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Journal articles on the topic 'Piecewise linear systems. eng'

Author: Grafiati

Published: 4 June 2021

Last updated: 14 February 2022

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1

AL-FHAID, M. "Analysis and Identification of Time-Delay Systems via Piecewise Linear Polynomial Functions." Journal of King Abdulaziz University-Engineering Sciences 11, no. 2 (1999): 41–49. http://dx.doi.org/10.4197/eng.11-2.3.

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2

Rathbun, David B., Martin C. Berg, and Keith W. Buffinton. "Piecewise-Linear-Gain Pulse Width Control for Precise Positioning of Structurally Flexible Systems Subject to Stiction and Coulomb Friction." Journal of Dynamic Systems, Measurement, and Control 126, no. 1 (2004): 139–43. http://dx.doi.org/10.1115/1.1649979.

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Pulse width control refers to the use of a control law to determine the duration of fixed-height force pulses for point-to-point position control of a plant that is subject to mechanical friction, including stiction. A quantitative measure of the performance of a pulse width control system is introduced. Applications of this measure suggest that piecewise-linear-gain pulse width control laws will often provide better performance than constant-gain pulse width control laws. A method for designing piecewise-linear-gain pulse width control laws is introduced. The performance measure and piecewise-linear-gain control law design method are demonstrated in applications to the control of the position of the end-effector of an industrial robot.

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3

SURESH, R., D. V. SENTHILKUMAR, M. LAKSHMANAN, and J. KURTHS. "GLOBAL AND PARTIAL PHASE SYNCHRONIZATIONS IN ARRAYS OF PIECEWISE LINEAR TIME-DELAY SYSTEMS." International Journal of Bifurcation and Chaos 22, no. 07 (2012): 1250178. http://dx.doi.org/10.1142/s0218127412501787.

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In this paper, we report the phenomena of global and partial phase synchronizations in linear arrays of unidirectionally coupled piecewise linear time-delay systems. In particular, in a linear array with open end boundary conditions, global phase synchronization (GPS) is achieved by a sequential synchronization of local oscillators in the array as a function of the coupling strength (a second order transition). Several phase synchronized clusters are also formed during the transition to GPS at intermediate values of the coupling strength, as a prelude to full scale synchronization. On the other hand, in a linear array with closed end boundary conditions (ring topology), partial phase synchronization (PPS) is achieved by forming different groups of phase synchronized clusters above some threshold value of the coupling strength (a first order transition) where they continue to be in a stable PPS state. We confirm the occurrence of both global and partial phase synchronizations in two different piecewise linear time-delay systems using various qualitative and quantitative measures in three different frameworks, namely, using explicit phase, recurrence quantification analysis and the framework of localized sets.

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4

Huang, Jianfeng, and Yuye Jin. "Bifurcation of a Kind of 1D Piecewise Differential Equation and Its Application to Piecewise Planar Polynomial Systems." International Journal of Bifurcation and Chaos 29, no. 05 (2019): 1950072. http://dx.doi.org/10.1142/s021812741950072x.

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This paper deals with a kind of piecewise smooth equation which is linear in the dependent variable. We study the problem of lower bounds for the maximum number of limit cycles of such equations using Melnikov functions. First of all, using the first order Melnikov function, we prove that these differential equations have a sharp upper bound for the number of the limit cycles which bifurcate from the periodic orbits and cross the separation straight line. Furthermore, in some cases the maximum number of these limit cycles is three, up to any order analysis. In the end, we apply this result on a kind of piecewise smooth planar system which has a separation curve with [Formula: see text] up to homomorphism.

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Gang, Ting-Ting, Jun Yang, Qing Gao, Yu Zhao, and Jianbin Qiu. "A Fuzzy Approach to Robust Control of Stochastic Nonaffine Nonlinear Systems." Mathematical Problems in Engineering 2012 (2012): 1–17. http://dx.doi.org/10.1155/2012/439805.

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This paper investigates the stabilization problem for a class of discrete-time stochastic non-affine nonlinear systems based on T-S fuzzy models. Based on the function approximation capability of a class of stochastic T-S fuzzy models, it is shown that the stabilization problem of a stochastic non-affine nonlinear system can be solved as a robust stabilization problem of the stochastic T-S fuzzy system with the approximation errors as the uncertainty term. By using a class of piecewise dynamic feedback fuzzy controllers and piecewise quadratic Lyapunov functions, robust semiglobal stabilization condition of the stochastic non-affine nonlinear systems is formulated in terms of linear matrix inequalities. A simulation example illustrating the effectiveness of the proposed approach is provided in the end.

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6

OLVER, PETER J., and ARI STERN. "Dispersive fractalisation in linear and nonlinear Fermi–Pasta–Ulam–Tsingou lattices." European Journal of Applied Mathematics 32, no. 5 (2021): 820–45. http://dx.doi.org/10.1017/s095679252000042x.

