Approximate System Model Research Articles

Online neural sliding mode control with guaranteed stability

Model-based control systems allow engineers to leverage known system information in controllers, often resulting in improved control accuracy or robustness. However, these system models can change over time, be difficult to obtain for complex systems, or fail to capture higher-order effects in the system. In this work, we use a highly robust model-based control methodology, sliding mode control, without the need for an a priori model. We use a neural network to learn an approximate system model fully online, with no pretraining. The neural network term is found to increase control accuracy while alleviating chatter, the primary drawback of conventional sliding mode control. The controller is verified by simulating a non-planar 3 degree-of-freedom robotic arm picking up a load, and the proposed controller is shown to outperform conventional model-based sliding mode control, especially when the built-in load margin on the end effector in the conventional model-based controller is exceeded.

Symbolic number comparison and number priming do not rely on the same mechanism

In elementary symbolic number processing, the comparison distance effect (in a comparison task, the task is more difficult with smaller numerical distance between the values) and the priming distance effect (in a number processing task, actual number is easier to process with a numerically close previous number) are two essential phenomena. While a dominant model, the approximate number system model, assumes that the two effects rely on the same mechanism, some other models, such as the discrete semantic system model, assume that the two effects are rooted in different generators. In a correlational study, here we investigate the relation of the two effects. Critically, the reliability of the effects is considered; therefore, a possible null result cannot be attributed to the attenuation of low reliability. The results showed no strong correlation between the two effects, even though appropriate reliabilities were provided. These results confirm the models of elementary number processing that assume distinct mechanisms behind number comparison and number priming.

Generalized Cell Mapping Method with Deep Learning for Global Analysis and Response Prediction of Dynamical Systems

A novel method that combines generalized cell mapping and deep learning is developed to analyze the global properties and predict the responses of dynamical systems. The proposed method only requires some prior knowledge of the system governing equations and obtains dynamical properties of the system from observed data. By combining the theoretical demonstration and empirical inference results, appropriate network structure and training hyperparameters are computed. Then a robust and efficient neural network approximation with the estimated mapping parameters is obtained. By using the approximate dynamical system model, we construct the one-step transition probability matrix and introduce the digraph analysis method to analyze the global properties. System responses at any time can be obtained with the trained model on the basis of the property of Markov chain. Several examples with periodic or chaotic attractors are presented to validate the proposed method. The influence of the number of hidden layers and the size of training data on calculated results is discussed, and an admissible architecture of the neural network is found. Numerical results indicate that the proposed method is quite effective for both global analysis and response prediction.

Superconductor qubits hamiltonian approximations effect on quantum state evolution and control

Microwave IQ-mixer controllers are designed for the three approximated Hamiltonians of charge, phase and flux qubits and the controllers are exerted both on approximate and precise quantum system models. The controlled qubits are for the implementation of the two quantum-gates with these three fundamental types of qubits, Quantum NOT-gate and Hadamard-gate. In the charge-qubit, for implementation of both gates, in the approximated and precise model, we observed different controlled trajectories. But fortunately, applying the controller designed for the approximated system over the precise system leads to the passing of the quantum state from the desired state sooner that the expected time. Phase-qubit and flux qubit have similar behaviour under the control system action. In both of them, the implementation of NOT-gate operation led to same trajectories which arrive at final goal state at different times. But in both of those two qubits for implementation of Hadamard-gate, desired trajectory and precise trajectory have some angle of deviation, then by exerting the approximated design controller to precise system, it caused the quantum state to approach the goal state for Hadamard gate implementation, and since the quantum state does not completely reach the goal state, we can not obtain very high gate fidelity.

Probabilistic error bounds on constraint violation for empirical-analytical Lagrangian models of motion

In contrast to many systems studied in the field of classical mechanics, models of animal motion are often distinguished in that they are both highly uncertain and evolve in a high-dimensional configuration space Q. Often it is either suspected or known that a particular motion regime evolves on or near some smaller subset $$Q_0\subseteq Q$$ . In some cases, $$Q_0$$ may itself be a submanifold of Q. A general strategy is presented in this paper for constructing empirical-analytical Lagrangian (EAL) models of the mechanics of such systems. It is assumed that the set $$Q_0\,\subseteq \,Q$$ is defined by a collection of unknown holonomic constraints on the full configuration space. Since the analytic form of the holonomic constraints is unknown, EAL models are defined that use experimental observations $$\{z_1,\ldots ,z_N\}\subseteq Q^N$$ to ensure that the approximate system models evolve near the underlying submanifold $$Q_0$$ . This paper gives a precise characterization of a probabilistic measure of the distance from the EAL model to the underlying submanifold.

