Search results for: sparse identification of dynamical systems

Authors: Javad Khazaei, Rick Blum

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Distributed control is an efficient and flexible approach for coordination of multi-agent systems. One of the main challenges in designing a distributed controller is identifying the governing dynamics of the dynamical systems. Data-driven system identification is currently undergoing a revolution. With the availability of high-fidelity measurements and historical data, model-free identification of dynamical systems can facilitate the control design without tedious modeling of high-dimensional and/or nonlinear systems. This paper develops a distributed control design using consensus theory for linear and nonlinear dynamical systems using sparse identification of system dynamics. Compared with existing consensus designs that heavily rely on knowing the detailed system dynamics, the proposed model-free design can accurately capture the dynamics of the system with available measurements and input data and provide guaranteed performance in consensus and tracking problems. Heterogeneous damped oscillators are chosen as examples of dynamical system for validation purposes.

Keywords: consensus tracking, distributed control, model-free control, sparse identification of dynamical systems

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Authors: Vandana N. Purav

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The Dynamical systems concept is a mathematical formalization for any fixed rule that describes the time dependence of a points position in its ambient space. e.g. pendulum of a clock, the number of fish each spring in a lake, the number of rabbits spring in an enclosure, etc. The Dynamical system theory used to describe the complex nature that is dynamical systems with differential equations called continuous dynamical system or dynamical system with difference equations called discrete dynamical system. The concept of dynamical system has its origin in Newtonian mechanics.

Keywords: dynamical systems, Fibonacci numbers, Newtonian mechanics, discrete dynamical system

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Authors: Cemil Turan, Mohammad Shukri Salman

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The convergence rate of the least-mean-square (LMS) algorithm deteriorates if the input signal to the filter is correlated. In a system identification problem, this convergence rate can be improved if the signal is white and/or if the system is sparse. We recently proposed a sparse transform domain LMS-type algorithm that uses a variable step-size for a sparse system identification. The proposed algorithm provided high performance even if the input signal is highly correlated. In this work, we investigate the performance of the proposed TD-LMS algorithm for a large number of filter tap which is also a critical issue for standard LMS algorithm. Additionally, the optimum value of the most important parameter is calculated for all experiments. Moreover, the convergence analysis of the proposed algorithm is provided. The performance of the proposed algorithm has been compared to different algorithms in a sparse system identification setting of different sparsity levels and different number of filter taps. Simulations have shown that the proposed algorithm has prominent performance compared to the other algorithms.

Keywords: adaptive filtering, sparse system identification, TD-LMS algorithm, VSSLMS algorithm

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Authors: Aouiche Abdelaziz, Soudani Mouhamed Salah, Aouiche El Moundhe

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The present paper addresses the utilization of Artificial Neural Networks (ANNs) and Fuzzy Inference Systems (FISs) for the identification and control of dynamical systems with some degree of uncertainty. Because ANNs and FISs have an inherent ability to approximate functions and to adapt to changes in input and parameters, they can be used to control systems too complex for linear controllers. In this work, we show how ANNs and FISs can be put in order to form nets that can learn from external data. In sequence, it is presented structures of inputs that can be used along with ANNs and FISs to model non-linear systems. Four systems were used to test the identification and control of the structures proposed. The results show the ANNs and FISs (Back Propagation Algorithm) used were efficient in modeling and controlling the non-linear plants.

Keywords: non-linear systems, fuzzy set Models, neural network, control law

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Authors: Mohammad Javad Mollakazemi, Farhad Asadi, Aref Ghafouri

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In this paper, we considered and applied parametric modeling for some experimental data of dynamical system. In this study, we investigated the different distribution of output measurement from some dynamical systems. Also, with variance processing in experimental data we obtained the region of nonlinearity in experimental data and then identification of output section is applied in different situation and data distribution. Finally, the effect of the spanning the measurement such as variance to identification and limitation of this approach is explained.

Keywords: Gaussian process, nonlinearity distribution, particle filter, system identification

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Authors: Arcady Ponosov

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A novel mathematical approach is suggested, which facilitates a compressed representation and efficient validation of parameter-rich ordinary differential equation models describing the dynamics of complex, especially biology-related, systems and which is based on identification of the system's latent variables. In particular, an efficient parameter estimation method for the compressed non-linear dynamical systems is developed. The method is applied to the so-called 'power-law systems' being non-linear differential equations typically used in Biochemical System Theory.