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We investigate, both analytically and numerically, dispersive fractalisation and quantisation of solutions to periodic linear and nonlinear Fermi–Pasta–Ulam–Tsingou systems. When subject to periodic boundary conditions and discontinuous initial conditions, e.g., a step function, both the linearised and nonlinear continuum models for FPUT exhibit fractal solution profiles at irrational times (as determined by the coefficients and the length of the interval) and quantised profiles (piecewise constant or perturbations thereof) at rational times. We observe a similar effect in the linearised FPUT chain at times t where these models have validity, namely t = O(h−2), where h is proportional to the intermass spacing or, equivalently, the reciprocal of the number of masses. For nonlinear periodic FPUT systems, our numerical results suggest a somewhat similar behaviour in the presence of small nonlinearities, which disappears as the nonlinear force increases in magnitude. However, these phenomena are manifested on very long time intervals, posing a severe challenge for numerical integration as the number of masses increases. Even with the high-order splitting methods used here, our numerical investigations are limited to nonlinear FPUT chains with a smaller number of masses than would be needed to resolve this question unambiguously.

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7

Yuldasheva, Marina B., and Oleg I. Yuldashev. "Boundary least squares method with three-dimensional harmonic basis of higher order for solving linear div-curl systems with Dirichlet conditions." Russian Journal of Numerical Analysis and Mathematical Modelling 34, no. 3 (2019): 175–86. http://dx.doi.org/10.1515/rnam-2019-0015.

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Abstract Solving linear divergence-curl system with Dirichlet conditions is reduced to finding an unknown vector function in the space of piecewise-polynomial gradients of harmonic functions. In this approach one can use the boundary least squares method with a harmonic basis of a high order of approximation formulated by the authors previously. The justification of this method is given. The properties of the bilinear form and approximating properties of the basis are investigated. Convergence of approximate solutions is proved. A numerical example with estimates of experimental orders of convergence in $\begin{array}{} {\bf V}_h^p \end{array}$-norm for different parameters h, p (p ⩽ 10) is presented. The method does not require specification of penalty weight function.

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8

Joo, Hwanyub, and Sung Hyun Kim. "H∞LPV Control with Pole Placement Constraints for Synchronous Buck Converters with Piecewise-Constant Loads." Mathematical Problems in Engineering 2015 (2015): 1–8. http://dx.doi.org/10.1155/2015/686857.

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This paper addresses the output regulation problem of synchronous buck converters with piecewise-constant load fluctuations via linear parameter varying (LPV) control scheme. To this end, an output-error state-space model is first derived in the form of LPV systems so that it can involve a mismatch error that temporally arises from the process of generating a feedforward control. Then, to attenuate the mismatch error in parallel with improving the transient behavior of the converter, this paper proposes an LMI-based stabilization condition capable of achieving bothH∞and pole-placement objectives. Finally, the simulation and experimental results are provided to show the validity of our approach.

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9

Yoon, Ah-Yun, Hyun-Koo Kang, and Seung-II Moon. "Optimal Price Based Demand Response of HVAC Systems in Commercial Buildings Considering Peak Load Reduction." Energies 13, no. 4 (2020): 862. http://dx.doi.org/10.3390/en13040862.

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Electric utility companies (EUCs) play an intermediary role of retailers between wholesale market and end-users, maximizing their profits. Retail pricing can be well deployed with the support of EUCs to promote demand response (DR) programs for heating, ventilating, and air-conditioning (HVAC) systems in commercial buildings. This paper proposes a pricing strategy to help EUCs and building operators achieve an optimal DR of price-elastic HVAC systems, considering peak load reduction. The proposed strategy is implemented by adopting a bi-level decision model. The nonlinear thermal response of an experimental building room is modeled using piecewise linear equations, which helps convert the bi-level model to the single-level model. The pricing strategy is implemented considering a time-of-use (TOU) pricing scheme, leading to low price volatility. Case studies are conducted for two types of load curves and the results demonstrate that the proposed strategy helps EUC promote the price-based DR of the commercial buildings for conventional load curves. However, EUC cannot reduce the peak load on duck curve caused by the large introduction of photovoltaic generators, even with price-sensitive HVAC systems in commercial building. This will be addressed in future studies by inducing DR participation of HVAC systems in residential buildings.

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Picandet, Vincent, and Noël Challamel. "Nonlocality of one-dimensional bilinear hardening–softening elastoplastic axial lattices." Mathematics and Mechanics of Solids 25, no. 2 (2019): 475–97. http://dx.doi.org/10.1177/1081286519881668.