Using input-adaptive dictionaries trained by the method of optimal directions to estimate the permeability model of a reservoir

The thirst for perfect characterization of petroleum reservoirs is yet to be quenched. Sparse transform is an image compression method the full potential of which is still not employed by the geoscientists in the reservoir characterization workflow. Sparse transform is the state of representing an image model based on a weighted linear combination of a sparse set of columns from a matrix, called dictionary. The required dictionary in the sparse transform scheme is obtained by learning over a training set of model images using dictionary learning algorithms. Meanwhile, the sparse coding algorithms are used to select the sparse proper subset of columns from the trained dictionary and specify appropriate weight to each column in the linear combination. To enhance the results, the property of internal structure and generality for the implicit dictionaries are integrated with the property of adaptability for the explicit dictionaries to regularize and enhance the effectiveness of the input-adaptive dictionary in reconstructing the approximate model.This phenomenon can be employed in the geosciences to estimate the reservoir model if the dictionary is trained over a set of geologic models of a delighted property. The geologic models should be diverse enough to represent the possible variety of the desired property and the limited number of columns from the dictionary should be properly selected such that it adequately captures the variety inherent within the geologic models. In this study, the variety of the geologic models are provided by manipulating two training images by FilterSim multiple-point geostatistical method and generating a large set of realizations. The training images are extracted from a spectral decomposition profile to represent a stationary fracture system and a nonstationary delta system model in an Iranian petroleum reservoir. The dictionary learning algorithm is an alternation of dictionary updating and sparse coding steps. In this paper, the method of optimal directions is used as dictionary learning algorithm and the least angle regression with shrinkage algorithm is used as the sparse coding method.The resultant approximate model achieved by the sparse transform compression scheme is comparable to the reference models both in terms of physical structures and fluid flow characteristics. For the current study, the approximate fracture system model is shown to be superior to 86.16% of the model images in the corresponding population space in terms of fluid flow characteristics. In the case of the delta system, the approximate model is superior to 99.17% of the model images in the population space. Further experiments indicate similar deductions using other methods for dictionary learning, sparse coding, and multiple-point geostatistical modeling.

Ecology‐based coexistence scheme for heterogeneous cognitive radio networks over TV white space

Heterogeneous cognitive radio networks (H-CRNs) operating in the same TV white space (TVWS) spectrum cause severe mutual interferences, which heavily degrades the network performance of coexisting H-CRNs. Inspired by the Lotka–Volterra competition model of different species in a biological ecosystem, this study formulates the coexistence of H-CRNs over TVWS as an equilibrium assignment problem of a discrete non-linear control system (DNCS). By using the local linearisation method, the authors can find an approximate linear control system (ALCS) model to the DNCS. Further, they obtain an effective feedback control to the equilibrium assignment of the ALCS via solving a sufficient condition in the form of linear matrix inequalities. Third, they propose a novel ecology-inspired heterogeneous coexistence algorithm (EHCA) based on the obtained feedback control. It is shown in simulations that the proposed EHCA could guarantee any desired but feasible spectrum share among H-CRNs.

Performance Analysis for the ${N}$ -Continuous Precoded SM-OFDM System

Combined with N -continuous (NC) precoding, the spatial modulation (SM) orthogonal frequency division multiplexing (OFDM) system offers considerable sidelobe suppression for the downlink transmission, at the cost of additional interference to the transmit signal. Therefore, this paper focuses on investigating the impact of the NC precoder on the bit error rate (BER) performance of the SM-OFDM system. The BER performance is analyzed over the frequency-selective Rayleigh fading channel under two distinct scenarios, i.e., perfect channel estimation and interference suppression based minimum mean square error (MMSE) channel estimation. First, we propose an approximate system model for the NC precoded SM-OFDM system along with an analysis on the introduced interference, and then derive the average BER performance of the system with perfect channel estimation. Based on the above proposed approximate system model, we further analyze the interference based upon MMSE channel estimation, and investigate the characteristics of channel estimation errors. Furthermore, we derive the average BER performance of the NC precoded SM-OFDM system with imperfect channel estimation. The numerical results show that the analytical BER closely matches its simulated counterpart under different system configurations, and demonstrate that the proposed approximate system model is in good agreement with the precise one.

Approximate MLD System Model of Switched Linear Systems for Model Predictive Control

In this paper, to reduce the computation time for solving the finite-time optimal control problem (i.e., the model predictive control (MPC) problem), an approximate model of switched linear systems is proposed. A switched linear system is one of the typical subclasses of hybrid systems, and has several applications such as networked control systems. First, an approximation of the state variable in switched linear systems is derived. Next, using auxiliary binary and continuous variables, an approximate model given by a mixed logical dynamical system model is derived. Using this approximate model, the dimension of the auxiliary continuous variable can be reduced. As a result, the online computation time in MPC can decrease. Finally, the effectiveness of the proposed method is presented by a numerical example.