Keywords: generalized law of mass action, metamodels, principal components, synergetic systems

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Authors: Graziano Chesi

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The topological entropy plays a key role in linear dynamical systems, allowing one to establish the existence of stabilizing feedback controllers for linear systems in the presence of communications constraints. This paper addresses the determination of a robust value of the topological entropy in nonlinear dynamical systems, specifically the largest value of the topological entropy over all linearized models in a region of interest of the state space. It is shown that a sufficient condition for establishing upper bounds of the sought robust value of the topological entropy can be given in terms of a semidefinite program (SDP), which belongs to the class of convex optimization problems.

Keywords: non-linear system, communication constraint, topological entropy

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Authors: Fanqiang Kong, Chending Bian

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Sparse unmixing is a promising approach in a semisupervised fashion by assuming that the observed pixels of a hyperspectral image can be expressed in the form of linear combination of only a few pure spectral signatures (end members) in an available spectral library. However, the sparse unmixing problem still remains a great challenge at finding the optimal subset of endmembers for the observed data from a large standard spectral library, without considering the spatial information. Under such circumstances, a sparse unmixing algorithm termed as non-local simultaneous sparse unmixing (NLSSU) is presented. In NLSSU, the non-local simultaneous sparse representation method for endmember selection of sparse unmixing, is used to finding the optimal subset of endmembers for the similar image patch set in the hyperspectral image. And then, the non-local means method, as a regularizer for abundance estimation of sparse unmixing, is used to exploit the abundance image non-local self-similarity. Experimental results on both simulated and real data demonstrate that NLSSU outperforms the other algorithms, with a better spectral unmixing accuracy.

Keywords: hyperspectral unmixing, simultaneous sparse representation, sparse regression, non-local means

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Authors: Y. Wang

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The Traveling salesman problem (TSP) is NP-hard in combinatorial optimization. The research shows the algorithms for TSP on the sparse graphs have the shorter computation time than those for TSP according to the complete graphs. We present an improved iterative algorithm to compute the sparse graphs for TSP by frequency graphs computed with frequency quadrilaterals. The iterative algorithm is enhanced by adjusting two parameters of the algorithm. The computation time of the algorithm is O(CN_maxn²) where C is the iterations, N_max is the maximum number of frequency quadrilaterals containing each edge and n is the scale of TSP. The experimental results showed the computed sparse graphs generally have less than 5n edges for most of these Euclidean instances. Moreover, the maximum degree and minimum degree of the vertices in the sparse graphs do not have much difference. Thus, the computation time of the methods to resolve the TSP on these sparse graphs will be greatly reduced.

Keywords: frequency quadrilateral, iterative algorithm, sparse graph, traveling salesman problem

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Authors: Eugene Stepanov, Arkadi Ponossov

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Ordinary differential equations with switching nonlinearities constitute a very useful tool in many applications. The solutions of such equations can usually be calculated analytically if they cross the discontinuities transversally. Otherwise, one has trajectories that slides along the discontinuity, and the calculations become less straightforward in this case. For instance, one of the problems one faces is non-uniqueness of the sliding modes. In the presentation, it is proposed to apply the theory of hybrid dynamical systems to calculate the solutions that are ‘hidden’ in the discontinuities. Roughly, one equips the underlying switched system with an explicitly designed discrete dynamical system (‘automaton’), which governs the dynamics of the switched system. This construction ‘splits’ the dynamics, which, as it is shown in the presentation, gives uniqueness of the resulting hybrid trajectories and at the same time provides explicit formulae for them. Projecting the hybrid trajectories back onto the original continuous system explains non-uniqueness of its trajectories. The automaton is designed with the help of the attractors of the specially constructed adjoint dynamical system. Several examples are provided in the presentation, which supports the efficiency of the suggested scheme. The method can be of interest in control theory, gene regulatory networks, neural field models and other fields, where switched dynamics is a part of the analysis.

