler theorem, a new algorithm is given for the determination of stabilizing gains for linear time-invariant systems. This algorithm requires a test of the sign pattern of a rational function at the real roots of a polynomial. By applying this constant gain stabilization algorithm to three subsidiary plants, the set of all stabilizing first-order controllers can be determined. The method given is applicable to both continuous and discrete time systems. It is also applicable to plants with interval type uncertainty. Generalization of this method to high-order controller is outlined. The problem of determining all stabilizing first-order controllers that places the poles of the closed-loop system in a desired stability region is then solved. The algorithm given relies on a generalization of the Hermite-Biehler theorem to polynomials with complex coefficients. Finally, the concept of local convex directions is studied. A necessary and sufficient condition for a polynomial to be a local convex direction of another Hurwitz stable polynomial is derived. The condition given constitutes a generalization of Rantzer’s phase growth condition for global convex directions. It is used to determine convex directions for certain subsets of Hurwitz stable polynomials.Item Open Access Further stability results for a generalization of delayed feedback control(Springer, 2012-08-01) Morgül, Ö.In this paper, we consider the stabilization of unstable periodic orbits for one-dimensional and discrete time chaotic systems. Various control schemes for this problem are available and we consider a recent generalization of delayed control scheme. We prove that if a certain condition, which depends only on the period number, is satisfied then the stabilization is always possible. We will also present some simulation results.Item Open Access Global stabilization via local stabilizing actions(Institute of Electrical and Electronics Engineers, 2006) Özgüler, A. B.Stabilization of a linear, time-invariant system via stabilization of its main diagonal subsytems is the underlying problem in all diagonal dominance techniques for decentralized control. In these techniques as well as all Nyquist-based techniques, sufficient conditions are obtained under the assumption that the collection of the unstable poles of all diagonal subsystems is the same as the unstable poles of the overall system. We show that this assumption is by itself enough to construct a solution to the problem at least in cases where the diagonal subsystems have disjoint poles. © 2006 IEEE.Item Open Access High energy dissipative raman soliton laser through XPM stabilization(Optical Society of America (OSA), 2015-10) Ergeçen, E.; Tegin, Uğur; Elahi, Parviz; Şenel, Ç.; İlday, F. ÖmerDispersion, nonlinearity and gain determine the intracavity pulse behaviour. We show that pump depletion and XPM play a significant role in the stabilization of high energy dissipative Raman solitons. Using this theoretical knowledge, we predict and demonstrate 7-nJ femtosecond pulses at 1120 nm. © OSA 2015.Item Open Access Local convex directions(IEEE, 2001) Özgüler, Arif Bülent; Saadaoui, KarimA proof of a strengthened version of the phase growth condition for Hurwitz stable polynomials is given. Based on this result, a necessary and sufficient condition for a polynomial p(s) to be a local convex direction for a Hurwitz stable polynomial q(s) is obtained. The condition is in terms of polynomials associated with the even and odd parts of p(s) and q(s).Item Open Access Magnetic resonance electrical impedance tomography (MREIT) based on the solution of the convection equation using FEM with stabilization(Institute of Physics Publishing, 2012-07-27) Oran, O. F.; Ider, Y. Z.Most algorithms for magnetic resonance electrical impedance tomography (MREIT) concentrate on reconstructing the internal conductivity distribution of a conductive object from the Laplacian of only one component of the magnetic flux density (∇ 2B z) generated by the internal current distribution. In this study, a new algorithm is proposed to solve this ∇ 2B z-based MREIT problem which is mathematically formulated as the steady-state scalar pure convection equation. Numerical methods developed for the solution of the more general convectiondiffusion equation are utilized. It is known that the solution of the pure convection equation is numerically unstable if sharp variations of the field variable (in this case conductivity) exist or if there are inconsistent boundary conditions. Various stabilization techniques, based on introducing artificial diffusion, are developed to handle such cases and in this study the streamline upwind Petrov-Galerkin (SUPG) stabilization method is incorporated into the Galerkin weighted residual finite element method (FEM) to numerically solve the MREIT problem. The proposed algorithm is tested with simulated and also experimental data from phantoms. Successful conductivity reconstructions are obtained by solving the related convection equation using the Galerkin weighted residual FEM when there are no sharp variations in the actual conductivity distribution. However, when there is noise in the magnetic flux density data or when there are sharp variations in conductivity, it is found that SUPG stabilization is beneficial.Item Open Access Monoid actions, their categorification and applications(Bilkent University, 2016-12) Erdal, Mehmet AkifWe study actions of monoids and monoidal categories, and their relations with (co)homology theories. We start by discussing actions of monoids via bi-actions. We show that there is a well-defined functorial reverse action when a monoid action is given, which corresponds to acting by the inverses for group actions. We use this reverse actions to construct a homotopical structure on the category of monoid actions, which allow us to build the Burnside ring of a monoid. Then, we study categorifications of the previously introduced notions. In particular, we study actions of monoidal categories on categories and show that the ideas of action reversing of monoid actions extends to actions of monoidal categories. We use the reverse action for actions of monoidal categories, along with homotopy theory, to define homology, cohomology, homotopy and cohomotopy theories graded over monoidal categories. We show that most of the existing theories fits into our setting; and thus, we unify the existing definitions of these theories. Finally, we construct the spectral sequences for the theories