Power System Dynamic Model Reduction Based on Extended Krylov Subspace Method

Modern power systems have experienced a significant increase in its complexity, and extremely large-scale system models have to be addressed in the study of stability analysis and control. Model reduction is a technique for developing an approximate system model with lower dimensions that shares similar properties to the original system. This work proposes a computationally efficient approach for linear system model reduction in large-scale power systems that is based on the balanced truncation method using an extended Krylov subspace technique. Key algorithm improvements, including sparsity handling of the linearized power system models and efficient computational techniques for solving dual Lyapunov equations, are discussed in detail. In addition, application of the proposed model reduction is extended to unstable systems, and a power system stabilizer (PSS) parameter optimization method based on reduced system models is used to validate the effectiveness of the proposed method. Case studies show that the resulting reduced models preserve the unique characteristics of the original high-dimensional models, including time and frequency domain responses as well as eigenvalues. Numerical results based on test systems with up to 12 $\thinspace$ 685 buses demonstrate the computational efficiency and validity of the proposed approach.

Research on Exciting Current And Induced Current Analytical Model of Eaf System

In this paper, large amount of subsection calculations and complex calculation of the traditional algorithm of an electronic anti-fouling system excitation coil current is analyzed, and a method based on a signal superposition theory of a linear system is put forward. What's more, a model system consisting of the electronic anti-fouling system and aqueous solution in the tube is established and the induced current is calculated carrying on reasonable approximates. Then the correctness of the proposed method and rationality of approximate system model are proved using finite element numerical method. This research will improve the adaptability of the electronic anti-fouling system in different water quality and optimize the effect on anti-scaling, and it provides a useful theoretical basis for further research on anti-scaling mechanism of electronic anti-fouling system.

Replacement of Lyapunov Function by Locally Convergent Robust Fixed Point Transformations in Model-Based Control a Brief Summary

Lyapunov’s 2ndMethod is a popular approach in the model-based control of nonlinear systems since normally it can guaranteeglobal asymptotic stability. However, the cost of the application of Lyapunov function frequently can be inefficient and complicated parameter tuning process containing unnecessary number of almost arbitrary control parameters, and vulnerability of the tuning process against not modeled, unknown external disturbances. Improved versions of the original, model-based tuning are especially sensitive to the external perturbations. All these disadvantages can simply be avoided by the application of robust fixed point transformations at the cost of giving up the guarantee of global asymptotic stability. Instead of that simple,stable iterative controlof local basin of attraction can be constructed on the basis of an approximate system model that can well compensate the effects of unknown external disturbances, too. Since the basin of convergence of the method in principle can be left, setting the three adaptive parameters of this controller needs preliminary simulation investigations. These statements are illustrated and substantiated via simulation results obtained for the adaptive control of various physical systems.

Application and Evaluation of a Measured Spatially Variant System Model for PET Image Reconstruction

Accurate system modeling in tomographic image reconstruction has been shown to reduce the spatial variance of resolution and improve quantitative accuracy. System modeling can be improved through analytic calculations, Monte Carlo simulations, and physical measurements. The purpose of this work is to improve clinical fully-3-D reconstruction without substantially increasing computation time. We present a practical method for measuring the detector blurring component of a whole-body positron emission tomography (PET) system to form an approximate system model for use with fully-3-D reconstruction. We employ Monte Carlo simulations to show that a non-collimated point source is acceptable for modeling the radial blurring present in a PET tomograph and we justify the use of a Na22 point source for collecting these measurements. We measure the system response on a whole-body scanner, simplify it to a 2-D function, and incorporate a parameterized version of this response into a modified fully-3-D OSEM algorithm. Empirical testing of the signal versus noise benefits reveal roughly a 15% improvement in spatial resolution and 10% improvement in contrast at matched image noise levels. Convergence analysis demonstrates improved resolution and contrast versus noise properties can be achieved with the proposed method with similar computation time as the conventional approach. Comparison of the measured spatially variant and invariant reconstruction revealed similar performance with conventional image metrics. Edge artifacts, which are a common artifact of resolution-modeled reconstruction methods, were less apparent in the spatially variant method than in the invariant method. With the proposed and other resolution-modeled reconstruction methods, edge artifacts need to be studied in more detail to determine the optimal tradeoff of resolution/contrast enhancement and edge fidelity.