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The static behaviour of an elastoplastic axial lattice is studied in this paper through both discrete and nonlocal continuum analyses. The elastoplastic lattice system is composed of piecewise linear hardening–softening elastoplastic springs connected between each other via nodes, loaded by concentrated tension forces. This inelastic lattice evolution problem is ruled by some difference equations, which are shown to be equivalent to the finite difference formulation of a continuous elastoplastic bar problem under distributed tension load. Exact solutions of this inelastic discrete problem are obtained from the resolution of this piecewise linear difference equations system. Localization of plastic strain in the first elastoplastic spring, connected to the fixed end, is observed in the softening range. A continuous nonlocal elastoplastic theory is then built from the lattice difference equations using a continualization process, based on a rational asymptotic expansion of the associated pseudo-differential operators. The continualized lattice-based model is equivalent to a distributed nonlocal continuous elastoplastic theory coupled to a cohesive elastoplastic model, which is shown to capture efficiently the scale effects of the reference axial lattice. The hardening–softening localization process of the nonlocal elastoplastic continuous model strongly depends on the lattice spacing, which controls the size of the nonlocal length scales. An analogy with the one-dimensional lattice system in bending is also shown. The considered microstructured elastoplastic beam is a Hencky bar-chain connected by elastoplastic rotational springs. It is shown that the length scale calibration of the nonlocal model strongly depends on the degree of the difference equations of each lattice model (namely axial or bending lattice). These preliminary results valid for one-dimensional systems allow possible future developments of new nonlocal elastoplastic models, including two- or even three-dimensional elastoplastic interactions.

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Dębski, Roman. "High-performance simulation-based algorithms for an alpine ski racer’s trajectory optimization in heterogeneous computer systems." International Journal of Applied Mathematics and Computer Science 24, no. 3 (2014): 551–66. http://dx.doi.org/10.2478/amcs-2014-0040.

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Abstract Effective, simulation-based trajectory optimization algorithms adapted to heterogeneous computers are studied with reference to the problem taken from alpine ski racing (the presented solution is probably the most general one published so far). The key idea behind these algorithms is to use a grid-based discretization scheme to transform the continuous optimization problem into a search problem over a specially constructed finite graph, and then to apply dynamic programming to find an approximation of the global solution. In the analyzed example it is the minimum-time ski line, represented as a piecewise-linear function (a method of elimination of unfeasible solutions is proposed). Serial and parallel versions of the basic optimization algorithm are presented in detail (pseudo-code, time and memory complexity). Possible extensions of the basic algorithm are also described. The implementation of these algorithms is based on OpenCL. The included experimental results show that contemporary heterogeneous computers can be treated as μ-HPC platforms-they offer high performance (the best speedup was equal to 128) while remaining energy and cost efficient (which is crucial in embedded systems, e.g., trajectory planners of autonomous robots). The presented algorithms can be applied to many trajectory optimization problems, including those having a black-box represented performance measure

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12

Zhang, Yunong, Weibing Li, and Zhijun Zhang. "Physical-limits-constrained minimum velocity norm coordinating scheme for wheeled mobile redundant manipulators." Robotica 33, no. 6 (2014): 1325–50. http://dx.doi.org/10.1017/s0263574714000757.

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SUMMARYIn order to resolve the redundancy of a wheeled mobile redundant manipulator comprising a two-wheel-drive mobile platform and a 6-degree-of-freedom manipulator, a physical-limits-constrained (PLC) minimum velocity norm (MVN) coordinating scheme (termed as PLC-MVN-C scheme) is proposed and investigated. Such a scheme can not only coordinate the mobile platform and the manipulator to fulfill the end-effector task and to achieve the desired optimal index (i.e., minimizing the norm of the rotational velocities of the wheels and the joint velocities of the manipulator) but also consider the physical limits of the robot (i.e., the joint-angle limits and joint-velocity limits of the manipulator as well as the rotational velocity limits of the wheels). The scheme is then reformulated as a quadratic program (QP) subject to equality and bound constraints, and is solved by a discrete QP solver, i.e., a numerical algorithm based on piecewise-linear projection equations (PLPE). Simulation results substantiate the efficacy and accuracy of such a PLC-MVN-C scheme and the corresponding discrete PLPE-based QP solver.

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13

Zaghwan, Ashraf, and Indra Gunawan. "Energy Loss Impact in Electrical Smart Grid Systems in Australia." Sustainability 13, no. 13 (2021): 7221. http://dx.doi.org/10.3390/su13137221.

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This research draws attention to the potential and contextual influences on energy loss in Australia’s electricity market and smart grid systems. It further examines barriers in the transition toward optimising the benefit opportunities between electricity demand and electricity supply. The main contribution of this study highlights the impact of individual end-users by controlling and automating individual home electricity profiles within the objective function set (AV) of optimum demand ranges. Three stages of analysis were accomplished to achieve this goal. Firstly, we focused on feasibility analysis using ‘weight of evidence’ (WOE) and ‘information value’ (IV) techniques to check sample data segmentation and possible variable reduction. Stage two of sensitivity analysis (SA) used a generalised reduced gradient algorithm (GRG) to detect and compare a nonlinear optimisation issue caused by end-user demand. Stage three of analysis used two methods adopted from the machine learning toolbox, piecewise linear distribution (PLD) and the empirical cumulative distribution function (ECDF), to test the normality of time series data and measure the discrepancy between them. It used PLD and ECDF to derive a nonparametric representation of the overall cumulative distribution function (CDF). These analytical methods were all found to be relevant and provided a clue to the sustainability approach. This study provides insights into the design of sustainable homes, which must go beyond the concept of increasing the capacity of renewable energy. In addition to this, this study examines the interplay between the variance estimation of the problematic levels and the perception of energy loss to introduce a novel realistic model of cost–benefit incentives. This optimisation goal contrasted with uncertainties that remain as to what constitutes the demand impact and individual house effects in diverse clustering patterns in a specific grid system. While ongoing effort is still needed to look for strategic solutions for this class of complex problems, this research shows significant contextual opportunities to manage the complexity of the problem according to the nature of the case, representing dense and significant changes in the situational complexity.

