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Quasipolynomial approach to simultaneous robust control of time-delay systems
Nikolaj Semenič, Andrej Sarjaš, Amor Chowdhury, Rajko Svečko, izvirni znanstveni članek

Opis: A control law for retarded time-delay systems is considered, concerning infinite closed-loop spectrum assignment. An algebraic method for spectrum assignment is presented with a unique optimization algorithm for minimization of spectral abscissa and effective shaping of the chains of infinitely many closed-loop poles. Uncertainty of plant delays of a certain structure is considered in a sense of a robust simultaneous stabilization. Robust performance is achieved using mixed sensitivity design, which is incorporated into the addressed control law.
Ključne besede: time-delay systems, simultaneous robust control, algorithm
Objavljeno: 15.06.2017; Ogledov: 504; Prenosov: 286
.pdf Celotno besedilo (2,32 MB)
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Qualitative Studies of Some Polynomial Systems of Ordinary Differential Equations
Maša Dukarić, 2016, doktorska disertacija

Opis: This doctoral dissertation is devoted to the studies of some qualitative properties of certain polynomial systems of ordinary differential equations. The main problems that are considered in this thesis are the problems of integrability and cyclicity. Some results on the classification of the global phase portraits of a family of cubic systems are presented as well. In the first chapter basic notions and results of the qualitative theory of systems of ODE's are introduced. Since one of important tools for our study of these problems is the commutative computational algebra, some main notions and properties of polynomial ideals and their varieties, including various algorithms related to them, are also presented in the introduction. In the second chapter methods for investigation of trajectories near degenerated singularities are presented. They are further used for the classification of global phase portraits of a family of cubic systems with the nilpotent center at the origin. In the third chapter the main problem of these thesis is studied, the problem of integrability. The problem of integrability which is connected to the problem of distinguishing between a center and a focus is studied for two different families of cubic polynomial systems of ODE's. With the computational algebra approach the necessary conditions for the existence of the first integral of these systems were obtained. For all but one condition was proven, using various approaches, the existence of the first integrals. The center problem for the real systems can be generalized to the complex systems. The origin of the system obtained after the complexification of the real system is the so-called 1:-1 resonant singular point, from which one additional generalization follows. This is the generalization to the p:-q resonant center. In the third chapter the :-3 resonant singular point of a quadratic family of complex systems is studied. The fourth chapter is devoted to the study of the problem of integrability of a three dimensional polynomial system with quadratic nonlinearities. The problem of existence of two independent first integrals and the existence of one first integral in the system was investigated. In the last chapter local bifurcations of limit cycles of a family of cubic systems are studied. Estimations for the number of limit cycles bifurcated from each components of the center variety are obtained.
Ključne besede: planar systems of ODE's, higher dimensional systems of ODE's, phase portrait, nilpotent center, limit cylces, Poincaré compactification, center problem, Bautin ideal, focus quantities, time-reversibility, integrability problem, Darboux method, linearizability, limit cycle, cyclicity
Objavljeno: 19.07.2016; Ogledov: 1160; Prenosov: 129
.pdf Celotno besedilo (12,26 MB)

Co-processor for microkernel OS services
Domen Verber, 2011, objavljeni znanstveni prispevek na konferenci

Ključne besede: operating systems, embedded systems, real time, task scheduling, FPGA
Objavljeno: 10.07.2015; Ogledov: 586; Prenosov: 78
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Implementation of hard real-time embedded control systems
Matjaž Colnarič, Domen Verber, Roman Gumzej, Wolfgang A. Halang, 1998, samostojni znanstveni sestavek ali poglavje v monografski publikaciji