Keywords: hybrid dynamical systems, singular perturbation analysis, sliding modes, switched dynamics

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Authors: Farhad Asadi, Mohammad Javad Mollakazemi

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In this paper, Bayesian online inference in models of data series are constructed by change-points algorithm, which separated the observed time series into independent series and study the change and variation of the regime of the data with related statistical characteristics. variation of statistical characteristics of time series data often represent separated phenomena in the some dynamical system, like a change in state of brain dynamical reflected in EEG signal data measurement or a change in important regime of data in many dynamical system. In this paper, prediction algorithm for studying change point location in some time series data is simulated. It is verified that pattern of proposed distribution of data has important factor on simpler and smother fluctuation of hazard rate parameter and also for better identification of change point locations. Finally, the conditions of how the time series distribution effect on factors in this approach are explained and validated with different time series databases for some dynamical system.

Keywords: time series, fluctuation in statistical characteristics, optimal learning, change-point algorithm

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Authors: Giovanni Merola

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Sparse Principal Components Analysis aims to find principal components with few non-zero loadings. We derive such sparse solutions by adding a genuine sparsity requirement to the original Principal Components Analysis (PCA) objective function. This approach differs from others because it preserves PCA's original optimality: uncorrelatedness of the components and least squares approximation of the data. To identify the best subset of non-zero loadings we propose a branch-and-bound search and an iterative elimination algorithm. This last algorithm finds sparse solutions with large loadings and can be run without specifying the cardinality of the loadings and the number of components to compute in advance. We give thorough comparisons with the existing sparse PCA methods and several examples on real datasets.

Keywords: SPCA, uncorrelated components, branch-and-bound, backward elimination

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Authors: Mahdi Shamsi, Tohid Yousefi Rezaii, Siavash Eftekharifar

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Compressed sensing (CS) is a new powerful mathematical theory concentrating on sparse signals which is widely used in signal processing. The main idea is to sense sparse signals by far fewer measurements than the Nyquist sampling rate, but the reconstruction process becomes nonlinear and more complicated. Common dilemma in sparse signal recovery in CS is the lack of knowledge about sparsity order of the signal, which can be viewed as model order selection procedure. In this paper, we address the problem of sparsity order estimation in sparse signal recovery. This is of main interest in situations where the signal sparsity is unknown or the signal to be recovered is approximately sparse. It is shown that the proposed method also leads to some kind of signal denoising, where the observations are contaminated with noise. Finally, the performance of the proposed approach is evaluated in different scenarios and compared to an existing method, which shows the effectiveness of the proposed method in terms of order selection as well as denoising.

Keywords: compressed sensing, data denoising, model order selection, sparse representation

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Authors: Qiuyu Dai, Haochong Zhang, Xiangrong Liu

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Diagonal sparse matrix-vector multiplication is a well-studied topic in the fields of scientific computing and big data processing. However, when diagonal sparse matrices are stored in DIA format, there can be a significant number of padded zero elements and scattered points, which can lead to a degradation in the performance of the current DIA kernel. This can also lead to excessive consumption of computational and memory resources. In order to address these issues, the authors propose the DIA-Adaptive scheme and its kernel, which leverages the parallel instruction sets on MLU. The researchers analyze the effect of allocating a varying number of threads, clusters, and hardware architectures on the performance of SpMV using different formats. The experimental results indicate that the proposed DIA-Adaptive scheme performs well and offers excellent parallelism.

Keywords: adaptive method, DIA, diagonal sparse matrices, MLU, sparse matrix-vector multiplication

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Authors: Lana Horvat Dmitrović