THE LINEAR APROXIMATION OF THE ALMOST IDEAL DEMAND SYSTEM (LA/AIDS) MODEL: APPLICATION TO AGGREGATED DATA

During the years different models for demand system analysis were developed, but one formulation that avoids many shortcomings encountered in other models is the Almost Ideal Demand System (AIDS) model, developed by A. Deaton and J. Muellbauer in 1980. Several variations of AIDS were used in applied work since 1980 (Linear Approximation of AIDS, Dynamic AIDS, etc). This paper is an application of the Linear Approximate Almost Ideal Demand System (LA/AIDS) model on an aggregated demand system. The data used for this analysis are from a database collected by ACNielsen Co. on sliced packaged luncheon meats, for Canada, during December 2000 - September 2006. Because the data are very detailed some level of aggreg ation needs to be applied. The results will illustrate th at not all the theoretical assumptions of the deman d theory hold in the case of aggregation.

Valuing food-borne risks using time-series data: The case ofE. coli O157:H7 and BSE crises in Japan

This study evaluates changes in consumers' concerns on food safety after the outbreaks of E. coli O157 and bovine spongiform encephalopathy (BSE) in Japan using household consumption time-series data. A food demand system for Japanese households is estimated using the linear approximate almost-ideal demand system (AIDS) model to evaluate the willingness to accept (WTA) compensation for risk. The Kalman filtering method is applied to produce estimates without a priori assumption regarding timing of the changes. The WTA value rises immediately after a food safety crisis occurs and declines in a short time. However, it does not return to previous levels for an extended period. A possible explanation for remaining effects of a crisis might be that they are the results of habit formation and learning effects of consumption. [EconLit citations: D12, D18, Q13]. © 2006 Wiley Periodicals, Inc. Agribusiness 22: 219–232, 2006.

Unstable ones in understood algebraic questions of modelling for control design

The use of a necessarily approximate system model for the design of a feedback controller for an actual plant introduces strictures on the quality of the model which are different from those pertaining in open loop. This has been the focus of a raft of recent papers on closed loop modelling, model validation, and iterative control design where appropriate measures of approximation quality have been proposed, analysed and implemented. Our attention here will concentrate on underlying implicit or understood questions of an algebraic nature which need to be resolved prior to any quantitative analysis of approximation. For example, it should be evident that a model P is useful as a design input for a controller for the actual plant P only if the pair ([Pcirc], P) is simultaneously stabilizable. Yet this question has not really been asked. For given P and T we characterize the set of admissible models {[Pcirc]}, where admissible means that a controller designed from [Pcirc] and T yields a stable closed loop. Necessary conditions on (P, T) are derived for this set to be nonempty; they connect the unstable poles and zeros of P on the positive real axis with the unstable zeros and ones of T on that axis.

Application of fuzzy logic to reliability engineering

The analysis of system reliability often requires the use of subjective-judgments, uncertain data, and approximate system models. By allowing imprecision and approximate analysis fuzzy logic provides an effective tool for characterizing system reliability in these circumstances; it does not force precision where it is not possible. Here we apply the main concepts of fuzzy logic, fuzzy arithmetic and linguistic variables to the analysis of system structures, fault trees, event trees, the reliability of degradable systems, and the assessment of system criticality based on the severity of a failure and its probability of occurrence. >

Asymptotic normality of prediction error estimators for approximate system models

A general class of parameter estimation methods for stochastic dynamical systems is studied. The class contains the least squares method, output-error methods, the maximum likelihood method and several other techniques. It is shown that the class of estimates so obtained are asymptotically normal and expressions for the resulting asymptotic covariance matrices are given. The regularity conditions that are imposed to obtain these results, are fairly weak. It is, for example, not assumed that the true system can be described within the chosen model set, and, as a consequence, the results in this paper form a part of the so-called approximate modeling approach to system identification. It is also noteworthy that arbitrary feedback from observed system outputs to observed system inputs is allowed and stationarity is not required

Approximate optical system model

An analytical development is presented for on-axis far-field irradiance in terms of an optical system that specifies a laser beam quality, an optical train with both linear and nonlinear phase aberrations (power driven), and a focusing telescope with jitter. It was found that the far-field intensity does not increase linearly with laser power, in fact it turns over and decreases as nonlinear, power-driven aberrations begin to dominate. The same phenomena causes the wavelength scaling to be less than 1/lambda(2) (with decreasing wave-length) for far-field irradiance.

Optimal test signal design for linear S.I.S.O. system identification†

A sufficient condition for consistent estimates of parametera in linear S.I.S.O. system identification is that the input signal should be ‘ persistently exciting ’, However,. in practice the exact nature of the test signal has a direct bearing upon the identification accuracy. This paper shows how a-priori knowledge of the approximate system and noise model parameters may be used to design a test signal which will minimize the variance of the parameter estimates. The design procedure is computationally efficient as full advantage is taken of the special structure of linear S.I.S.O. systems. The optimal test signals are shown to result in a significant reduction in the parameter variances. This is of considerable practical importance as either the experiment time may be reduced for the same model accuracy or for fixed experiment time a model of much higher accuracy may be obtained.