graded over monoidal categories, which are the strongest tools for computation of cohomology and homotopy theories in existence.Item Open Access Neoliberal global remedies: From speculative-led growth to IMF-led crisis in Turkey(2006) Yeldan, E.Turkey experienced a severe economic and political crisis in November 2000, and again in February 2001. The IMF has been involved with the macro management of the Turkish economy both prior to and after the crisis, and provided financial assistance of $20.4 billion, net, between 1999 and 2003. The official stance is that the crisis was the result of the failure of the public sector to maintain the austerity targets and the failure to fully implement the free market rationale of globalization. I argue in this article, however, that contrary to the official wisdom, the current economic and political crisis is not the end result of a set of technical errors or administrative mismanagement unique to Turkey, but is the result of a series of pressures emanating from the process of integration with the global capital markets. I document the fragility indicators of the Turkish financial and fiscal system, and show that the IMF program led to an increase in vulnerability of the financial system throughout 2000-2001. I further argue that the recent wave of structural reforms destined for stability and credibility serve, in fact, mainly the interests of foreign finance capital, and primarily aim at securing the debt obligations of the Turkish arbiters. © 2006 Union for Radical Political Economics.Item Open Access A new method for the computation of all stabilizing controllers of a given order(Taylor & Francis, 2005) Saadaoui, K.; Özgüler, A. B.A new method is given for computing the set of all stabilizing controllers of a given order for linear, time invariant, scalar plants. The method is based on a generalized Hermite-Biehler theorem and the successive application of a modified constant gain stabilizing algorithm to subsidiary plants. It is applicable to both continuous and discrete time systems.Item Open Access A nonlinear control scheme for discrete time chaotic systems(The International Federation of Automatic Control, 2012-06) Morgül, ÖmerIn this paper we consider the stabilization problem of unstable periodic orbits of discrete time chaotic systems. We consider both one dimensional and higher dimensional cases. We propose a nonlinear feedback law and present some stability results. These results show that for period 1 all hyperbolic periodic orbits can be stabilized with the proposed method. By restricting the gain matrix to a special form we obtain some novel stability results. The stability proofs also give the possible feedback gains which achieve stabilization. We also present some simulation results.Item Open Access Observer design and output feedback Stabilization of time varying systems(Bilkent University, 2018-07) Ahmed, SaeedWe study observer design and output feedback stabilization of switched and nonlinear time varying systems. To establish the stability of feedback switched systems with delay, we develop a new extension of a recently proposed trajectory based approach which is fundamentally different from classical Lyapunov function based methods. This new extension of trajectory based approach, which is of interest for its own sake, can be applied to a wide range of time varying systems with time varying delays and it tackles the issue of finding appropriate Lyapunov functions to establish stability results. Our stabilization methodology does not require stabilizability and detectability of all of the subsystems of the switched system and we do not impose any constraint on the derivative of the time varying delay. For nonlinear time varying systems, we build a new type of finite-time smooth observer in the case where a state dependent disturbance affects the linear approximation. We combine this finite time observer design and a switched systems approach to develop stabilizing feedbacks for nonlinear time varying systems whose outputs are only available on some finite time intervals. Again, we use an extension of the trajectory based approach to conclude the stability of the closed-loop system. Motivated by the fact that the measured components of the state do not need to be estimated, we also construct reduced order finite time observers for a broad class of nonlinear time varying systems. We show how these reduced order finite time observers can be used to solve dynamic output feedback stabilization problem for multiple input, multiple output nonlinear time varying systems. Finally, we design a finite time observer to estimate the exact state of a continuous-time linear time varying system from sampled output in the presence of a piecewise continuous disturbance.Item Open Access Observer-based control of a class of chaotic systems(Elsevier, 2001) Solak, E.; Morgül, O.; Ersoy, U.We consider the control of a class of chaotic systems, which covers the forced chaotic oscillators. We focus on two control problems. The first one is to change the dynamics of the system to a new one which exhibits a desired behavior, and the second one is the tracking problem, i.e., to force the solutions of the chaotic system to track a given trajectory. To solve these problems we use observers which could be used to estimate the unknown states of the system to be controlled. We apply the proposed method to the control of Duffing equation and the Van der Pol oscillator and present some simulation results. © 2001 Elsevier Science B.V.Item Open Access On the set of all stabilizing first-order controllers(IEEE, 2003) Saadaoui, Karim; Özgüler, Arif BülentA computational method is given for determining the set of all stabilizing proper first-order controllers for finite dimensional, linear, time invariant, scalar plants. The method is based on a generalized Hermite-Biehler theorem.Item Open Access On the stabilization of a flexible beam with a tip mass(Society for Industrial and Applied Mathematics, 1998-11) Conrad, F.; Morgül, Ö.We study the stability of a flexible beam that is clamped at one end and free at the other; a mass is also attached to the free end of the beam. To stabilize this system we apply a boundary control force at the free end of the beam. We prove that the closed-loop system is well-posed and is exponentially stable. We then analyze the spectrum of the system for a special case and prove that the spectrum determines the exponential decay rate for the considered case.