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The main purpose of this paper is to study the box dimension as fractal property of bifurcations of discrete dynamical systems in higher dimensions. The paper contains the fractal analysis of the orbits near the hyperbolic and non-hyperbolic fixed points in discrete dynamical systems. It is already known that in one-dimensional case the orbit near the hyperbolic fixed point has the box dimension equal to zero. On the other hand, the orbit near the non-hyperbolic fixed point has strictly positive box dimension which is connected to the non-degeneracy condition of certain bifurcation. One of the main results in this paper is the generalisation of results about box dimension near the hyperbolic and non-hyperbolic fixed points to higher dimensions. In the process of determining box dimension, the restriction of systems to stable, unstable and center manifolds, Lipschitz property of box dimension and the notion of projective box dimension are used. The analysis of the bifurcations in higher dimensions with one multiplier on the unit circle is done by using the normal forms on one-dimensional center manifolds. This specific change in box dimension of an orbit at the moment of bifurcation has already been explored for some bifurcations in one and two dimensions. It was shown that specific values of box dimension are connected to appropriate bifurcations such as fold, flip, cusp or Neimark-Sacker bifurcation. This paper further explores this connection of box dimension as fractal property to some specific bifurcations in higher dimensions, such as fold-flip and flip-Neimark-Sacker. Furthermore, the application of the results to the unit time map of continuous dynamical system near hyperbolic and non-hyperbolic singularities is presented. In that way, box dimensions which are specific for certain bifurcations of continuous systems can be obtained. The approach to bifurcation analysis by using the box dimension as specific fractal property of orbits can lead to better understanding of bifurcation phenomenon. It could also be useful in detecting the existence or nonexistence of bifurcations of discrete and continuous dynamical systems.

Keywords: bifurcation, box dimension, invariant manifold, orbit near fixed point

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Authors: Chia Jui Hsieh, Jyh Cheng Chen, Chih Wei Kuo, Ruei Teng Wang, Woei Chyn Chu

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Compressed sensing (CS) based computed tomographic (CT) reconstruction algorithm utilizes total variation (TV) to transform CT image into sparse domain and minimizes L1-norm of sparse image for reconstruction. Different from the traditional CS based reconstruction which only calculates x-coordinate and y-coordinate TV to transform CT images into sparse domain, we propose a multi-directional TV to transform tomographic image into sparse domain for low-dose reconstruction. Our method considers all possible directions of TV calculations around a pixel, so the sparse transform for CS based reconstruction is more accurate. In 2D CT reconstruction, we use eight-directional TV to transform CT image into sparse domain. Furthermore, we also use 26-directional TV for 3D reconstruction. This multi-directional sparse transform method makes CS based reconstruction algorithm more powerful to reduce noise and increase image quality. To validate and evaluate the performance of this multi-directional sparse transform method, we use both Shepp-Logan phantom and a head phantom as the targets for reconstruction with the corresponding simulated sparse projection data (angular sampling interval is 5 deg and 6 deg, respectively). From the results, the multi-directional TV method can reconstruct images with relatively less artifacts compared with traditional CS based reconstruction algorithm which only calculates x-coordinate and y-coordinate TV. We also choose RMSE, PSNR, UQI to be the parameters for quantitative analysis. From the results of quantitative analysis, no matter which parameter is calculated, the multi-directional TV method, which we proposed, is better.

Keywords: compressed sensing (CS), low-dose CT reconstruction, total variation (TV), multi-directional gradient operator

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Authors: Sergey Kuznetsov, Yuri Urman

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We present an approach to investigate non-linear dynamical effects occurring in the noncontact superconducting and diamagnetic suspensions, when levitated body has finite size. This approach is based on the calculation of interaction energy between spherical finite size superconducting or diamagnetic body with external magnetic field. Effects of small deviations from spherical shape may be also taken into account by introducing small corrections to the energy. This model allows investigating dynamical effects important for practical applications, such as nonlinear resonances, change of vibration plane, coupling of rotational and translational motions etc. We also show how the geometry of suspension affects various dynamical effects and how an inverse problem may be formulated to enforce or diminish various dynamical effects.

Keywords: levitation, non-linear dynamics, superconducting, diamagnetic stability

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Authors: Dawood Al Chanti, Alice Caplier

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Sparse representations of signals have received a great deal of attention in recent years. In this paper, the interest of using sparse representation as a mean for performing sparse discriminative analysis between spontaneous facial expressions is demonstrated. An automatic facial expressions recognition system is presented. It uses a KSVD-SVM approach which is made of three main stages: A pre-processing and feature extraction stage, which solves the problem of shared subspace distribution based on the random projection theory, to obtain low dimensional discriminative and reconstructive features; A dictionary learning and sparse coding stage, which uses the KSVD model to learn discriminative under or over dictionaries for sparse coding; Finally a classification stage, which uses a SVM classifier for facial expressions recognition. Our main concern is to be able to recognize non-basic affective states and non-acted expressions. Extensive experiments on the JAFFE static acted facial expressions database but also on the DynEmo dynamic spontaneous facial expressions database exhibit very good recognition rates.

