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60th Israel Annual conference on Aerospace Sciences, IACAS 2020

作者： Diepolder, Johannes Ben-Asher, Joseph Z. Piprek, Patrick Holzapfel, Florian Technische Universität München Munich80333 Germany Technion Institute of Technology Haifa3200003 Israel Institute of Flight System Dynamics Faculty of Aerospace Engineering Head of Institute Institute of Flight System Dynamics

In this paper we consider the application of generalized polynomial chaos (gPC) methods for uncertainty quantification in the context of optimal control based flight control law clearance using quasi-linear models. The closed loop aircraft model is assumed to be linear and may be obtained from linearization in a reference flight condition. In addition, nonlinear effects related to actuator rate and position limits are introduced in the analysis, which are crucial for the investigation of worst case inputs. For the presented approach the plant is modeled as uncertain, that is the system matrix depends on uncertain parameters subject to a distribution. Under this type of modeling, stochastic moments of the linearized worst case criterion can be obtained using gPC with a stochastic collocation approach. The example problem considered in this paper investigates the maximum load factor under worst case pilot inputs in the longitudinal plane including rate and position saturations for the elevator servo. In this example, the uncertain plant depends on distributed parameters for pitch damping and pitch stiffness. The mean and standard deviation of the criterion are computed based on the gPC method. The comparison of the results to a Monte Carlo analysis show rapid convergence and excellent correspondence with the values of the estimated stochastic moments. In particular, the presented approach for uncertainty quantification of the criterion under worst case pilot inputs requires only a fraction of the samples needed for standard Monte Carlo analysis. Copyright © IACAS 2020 - 60th Israel Annual conference on Aerospace Sciences. All rights reserved.

关键词： Linearization

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Design of an Enhanced Reconfigurable Chaotic Oscillator using G⁴FET-NDR Based Discrete Map 14

Design of an Enhanced Reconfigurable Chaotic Oscillator usin...

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14th IEEE Dallas Circuits and Systems conference (DCAS)

作者： Hasan, Md Sakib Shanta, Aysha S. Paul, Partha Sarathi Sadia, Maisha Majumder, Md Badruddoja Rose, Garrett S. Univ Mississippi Dept Elect & Comp Engn University MS 38677 USA Univ Tennessee Dept Elect Engn & Comp Sci Knoxville TN 37996 USA

ISBN: (纸本)9781728185101

In this paper, a novel chaotic map is introduced using a voltage controlled negative differential resistance (NDR) circuit composed of an n-channel and a p-channel silicon-on-insulator (SOI) four-gate transistor (G(4)FET). The multiple gates of the G(4)FET are leveraged to create a discrete chaotic map with three bifurcation parameters. The three tunable parameters are the gain of a transimpedance amplifier (TIA), top-gate voltage of n-channel G(4)FET, and top-gate voltage of p-channel G(4)FET. Two methods are proposed for building chaotic oscillators using this discrete map. The effect of altering bifurcation parameters on chaotic operation is illustrated using bifurcation diagrams and Lyapunov exponent. A design methodology for building flexible and reconfigurable logic gate is outlined and the consequent enhancement in functionality space caused by the existence of three independent bifurcation parameters is demonstrated and compared with previous work.

关键词： nonlinear dynamics discrete chaotic map chaos computing SOI G(4)FET VLSI NDR hardware security

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Visualization of amplitude-frequency characteristics of EEG of pathological and cognitive functions of the brain from a position of nonlinear dynamics

Visualization of amplitude-frequency characteristics of EEG ...

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Mechanical Science and Technology Update (MSTU) conference

作者： Krysko, V. A. Papkova, I., V Saltykova, O. A. Yakovleva, T., V Pavlov, S. P. Zhigalov, M., V Petrov, D. Yu Krysko, A., V Yuri Gagarin Saratov State Tech Univ Dept Math & Modelling Polytech Skaya St 77 Saratov 410054 Russia

In recent years, medical imaging methods have been intensively developed to provide comprehensive and extensive data for studying the work of the brain, which makes the present study relevant. The purpose of this work is to develop a new approach for analyzing EEG signals based on nonlinear dynamics methods. To achieve this goal, it is necessary to adapt the methods of nonlinear dynamics to solving EEG analysis tasks. In this paper, the following methods are used: the principal component method for noise clearance, the wavelet transform, the Wolf, Kanz, Rosenstein, neural networks methods to calculate the spectrum of the Lyapunov exponent (LCEs). Studies have shown that the chaos of the schizophrenic's EEG signals is higher than for healthy people. It has been revealed that the best visualization of the amplitude-frequency characteristics of the brain's EEG pathological functions is provided by the Morle and Gauss 32 wavelets.