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CHUA, LEON O. "CHUA’S CIRCUIT: AN OVERVIEW TEN YEARS LATER." Journal of Circuits, Systems and Computers 04, no. 02 (1994): 117–59. http://dx.doi.org/10.1142/s0218126694000090.

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More than 200 papers, two special issues (Journal of Circuits, Systems, and Computers, March, June, 1993, and IEEE Trans. on Circuits and Systems, vol. 40, no. 10, October, 1993), an International Workshop on Chua’s Circuit: chaotic phenomena and applica tions at NOLTA’93, and a book (edited by R.N. Madan, World Scientific, 1993) on Chua’s circuit have been published since its inception a decade ago. This review paper attempts to present an overview of these timely publications, almost all within the last six months, and to identify four milestones of this very active research area. An important milestone is the recent fabrication of a monolithic Chua’s circuit. The robustness of this IC chip demonstrates that an array of Chua’s circuits can also be fabricated into a monolithic chip, thereby opening the floodgate to many unconventional applications in information technology, synergetics, and even music. The second milestone is the recent global unfolding of Chua’s circuit, obtained by adding a linear resistor in series with the inductor to obtain a canonical Chua’s circuit— now generally referred to as Chua’s oscillator. This circuit is most significant because it is structurally the simplest (it contains only 6 circuit elements) but dynamically the most complex among all nonlinear circuits and systems described by a 21-parameter family of continuous odd-symmetric piecewise-linear vector fields. The third milestone is the recent discovery of several important new phenomena in Chua’s circuits, e.g., stochastic resonance, chaos-chaos type intermittency, 1/f noise spectrum, etc. These new phenomena could have far-reaching theoretical and practical significance. The fourth milestone is the theoretical and experimental demonstration that Chua’s circuit can be easily controlled from a chaotic regime to a prescribed periodic or constant orbit, or it can be synchronized with 2 or more identical Chua’s circuits, operating in an oscillatory, or a chaotic regime. These recent breakthroughs have ushered in a new era where chaos is deliberately created and exploited for unconventional applications, e.g. secure communication.

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Matin, Ethel, David C. Nofer, Androula Christodoulou, and Hope Koski. "Perception Time Measured with the Slope-Transition Paradigm (STP): Category, Set Size, and Task Manipulations." Perception 34, no. 12 (2005): 1423–39. http://dx.doi.org/10.1068/p5436.

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A perception time measure was obtained with the ‘slope-transition paradigm’ (STP), which is described in detail. In two experiments with the paradigm, participants viewed two sequential data frames, each presented for a wide range of durations. They made a binary response based on combined information from the two frames. The results showed piecewise linear response-time versus frame-duration functions with a slope-0 branch at short durations, followed by a slope-1 branch. The duration where the two branches met (the slope transition) was interpreted as the end of the perception of frame 1. For longer durations, the participant had completed the perception of frame 1 and was forced to waste time waiting for data from frame 2. In experiment 1, an odd-digit enumeration task was used, and set size and distractor category (even digits versus consonants) were varied. In experiment 2, a same/different task with digits was used and the type of judgment (literal versus parity) was varied. Perception time increased with set size. Distractor category and judgment type affected post-perceptual processes. The perception time measure of the STP is considered in relation to the attentional blink, repetition blindness, and object files.

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Ye, Fei, Yunbin Yuan, and Zhiguo Deng. "Improved Ultra-Rapid UT1-UTC Determination and Its Preliminary Impact on GNSS Satellite Ultra-Rapid Orbit Determination." Remote Sensing 12, no. 21 (2020): 3584. http://dx.doi.org/10.3390/rs12213584.

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Errors in ultra-rapid UT1-UTC primarily affect the overall rotation of spatial datum expressed by GNSS (Global Navigation Satellite System) satellite ultra-rapid orbit. In terms of existing errors of traditional strategy, e.g., piecewise linear functions, for ultra-rapid UT1-UTC determination, and the requirement to improve the accuracy and consistency of ultra-rapid UT1-UTC, the potential to improve the performance of ultra-rapid UT1-UTC determination based on an LS (Least Square) + AR (Autoregressive) combination model is explored. In this contribution, based on the LS+AR combination model and by making joint post-processing/rapid UT1-UTC observation data, we propose a new strategy for ultra-rapid UT1-UTC determination. The performance of the new strategy is subsequently evaluated using data provided by IGS (International GNSS Services), iGMAS (international GNSS Monitoring and Assessment System), and IERS (International Earth Rotation and Reference Systems Service). Compared to the traditional strategy, the numerical results over more than 1 month show that the new strategy improved ultra-rapid UT1-UTC determination by 29–43%. The new strategy can provide a reference for GNSS data processing to improve the performance of ultra-rapid products.