Opis: Although the domain of hard real-time systems has been thoroughly elaborated in the academic sphere, embedded computer control systems - being an important in mechatronic design - are seldom dealt with consistemntly. Often, off-the-shelf computer systems are used, with no guarantee that they will be able to meet the requirements specified. In this paper, a design for embedded control systems is presented. particulary, the paper deals with the hardware architecture and design details, the operating sustem, and the high-level real-time language support. It is shown how estimates of process run-times necessary for schedulability analysis can be acquired on the basis of deterministic behavior of the hardware platform.
Ključne besede: kontrolni sistemi, realni čas, mikrokontrolerji, programski jeziki, embedded compuer control systems, hard real-time systems, microcontrollers, transputers, earliest-deadline-first scheduling, real-time programming languages
Objavljeno: 10.07.2015; Ogledov: 662; Prenosov: 82
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Statistical Properties of Time-dependent Systems
Diego Fregolente Mendes De Oliveira, 2012, doktorska disertacija

Opis: In the dissertation I have dealt with time-dependent (nonautonomous) systems, the conservative (Hamiltonian) as well as dissipative, and investigated their dynamical and statistical properties. In conservative (Hamiltonian) time-dependent systems the energy is not conserved, whilst the Liouville theorem about the conservation of the phase space volume still applies. We are interested to know, whether the system can gain energy, and whether this energy can grow unbounded, up to infinity, and we are interested in the system's behaviour in the mean, as well as its statistical properties. An example of such a system goes back to the 1940s, when Fermi proposed the acceleration of cosmic rays (in the first place protons) upon the collisions with moving magnetic domains in the interstellar medium of our Galaxy, and in other galaxies. He then proposed a simple mechanical one-dimensional model, the so-called Fermi-Ulam Model (FUM), where a point particle is moving between two rigid walls, one being at rest and the other one oscillating. If the oscillation is periodic and smooth, it turned out in a nontrivial way, which is, in the modern era of understanding the chaotic dynamical systems, well understood, namely that the unbounded increasing of the energy (the so-called Fermi acceleration) is not possible, due to the barriers in form of invariant tori, which partition the phase space into regions, between which the transitions are not possible. The research has then been extended to other simple dyanamical systems, which have complex dynamics. The first was so-called bouncer model, in which a point particle bounces off the oscillating platform in a gravitational field. In this simple system the Fermi acceleration is possible. Later the research was directed towards two-dimensional billiard systems. It turned out that the Fermi acceleration is possible in all such systems, which are at least partially chaotic (of the mixed type), or even in a system that is integrable as static, namely in case of the elliptic billiard. (The circle billiard is an exception, because it is always integrable, as the angular momentum is conserved even in time-dependent case.) The study of time-dependent systems has developed strongly worldwide around the 1990s, in particular in 2000s, and became one of the central topics in nonlinear dynamics. It turned out, quite generally, but formal and implicit, in the sense of mathematical existence theorems, that in nonautonomous Hamilton systems the energy can grow unbounded, meaning that the system ``pumps" the energy from the environment with which it interacts. There are many open questions: how does the energy increase with time, in particular in the mean of some representative ensemble of initial conditions (typically the phase space of two-dimensional time-dependent billiards is four-dimensional.) It turned out that almost everywhere the power laws apply, empirically, based on the numerical calculations, but with various acceleration exponents. If the Fermi acceleration is not posssible, like e.g. in the FUM, due to the invariant tori, then after a certain time of acceleration stage the crossover into the regime of saturation takes place, whose characteristics also follow the power laws. One of the central themes in the dissertation is the study of these power laws, their critical exponents, analytical relationships among them, using the scaling analysis (Leonel, McClintock and Silva, Phys. Rev. Lett. 2004). Furthermore, the central theme is the question, what happens, if, in a nonautonomous Hamilton system which exhibits Fermi acceleration, we introduce dissipation, either at the collisions with the walls (collisional dissipation) or during the free motion (in-flight dissipation, due to the viscosity of the fluid or the drag force etc.). Dissipation typically transforms the periodic points into point attractors and chaotic components into chaotic attractors. The Fermi acceleration is always suppressed. We are interested in the phase portraits of
Ključne besede: nonlinear dynamics, dynamical systems, conservative and dissipative systems, time-dependent systems, Fermi acceleration, billiards, kicked systems, chaos, chaotic and periodic attractors, bifurcations, boundary crisis
Objavljeno: 19.09.2012; Ogledov: 2302; Prenosov: 100
.pdf Celotno besedilo (16,09 MB)