关键词： Visualization

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On the nonlinear dynamics of coupled micro-resonators 14

On the nonlinear dynamics of coupled micro-resonators

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14th conference on Integrated Optics - Sensors, Sensing Structures, and methods (IOS)

作者： Nguyen Duy Cuong Dinh Xuan Khoa Le Xuan The Tai Nguyen Viet Hung Trippenbach, Marek Ind Univ Vinh 26 Nguyen Thai Hoc St Vinh City Vietnam Vinh Univ 182 Le Duan St Vinh City Vietnam Univ Warsaw Phys Dept Ul Pasteura 5 PL-02093 Warsaw Poland Hanoi Univ Sci & Technol Adv Inst Sci & Technol Hanoi Vietnam

ISBN: (数字)9781510631519

ISBN: (纸本)9781510631519

We present the study of the dynamics of a two-ring waveguide structure with space-dependent coupling, linear gain and nonlinear absorption;the system that can be implemented in polariton condensates, optical waveguides and nanocavities. We find that due to the modulation instability, it is possible to observe several complex nonlinear phenomena, including spontaneous symmetry breaking, stable inhomogeneous states, oscillating states (limit cycle) and even chaotic dynamics. We compare two systems of coupled rings, with one and two symmetrically located coupling centres.

关键词： nonlinear dynamics microcavities modulational instability chaos

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Computation of Positively Invariant Sets of the Duffing System and the nonlinear Pendulum under Bounded Excitation

Computation of Positively Invariant Sets of the Duffing Syst...

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International conference on Control, Decision and Information Technologies (CoDIT)

作者： Klaus Röbenack Daniel Gerbet Institute of Control Theory Technische Universität Dresden Dresden Germany

ISBN: (数字)9781728159539

ISBN: (纸本)9781728159546

The Duffing system and the nonlinear pendulum are a comparatively simple dynamical systems that can generate complex dynamics such as subharmonics, intermittency and chaos. Both system has been used to model a variety of technical systems, where nonlinear oscillations occur. The dynamics can usually not be computed analytically but only simulated numerically. In this paper we provide a method to compute analytically exact bounds on the trajectories of the excited Duffing system and the nonlinear pendulum. These computations are carried out using quantifier elimination.

关键词： Mathematical model Information technology Computational modeling Stability analysis Power system dynamics nonlinear dynamical systems Lyapunov methods

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Bifurcation and chaos of Rotating Inextensional Ring 2

Bifurcation and Chaos of Rotating Inextensional Ring

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2nd International conference on Modeling in Mechanics and Materials

作者： Wang, Ligang Wang, Jiaoyang Asokanthan, S.F. School of Science Harbin Engineering University Harbin150001 China Department of Mechanical and Materials Engineering University of Western Ontario LondonONN6A 5B9 Canada

In this paper, the nonlinear dynamics of the inextensional ring structure is investigated. Based on the elasticity theory and the assumption of the inextension of ring, a dynamical model of the ring is established considering the elastic support, the external load and the damping. Then, according to the Galerkin method, the nonlinear mode functions of inextensional ring are used to obtain the order differential equations of ring. Finally, the numerical simulation is carried out and the nonlinear behavior, such as double-period bifurcation, quasi-periodic motion and chaos, is discussed. And the effect of the disturbance of the rotating velocity on the nonlinear behavior of ring is investigated. © Published under licence by IOP Publishing Ltd.

关键词： Galerkin methods

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Chaotic dynamics size-dependent flexible rectangular flat shells 12

Chaotic dynamics size-dependent flexible rectangular flat sh...

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12th International conference on Mesh methods for Boundary - Value Problems and Applications

作者： Krysko, V. A-Ju Papkova, I. V. Krysko, V. A. 77 Politech Skaya St Saratov 410054 Russia

In this paper was constructed mathematical model nonlinear vibrations flexible size-dependent spherical rectangular shell. Sheath viewed as a continuum Cosserat with constrained rotation of the particles (pseudo-continuum). The equations of motion of the shell element and the boundary conditions are obtained from the Ostrogradski-Hamilton energy principle on the basis of Kirchhoff-Love kinematic hypotheses. The geometric nonlinearity is taken into account by the model of T. von Karman. The equations of motion of the shell element in the work are written in a mixed form. A system of nonlinear partial differential equations reduces to an ODE system by the Bubnov-Galerkin method in higher approximations. The system is regarded as a system with an infinite number of degrees of freedom. The Cauchy problems are solved by methods of Runge-Kutta type from the second to the eighth order of accuracy. The convergence of each method depending on the time step and the number of terms in the expansion series of functions in the Bubnov-Galerkin method. The influence of the sizedependent parameter to the nonlinear dynamics of the rectangular plane into a spherical shell. The largest Lyapunov exponent is determined using three methods: Wolf, Kantz, and Rosenstein to prove the truth of chaos.