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17

Wang, Shilong, Yu Zhao, Jie Zhou, Chuan Li, and Xiaoyong Li. "Static response of stranded wire helical springs to axial loads: A two-state model." Proceedings of the Institution of Mechanical Engineers, Part C: Journal of Mechanical Engineering Science 227, no. 7 (2012): 1608–18. http://dx.doi.org/10.1177/0954406212466520.

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Stranded wire helical springs are fundamental mechanical components used in high-end vibration absorption systems. The static axial response model is an important tool for the design and manufacturing of the spring. The wires within the spring have been assumed to be in contact with each other when the spring is unloaded by commonly used models for modelling the static axial response; hence, significant error has been introduced. To improve the estimation accuracy of the static axial response, this article proposes a two-state model by assuming that the spring possesses two states during the loading process. Moreover, in this model, the friction between adjacent wires is neglected and the spring is unwound to be a straight strand in the initial step of the analysis. The model is almost piecewise linear and is able to model the nonlinearity of the load–strain relationship of the spring. Adopting the proposed model, the dependence of the stiffness of the spring on the spring geometries is analysed. To evaluate the presented model, the compression experiments are carried out. Compared to a commonly used static response model, the proposed two-state model features better accuracy that is validated by the experimental results.

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Kengne, J. "Coexistence of Chaos with Hyperchaos, Period-3 Doubling Bifurcation, and Transient Chaos in the Hyperchaotic Oscillator with Gyrators." International Journal of Bifurcation and Chaos 25, no. 04 (2015): 1550052. http://dx.doi.org/10.1142/s0218127415500522.

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In this paper, the dynamics of the paradigmatic hyperchaotic oscillator with gyrators introduced by Tamasevicius and co-workers (referred to as the TCMNL oscillator hereafter) is considered. This well known hyperchaotic oscillator with active RC realization of inductors is suitable for integrated circuit implementation. Unlike previous literature based on piecewise-linear approximation methods, I derive a new (smooth) mathematical model based on the Shockley diode equation to explore the dynamics of the oscillator. Various tools for detecting chaos including bifurcation diagrams, Lyapunov exponents, frequency spectra, phase portraits and Poincaré sections are exploited to establish the connection between the system parameters and various complex dynamic regimes (e.g. hyperchaos, period-3 doubling bifurcation, coexistence of attractors, transient chaos) of the hyperchaotic oscillator. One of the most interesting and striking features of this oscillator discovered/revealed in this work is the coexistence of a hyperchaotic attractor with a chaotic one over a broad range of system parameters. This phenomenon was not reported previously and therefore represents a meaningful contribution to the understanding of the behavior of nonlinear dynamical systems in general. A close agreement is observed between theoretical and experimental analyses.

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19

Trigui, Omar, Sawsan Daoud, Mohamed Ghorbel, and Chokri Mhiri. "SSVEP Enhancement Using Moving Average Filter Controlled by Phase Features." Computational Intelligence and Neuroscience 2020 (May 8, 2020): 1–11. http://dx.doi.org/10.1155/2020/7459587.

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Brain-computer interface (BCI) systems translate the human neurophysiological activities into commands through EEG analysis. Improving the BCI performances leads to faster and easier use and less fatigue. In this study, we proposed a new prepossessing approach to increase the robustness of a steady-state visual evoked potential (SSVEP) based BCI. Inspiring from the known properties of the SSVEP frequency components, the goal was to enhance the signal quality by making it more convenient to be interpreted by the decision-making step. We first investigated the potential to detect the deteriorating periods based on the physiological properties of the SSVEP. The proposed system localizes the intervals which can obscure the SSVEP frequencies by a new algorithm founded on the processing and the analysis of the instantaneous phase. The piecewise linear regression allows a sampler comprehension of the phase signal. Then, these intervals are filtered by the moving average filter to enhance the SSVEP quality. Finally, the decision making is made by the canonical correlation analysis (CCA) algorithm. The results of experiments, using real EEG signals from five subjects, show that the proposed approach significantly increases the performances in terms of accuracy and information transfer rate by about 7.3% and 3.85 bits/min, respectively, in case of 2 s segment length. On the other hand, the spatial filtering methods of the literature weaken the system performances.

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20

Onur, M., and A. C. Reynolds. "Well Testing Applications of Numerical Laplace Transformation of Sampled-Data." SPE Reservoir Evaluation & Engineering 1, no. 03 (1998): 268–77. http://dx.doi.org/10.2118/36554-pa.