Introducing nonlinear time series analysis in undergraduate courses
Matjaž Perc, 2006, strokovni članek

Opis: This article is written for undergraduate students and teachers who would like to get familiar with basic nonlinear time series analysis methods. We present a step-by-step study of a simple example and provide user-friendly programs that allow an easy reproduction of presented results. In particular, we study an artificial time series generated by the Lorenz system. The mutual information and false nearest neighbour method are explained in detail, and used to obtain the best possible attractor reconstruction. Subsequently, the times series is tested for stationarity and determinism, which are both important properties that assure correct interpretation of invariant quantities that can be extracted from the data set. Finally, as the most prominent invariant quantity that allows distinguishing between regular and chaotic behaviour, we calculate the maximal Lyapunov exponent. By following the above steps, we are able to convincingly determine that the Lorenz system is chaotic directly from the generated time series, without the need to use the differential equations. Throughout the paper, emphasis on clear-cut guidance and a hands-on approach is given in order to make the reproduction of presented results possible also for undergraduates, and thus encourage them to get familiar with the presented theory.
Ključne besede: nonlinear systems, nonlinear time series analyses, physics education
Objavljeno: 07.06.2012; Ogledov: 983; Prenosov: 23
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Singing of Neoconocephalus robustus as an example of deterministic chaos in insects
Tina P. Benko, Matjaž Perc, 2007, izvirni znanstveni članek

Opis: We use nonlinear time series analysis methods to analyse the dynamics of the sound-producing apparatus of the katydid Neoconocephalus robustus. We capture the dynamics by analysing a recording of the singing activity. First, we reconstruct the phase space from the sound recording and test it against determinism and stationarity. After confirming determinism and stationarity, we show that the maximal Lyapunov exponent of the series is positive, which is a strong indicator for the chaotic behaviour of the system. We discuss that methods of nonlinear time series analysis can yield instructive insights and foster the understanding of acoustic communication among insects.
Ključne besede: chaotic systems, chaos, time series, time series analyses, insect sounds, katydid
Objavljeno: 07.06.2012; Ogledov: 1291; Prenosov: 314
.pdf Celotno besedilo (1,05 MB)
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Establishing the stochastic nature of intracellular calcium oscillations from experimental data
Matjaž Perc, Anne K. Green, C. Jane Dixon, Marko Marhl, 2008, izvirni znanstveni članek

Opis: Calcium has been established as a key messenger in both intra- and intercellular signaling. Experimentally observed intracellular calcium responses to different agonists show a variety of behaviors from simple spiking to complex oscillatory regimes. Here we study typical experimental traces of calcium oscillations in hepatocytes obtained in response to phenylephrine and ATP. The traces were analyzed with methods of nonlinear time series analysis in order to determine the stochastic/deterministic nature of the intracellular calcium oscillations. Despite the fact that the oscillations appear, visually, to be deterministic yet perturbed by noise, our analyses provide strong evidence that the measured calcium traces in hepatocytes are prevalently of stochastic nature. In particular, bursting calcium oscillations are temporally correlated Gaussian series distorted by a monotonic, instantaneous, time-independent function, whilst the spiking behavior appears to have a dynamical nonlinear component whereby the overall determinism level is still low. The biological importance of this finding is discussed in relation to the mechanisms incorporated in mathematical models as well as the role of stochasticity and determinism at cellular and tissue levels which resemble typical statistical and thermodynamic effects in physics.
Ključne besede: dynamic systems, stochastic processes, cellular signaling, calcium oscillations, time series analyses, noise, temporal correlation
Objavljeno: 07.06.2012; Ogledov: 1252; Prenosov: 103
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