关键词： Equations of motion

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Study of chaotic dynamics of the parameters of biomedical systems

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AIP conference Proceedings 2022年第1期2467卷

作者： V. V. Grigorenko S. A. Lysenkova N. B. Nazina A. A. Egorov Surgut State University 1 Lenina st. Surgut 628400 Russia

In the article, the study of chaotic dynamics of complex non-stationary biomedical systems, and in particular, a special type of chaos arising in the parameters that describe these systems is discussed. A special type of chaos is understood as the existence of irreproducible aperiodic regimes in the dynamic systems: x(t0) = var and f(xi) = var, when t → ∞. In contrast to the Lorenz deterministic chaos, in such systems not only the process is irreproducible, but the initial state of the system is also always irreproducible x(t0). The study is based on the use of methods of nonparametric mathematical statistics, methods of nonlinear dynamics (calculation of the senior Lyapunov exponent), as well as calculation of the parameters of quasi-attractors, which qualitatively and quantitatively describe the chaotic dynamics of biomedical signals. Using the analysis of autocorrelation, it was shown that the parameters of biomedical systems, using the example of cardio signal elements (time series of cardio intervals) of the cardiovascular system, have a strictly chaotic structure and a non- linear trend line. The calculation of the senior Lyapunov exponent showed that there is a constant change of sign (+, -, 0) at different time intervals of the cardio signal, which also proves the presence of chaos, different from Lorentz chaos, which has a positive sign for the senior Lyapunov exponent, as well as a repeated initial state of the system x(t0). A method has been developed that made it possible to quantitatively and qualitatively describe the chaotic dynamics of the behavior of the state vector of the system, obtain objective information about changes in the functional state of the system, and also warn about these changes in time (if pathologies), what creates conditions for physiological monitoring of the status of the functional systems of the human body.

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Inverse Stochastic Quadcopter Trajectory Generation using Flat Inverse dynamics and Polynomial chaos Uncertainty Propagation 6

Inverse Stochastic Quadcopter Trajectory Generation using Fl...

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6th International conference on Control, Decision and Information Technologies (CoDIT)

作者： Lefebvre, Tom De Belie, Frederik Crevecoeur, Guillaume Univ Ghent Dept Elect Energy Met Mech Construct & Syst B-9052 Ghent Belgium Flanders Make EEDT Decis & Control Leuven Belgium

ISBN: (纸本)9781728105215

We propose a series of methods to generate inverse stochastic trajectories given parametric model uncertainties. The methods are applied for the generation of robust quadcopter trajectories. Our aim is to generate unique reference trajectories such that the corresponding uncertain control policies are less sensitive to parameter variations. Such robust trajectories exhibit interesting properties w.r.t. to tracking. The proposed methods can be applied on any system represented by nonlinear dynamics given that an inverse dynamic model is available, be it in a flat interpretation as is the case for quadcopters. Results show a decrease of 78% of parameter induced policy uncertainty when compared with nominal trajectories.

关键词： Trajectory Stochastic processes Uncertainty nonlinear dynamical systems Optimization Market research Numerical models

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Refined nonlinear Gaussian Quadrature Filter

Refined Nonlinear Gaussian Quadrature Filter

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American Control conference

作者： Bin Jia Ming Xin Intelligent Fusion Technology. Inc. Germantown Maryland USA University of Missouri Columbia MO 65211 USA

ISBN: (纸本)9781538679012;9781538679265

Gaussian filters have been widely used in various applications due to their simplicity and effectiveness. For nonlinear estimation problems, Gaussian filters are usually developed from numerical quadrature rules to approximate the Gaussian weighted integrals in nonlinear filtering algorithms. However, the Gaussian assumption may not be viable after propagation of quadrature through nonlinear dynamics, which leads to degraded quadrature and inaccurate update of mean and covariance. In this paper, we propose a new refined nonlinear Gaussian quadrature filter in which the predicted probability density function (PDF) is not assumed Gaussian. A set of Monte Carlo samples are first propagated through nonlinear dynamics. The statistic moments can be directly obtained from the propagated Monte Carlo samples. The refined quadrature points and weights are generated from the moments' information using the arbitrary polynomial chaos method. Since the refined quadrature points contain higher order statistic information of the propagated PDF, they have the potential to better represent the uncertainty and provide a more accurate estimate. Numerical examples show the effectiveness of the proposed filter.

关键词： chaos higher order statistics integration Monte Carlo methods nonlinear estimation nonlinear filters polynomials probability

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