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Abstract In recent years, the numerical Laplace transformation of sampled-data has proven to be useful for well test analysis applications. However, the success of this approach is highly dependent on the algorithms used to transform sampled-data into Laplace space and to perform the numerical inversion. In this work, we investigate several functional approximations (piecewise linear, quadratic, and log-linear) for sampled-data to achieve the "forward" Laplace transformation and present new methods to deal with the "tail" effects associated with transforming sampled-data. New algorithms that provide accurate transformation of sampled-data into Laplace space are provided. The algorithms presented can be applied to generate accurate pressure-derivatives in the time domain. Three different algorithms investigated for the numerical inversion of sampled-data. Applications of the algorithms to convolution, deconvolution, and parameter estimation in Laplace space are also presented. By using the algorithms presented here, it is shown that performing curve-fitting in the Laplace domain without numerical inversion is computationally more efficient than performing it in the time domain. Both synthetic and field examples are considered to illustrate the applicability of the proposed algorithms. Introduction Due to its efficiency, the Stehfest algorithm for the numerical inversion of the Laplace transform is now a well established tool in pressure transient analysis research and applications. Roumboutsos and Stewart showed that convolution and deconvolution in Laplace domain with the aid of the numerical Laplace transformation of measured pressure and/or rate data is more efficient and stable than techniques based on the discretized form of convolution integral in the time domain. Use of the numerical Laplace transformation of tabulated (pressure and/or rate) data has become increasingly popular in recent years for other well testing analysis purposes in a variety of applications; see for example, Refs. 3-10. Guillot and Horne were the first to use piecewise constant and cubic spline interpolations to represent measured flow rate data in Laplace space for the purpose of analyzing pressure tests under variable (downhole or surface) flow rate history by nonlinear regression. Roumboutsos and Stewart were the first to introduce the idea of using the numerical Laplace transformation of measured data for convolution and deconvolution purposes. They presented an algorithm based on piecewise linear interpolation of sampled-data, which can be used to transform measured pressure or rate data into Laplace space. Mendes et al. presented a Laplace domain deconvolution algorithm based on cubic spline interpolation of sampled-data. By considering deconvolution of DST data, they showed that Laplace domain deconvolution is fast and more stable than deconvolution methods based on the discretized forms of the convolution integral in the time domain. However, they noted that noise in pressure and flow rate measurements can also cause instability in Laplace space deconvolution methods, but they did not present any specific results on this issue. Both Corre and Thompson et al. showed that the convolution methods based on a representation of the linear interpolation of the tabulated unit-rate response solution and numerical inversion to the time domain are far more computationally efficient for generating variable rate solutions for complex well/reservoir systems (e.g., partially penetrating wells and horizontal wells) than convolution methods based on the direct use of analytical solutions in Laplace space. Using the numerical Laplace transformation of measured pressure data, Bourgeois and Horne introduced the so-called Laplace pressure and its derivative, and presented Laplace type curves based on these functions for model recognition and parameter estimation purposes. They also deconvolved data using these Laplace pressure functions in the Laplace domain without inversion to the time domain. Wilkinson investigated the applicability of performing nonlinear regression based on the Laplace pressure as suggested in Ref. 7 for parameter estimation purposes.

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21

Veliov, Vladimir M., and Michail I. Krastanov. "Controllability of piecewise linear systems." Systems & Control Letters 7, no. 5 (1986): 335–41. http://dx.doi.org/10.1016/0167-6911(86)90050-2.

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BILLINGS, S. A., and W. S. F. VOON. "Piecewise linear identification of non-linear systems." International Journal of Control 46, no. 1 (1987): 215–35. http://dx.doi.org/10.1080/00207178708933894.

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23

Feldmann, U., and W. Schwarz. "Linear conjugacy of n-dimensional piecewise linear systems." IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 41, no. 2 (1994): 190–92. http://dx.doi.org/10.1109/81.269062.

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24

Verriest, E. I., and A. H. Haddad. "Linear Markov approximations of piecewise linear stochastic systems." Stochastic Analysis and Applications 5, no. 2 (1987): 213–44. http://dx.doi.org/10.1080/07362998708809114.

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25

Freire, Emilio, Enrique Ponce, and Francisco Torres. "Canonical Discontinuous Planar Piecewise Linear Systems." SIAM Journal on Applied Dynamical Systems 11, no. 1 (2012): 181–211. http://dx.doi.org/10.1137/11083928x.

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Johansen, Tor A., Renévan De Molengraft, and Henk Nijmeijer. "Switched, piecewise and polytopic linear systems." International Journal of Control 75, no. 16-17 (2002): 1241–42. http://dx.doi.org/10.1080/0020717021000023672.

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27

Heck, B. S., and A. H. Haddad. "Singular perturbation in piecewise-linear systems." IEEE Transactions on Automatic Control 34, no. 1 (1989): 87–90. http://dx.doi.org/10.1109/9.8652.