Keywords: dictionary learning, random projection, pose and spontaneous facial expression, sparse representation

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Authors: L. Kiefer, C. Richter, G. Reinhart

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The uprising complexity in production systems due to an increasing amount of variants up to customer innovated products leads to requirements that hierarchical control systems are not able to fulfil. Therefore, factory planners can install autonomous manufacturing systems. The fundamental requirement for an autonomous control is the identification of objects within production systems. In this approach an attribute-based identification is focused for avoiding dose-dependent identification costs. Instead of using an identification mark (ID) like a radio frequency identification (RFID)-Tag, an object type is directly identified by its attributes. To facilitate that it’s recommended to include the identification and the corresponding sensors within handling processes, which connect all manufacturing processes and therefore ensure a high identification rate and reduce blind spots. The presented methodology reduces the individual effort to integrate identification processes in handling systems. First, suitable object attributes and sensor systems for object identification in a production environment are defined. By categorising these sensor systems as well as handling systems, it is possible to match them universal within a compatibility matrix. Based on that compatibility further requirements like identification time are analysed, which decide whether the combination of handling and sensor system is well suited for parallel handling and identification within an autonomous control. By analysing a list of more than thousand possible attributes, first investigations have shown, that five main characteristics (weight, form, colour, amount, and position of subattributes as drillings) are sufficient for an integrable identification. This knowledge limits the variety of identification systems and leads to a manageable complexity within the selection process. Besides the procedure, several tools, as an example a sensor pool are presented. These tools include the generated specific expert knowledge and simplify the selection. The primary tool is a pool of preconfigured identification processes depending on the chosen combination of sensor and handling device. By following the defined procedure and using the created tools, even laypeople out of other scientific fields can choose an appropriate combination of handling devices and sensors which enable parallel handling and identification.

Keywords: agent systems, autonomous control, handling systems, identification

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Authors: M. P. Nanda Kumar, K. Dheeraj

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The design of a feedback controller, so as to minimize a given performance criterion, for a general non-linear dynamical system is difficult; if not impossible. But for a large class of non-linear dynamical systems, the open loop control that minimizes a performance criterion can be obtained using calculus of variations and Pontryagin’s minimum principle. In this paper, the open loop optimal trajectories, that minimizes a given performance measure, is used to train the neural network whose inputs are state variables of non-linear dynamical systems and the open loop optimal control as the desired output. This trained neural network is used as the feedback controller. In other words, attempts are made here to solve the “inverse optimal control problem” by using the state and control trajectories that are optimal in an open loop sense.

Keywords: inverse optimal control, radial basis function, neural network, controller design

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Authors: Ting Gao, Mingyue He

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Reconfigurable intelligent surfaces (RISs) are expected to be an important part of next-generation wireless communication networks due to their potential to reduce the hardware cost and energy consumption of millimeter Wave (mmWave) massive multiple-input multiple-output (MIMO) technology. However, owing to the lack of signal processing abilities of the RIS, the perfect channel state information (CSI) in RIS-assisted communication systems is difficult to acquire. In this paper, the uplink channel estimation for mmWave systems with a hybrid active/passive RIS architecture is studied. Specifically, a deep learning-based estimation scheme is proposed to estimate the channel between the RIS and the user. In particular, the sparse structure of the mmWave channel is exploited to formulate the channel estimation as a sparse reconstruction problem. To this end, the proposed approach is derived to obtain the distribution of non-zero entries in a sparse channel. After that, the channel is reconstructed by utilizing the least-squares (LS) algorithm and compressed sensing (CS) theory. The simulation results demonstrate that the proposed channel estimation scheme is superior to existing solutions even in low signal-to-noise ratio (SNR) environments.