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Radons, Manuel. "Direct solution of piecewise linear systems." Theoretical Computer Science 626 (May 2016): 97–109. http://dx.doi.org/10.1016/j.tcs.2016.02.009.

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29

Kirillova, F. M., and N. V. Balashevich. "Optimization of Piecewise Linear Control Systems." IFAC Proceedings Volumes 34, no. 6 (2001): 51–56. http://dx.doi.org/10.1016/s1474-6670(17)35147-9.

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30

Brugnano, Luigi, and Vincenzo Casulli. "Iterative Solution of Piecewise Linear Systems." SIAM Journal on Scientific Computing 30, no. 1 (2008): 463–72. http://dx.doi.org/10.1137/070681867.

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31

Çamlibel, M. K., and I. Üstoĝlu. "FEEDBACK LINEARIZATION OF PIECEWISE LINEAR SYSTEMS." IFAC Proceedings Volumes 38, no. 1 (2005): 478–83. http://dx.doi.org/10.3182/20050703-6-cz-1902.00650.

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32

Zhang, Yu, Gang Feng, and Jitao Sun. "Stability of impulsive piecewise linear systems." International Journal of Systems Science 44, no. 1 (2013): 139–50. http://dx.doi.org/10.1080/00207721.2011.598957.

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33

Sun, Zhendong. "Stability of piecewise linear systems revisited." Annual Reviews in Control 34, no. 2 (2010): 221–31. http://dx.doi.org/10.1016/j.arcontrol.2010.08.003.

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34

Koncar, V., and C. Vasseur. "Control of linear systems using piecewise continuous systems." IEE Proceedings - Control Theory and Applications 150, no. 6 (2003): 565–76. http://dx.doi.org/10.1049/ip-cta:20030964.

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35

Yassin, Fuad, Saman Razavi, Mohamed Elshamy, Bruce Davison, Gonzalo Sapriza-Azuri, and Howard Wheater. "Representation and improved parameterization of reservoir operation in hydrological and land-surface models." Hydrology and Earth System Sciences 23, no. 9 (2019): 3735–64. http://dx.doi.org/10.5194/hess-23-3735-2019.

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Abstract. Reservoirs significantly affect flow regimes in watershed systems by changing the magnitude and timing of streamflows. Failure to represent these effects limits the performance of hydrological and land-surface models (H-LSMs) in the many highly regulated basins across the globe and limits the applicability of such models to investigate the futures of watershed systems through scenario analysis (e.g., scenarios of climate, land use, or reservoir regulation changes). An adequate representation of reservoirs and their operation in an H-LSM is therefore essential for a realistic representation of the downstream flow regime. In this paper, we present a general parametric reservoir operation model based on piecewise-linear relationships between reservoir storage, inflow, and release to approximate actual reservoir operations. For the identification of the model parameters, we propose two strategies: (a) a “generalized” parameterization that requires a relatively limited amount of data and (b) direct calibration via multi-objective optimization when more data on historical storage and release are available. We use data from 37 reservoir case studies located in several regions across the globe for developing and testing the model. We further build this reservoir operation model into the MESH (Modélisation Environmentale-Surface et Hydrologie) modeling system, which is a large-scale H-LSM. Our results across the case studies show that the proposed reservoir model with both parameter-identification strategies leads to improved simulation accuracy compared with the other widely used approaches for reservoir operation simulation. We further show the significance of enabling MESH with this reservoir model and discuss the interdependent effects of the simulation accuracy of natural processes and that of reservoir operations on the overall model performance. The reservoir operation model is generic and can be integrated into any H-LSM.

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36

Saito, Toshimichi. "Piecewise linear switched dynamical systems: A review." Nonlinear Theory and Its Applications, IEICE 11, no. 4 (2020): 373–90. http://dx.doi.org/10.1587/nolta.11.373.

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37

Prohens, Rafel, and Antonio E. Teruel. "Canard trajectories in 3D piecewise linear systems." Discrete & Continuous Dynamical Systems - A 33, no. 10 (2013): 4595–611. http://dx.doi.org/10.3934/dcds.2013.33.4595.

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38

Lincoln, Bo, and Anders Rantzer. "Relaxed Optimal Control of Piecewise Linear Systems." IFAC Proceedings Volumes 36, no. 6 (2003): 385–90. http://dx.doi.org/10.1016/s1474-6670(17)36462-5.

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39

Carmona, V., E. Freire, E. Ponce, and F. Torres. "On simplifying and classifying piecewise-linear systems." IEEE Transactions on Circuits and Systems I: Fundamental Theory and Applications 49, no. 5 (2002): 609–20. http://dx.doi.org/10.1109/tcsi.2002.1001950.

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40

Storace, M., and O. DeFeo. "Piecewise-Linear Approximation of Nonlinear Dynamical Systems." IEEE Transactions on Circuits and Systems I: Regular Papers 51, no. 4 (2004): 830–42. http://dx.doi.org/10.1109/tcsi.2004.823664.