Keywords: channel estimation, reconfigurable intelligent surface, wireless communication, deep learning

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Authors: Mitsuyoshi Tomiya, Kentaro Kawamura, Shoichi Sakamoto

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In chaotic billiard systems, scar-like localization has been found on time-evolving wave packet. We may call it the “dynamical scar” to separate it to the original scar in stationary states. It also comes out along the vicinity of classical unstable periodic orbits, when the wave packets are launched along the orbits, against the hypothesis that the waves become homogenous all around the billiard. Then time-evolving wave packets are investigated numerically in phase space. The Wigner function is adopted to detect the wave packets in phase space. The 2-dimensional Poincaré sections of the 4-dimensional phase space are introduced to clarify the dynamical behavior of the wave packets. The Poincaré sections of the coordinate (x or y) and the momentum (Px or Py) can visualize the dynamical behavior of the wave packets, including the behavior in the momentum degree also. For example, in “dynamical scar” states, a bit larger momentum component comes first, and then the a bit smaller and smaller components follow next. The sections made in the momentum space (Px or Py) elucidates specific trajectories that have larger contribution to the “dynamical scar” states. It is the fixed point observation of the momentum degrees at a specific fixed point(x0, y0) in the phase space. The accumulation are also calculated to search the “dynamical scar” in the Poincare sections. It is found the scars as bright spots in momentum degrees of the phase space.

Keywords: chaotic billiard, Poincaré section, scar, wave packet

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Authors: R. Vigneswaran, S. Thilakanathan

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Variable time-stepping algorithms for solving dynamical systems performed poorly for long time computations which pass close to a fixed point. To overcome this difficulty, several authors considered phase space error controls for numerical simulation of dynamical systems. In one generalized phase space error control, a step-size selection scheme was proposed, which allows this error control to be incorporated into the standard adaptive algorithm as an extra constraint at negligible extra computational cost. For this generalized error control, it was already analyzed the forward Euler method applied to the linear system whose coefficient matrix has real and negative eigenvalues. In this paper, this result was extended to the linear system whose coefficient matrix has complex eigenvalues with negative real parts. Some theoretical results were obtained and numerical experiments were carried out to support the theoretical results.

Keywords: adaptivity, fixed point, long time simulations, stability, linear system

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Authors: Eugene Stepanov, Arcady Ponosov

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To model gene regulatory networks one uses ordinary differential equations with switching nonlinearities, where the initial value problem is known to be well-posed if the trajectories cross the discontinuities transversally. Otherwise, the initial value problem is usually ill-posed, which lead to theoretical and numerical complications. In the presentation, it is proposed to apply the theory of hybrid dynamical systems, rather than switched ones, to regularize the problem. 'Hybridization' of the switched system means that one attaches a dynamic discrete component ('automaton'), which follows the trajectories of the original system and governs its dynamics at the points of ill-posedness of the initial value problem making it well-posed. The construction of the automaton is based on the classification of the attractors of the specially designed adjoint dynamical system. Several examples are provided in the presentation, which support the suggested analysis. The method can also be of interest in other applied fields, where differential equations contain switchings, e.g. in neural field models.

Keywords: hybrid dynamical systems, ill-posed problems, singular perturbation analysis, switching nonlinearities

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Authors: Brouri Adil, Giri Fouad

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The problem of identifying Wiener-Hammerstein systems is addressed in the presence of two linear subsystems of structure totally unknown. Presently, the nonlinear element is allowed to be noninvertible. The system identification problem is dealt by developing a two-stage frequency identification method such a set of points of the nonlinearity are estimated first. Then, the frequency gains of the two linear subsystems are determined at a number of frequencies. The method involves Fourier series decomposition and only requires periodic excitation signals. All involved estimators are shown to be consistent.

Keywords: Wiener-Hammerstein systems, Fourier series expansions, frequency identification, automation science

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Authors: N. Kaewpraek, W. Assawinchaichote

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This paper considers an H_∞ TS fuzzy state-derivative feedback controller for a class of nonlinear dynamical systems. A Takagi-Sugeno (TS) fuzzy model is used to approximate a class of nonlinear dynamical systems. Then, based on a linear matrix inequality (LMI) approach, we design an H_∞ TS fuzzy state-derivative feedback control law which guarantees L₂-gain of the mapping from the exogenous input noise to the regulated output to be less or equal to a prescribed value. We derive a sufficient condition such that the system with the fuzzy controller is asymptotically stable and H_∞ performance is satisfied. Finally, we provide and simulate a numerical example is provided to illustrate the stability and the effectiveness of the proposed controller.

Keywords: h-infinity fuzzy control, an LMI approach, Takagi-Sugano (TS) fuzzy system, the photovoltaic systems

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Authors: A. Brouri, F. Giri, A. Mkhida, A. Elkarkri, M. L. Chhibat

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Standard Hammerstein-Wiener models consist of a linear subsystem sandwiched by two memoryless nonlinearities. Presently, the linear subsystem is allowed to be parametric or not, continuous- or discrete-time. The input and output nonlinearities are polynomial and may be noninvertible. A two-stage identification method is developed such the parameters of all nonlinear elements are estimated first using the Kozen-Landau polynomial decomposition algorithm. The obtained estimates are then based upon in the identification of the linear subsystem, making use of suitable pre-ad post-compensators.

Keywords: nonlinear system identification, Hammerstein-Wiener systems, frequency identification, polynomial decomposition

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Authors: Ali Pour Yazdanpanah, Farideh Foroozandeh Shahraki, Emma Regentova

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The reconstruction from sparse-view projections is one of important problems in computed tomography (CT) limited by the availability or feasibility of obtaining of a large number of projections. Traditionally, convex regularizers have been exploited to improve the reconstruction quality in sparse-view CT, and the convex constraint in those problems leads to an easy optimization process. However, convex regularizers often result in a biased approximation and inaccurate reconstruction in CT problems. Here, we present a nonconvex, Lipschitz continuous and non-smooth regularization model. The CT reconstruction is formulated as a nonconvex constrained L1 − L2 minimization problem and solved through a difference of convex algorithm and alternating direction of multiplier method which generates a better result than L0 or L1 regularizers in the CT reconstruction. We compare our method with previously reported high performance methods which use convex regularizers such as TV, wavelet, curvelet, and curvelet+TV (CTV) on the test phantom images. The results show that there are benefits in using the nonconvex regularizer in the sparse-view CT reconstruction.

Keywords: computed tomography, non-convex, sparse-view reconstruction, L1-L2 minimization, difference of convex functions

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Authors: Abdullah Eqal Al Mazrooei

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In this paper, a nonlinear dynamical system is presented. This system is a bilinear class. The bilinear systems are very important kind of nonlinear systems because they have many applications in real life. They are used in biology, chemistry, manufacturing, engineering, and economics where linear models are ineffective or inadequate. They have also been recently used to analyze and forecast weather conditions. Bilinear systems have three advantages: First, they define many problems which have a great applied importance. Second, they give us approximations to nonlinear systems. Thirdly, they have a rich geometric and algebraic structures, which promises to be a fruitful field of research for scientists and applications. The type of nonlinearity that is treated and analyzed consists of bilinear interaction between the states vectors and the system input. By using some properties of the tensor product, these systems can be transformed to linear systems. But, here we discuss the nonlinearity when the state vector is multiplied by itself. So, this model will be able to handle evolutions according to the Lotka-Volterra models or the Lorenz weather models, thus enabling a wider and more flexible application of such models. Here we apply by using an estimator to estimate temperatures. The results prove the efficiency of the proposed system.

Keywords: Lorenz models, nonlinear systems, nonlinear estimator, state-space model

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Authors: Kourosh Modarresi

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The abundance of media channels and devices has given users a variety of options to extract, discover, and explore information in the digital world. Since, often, there is a long and complicated path that a typical user may venture before taking any (significant) action (such as purchasing goods and services), it is critical to know how each node (media channel) in the path of user has contributed to the final action. In this work, the significance of each media channel is computed using statistical analysis and machine learning techniques. More specifically, “Regularized Singular Value Decomposition”, and “Sparse Principal Component” has been used to compute the significance of each channel toward the final action. The results of this work are a considerable improvement compared to the present approaches.

Keywords: multimedia attribution, sparse principal component, regularization, singular value decomposition, feature significance, machine learning, linear systems, variable shrinkage

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