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41

Borges, José, Vincent Verdult, and Michel Verhaegen. "ITERATIVE SUBSPACE IDENTIFICATION OF PIECEWISE LINEAR SYSTEMS." IFAC Proceedings Volumes 39, no. 1 (2006): 368–73. http://dx.doi.org/10.3182/20060329-3-au-2901.00054.

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42

Chen, Shyh-Leh, and Steven W. Shaw. "Normal modes for piecewise linear vibratory systems." Nonlinear Dynamics 10, no. 2 (1996): 135–64. http://dx.doi.org/10.1007/bf00045454.

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43

Fowler, Jeffrey M., and Raffaello D'Andrea. "Structured analysis of piecewise-linear interconnected systems." International Journal of Robust and Nonlinear Control 17, no. 18 (2007): 1754–70. http://dx.doi.org/10.1002/rnc.1191.

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BANKS, S. P., and SAADI A. KHATHUR. "Structure and control of piecewise-linear systems." International Journal of Control 50, no. 2 (1989): 667–86. http://dx.doi.org/10.1080/00207178908953388.

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45

Ferrer, J., M. D. Magret, J. R. Pacha, and M. Peña. "Planar bimodal piecewise linear systems. Bifurcation diagrams." SeMA Journal 51, no. 1 (2010): 55–62. http://dx.doi.org/10.1007/bf03322554.

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FERRER, JOSEP, M. DOLORS MAGRET, and MARTA PEÑA. "BIMODAL PIECEWISE LINEAR DYNAMICAL SYSTEMS: REDUCED FORMS." International Journal of Bifurcation and Chaos 20, no. 09 (2010): 2795–808. http://dx.doi.org/10.1142/s0218127410027362.

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Piecewise linear systems constitute a class of nonlinear systems which have recently attracted the interest of researchers because of their interesting properties and the wide range of applications from which they arise. Different authors have used reduced forms when studying these systems, mostly in the case where they are observable. In this work, we focus on bimodal continuous dynamical systems (those consisting of two linear systems on each side of a given hyperplane, having continuous dynamics along that hyperplane) depending on two or three state variables, which are the most common piecewise linear systems found in practice. Reduced forms are obtained for general systems, not necessarily observable. As an application, we calculate the dimension of the equivalence classes.

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47

Xu, Bin, Fenghong Yang, Yun Tang, and Mu Lin. "Homoclinic Bifurcations in Planar Piecewise-Linear Systems." Discrete Dynamics in Nature and Society 2013 (2013): 1–9. http://dx.doi.org/10.1155/2013/732321.

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The problem of homoclinic bifurcations in planar continuous piecewise-linear systems with two zones is studied. This is accomplished by investigating the existence of homoclinic orbits in the systems. The systems with homoclinic orbits can be divided into two cases: the visible saddle-focus (or saddle-center) case and the case of twofold nodes with opposite stability. Necessary and sufficient conditions for the existence of homoclinic orbits are provided for further study of homoclinic bifurcations. Two kinds of homoclinic bifurcations are discussed: one is generically related to nondegenerate homoclinic orbits; the other is the discontinuity induced homoclinic bifurcations related to the boundary. The results show that at least two parameters are needed to unfold all possible homoclinc bifurcations in the systems.

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48

Savona, Catherine. "Approximate nonlinear filtering for piecewise linear systems." Systems & Control Letters 11, no. 4 (1988): 327–32. http://dx.doi.org/10.1016/0167-6911(88)90078-3.

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49

Zhao, Wei, Jingjing Tong, Jie Liu, Jin Liu, Jinghua Li, and Yongtong Cao. "The Dose-Response Relationship between Gamma-Glutamyl Transferase and Risk of Diabetes Mellitus Using Publicly Available Data: A Longitudinal Study in Japan." International Journal of Endocrinology 2020 (February 21, 2020): 1–7. http://dx.doi.org/10.1155/2020/5356498.

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Purpose. The purpose of this study was to examine the association between baseline serum gamma-glutamyl transferase (GGT) and incident diabetes mellitus and to explore their dose-response relationship in a cohort of Japanese adults. Patients and Methods. Data were drawn from the NAGALA (NAfld in the Gifu Area, Longitudinal Analysis) study between 2004 and 2015, including hierarchical information on participants ≥18 years of age without diabetes mellitus, preexisting diabetes mellitus, heavy alcohol drinking, or other liver diseases (e.g., hepatitis B/C). The final analytic sample included 15464 participants, 373 of who were diagnosed as diabetes mellitus with a maximum 13-year follow-up. The risk of incident diabetes mellitus according to baseline serum GGT was estimated using multivariable Cox proportional hazards models and a two-piecewise linear regression model was developed to find out the threshold effect. Results. Being in the highest quintile versus the lowest quintile of GGT levels was associated with an almost twofold increased risk of incident diabetes mellitus (hazard ratio 1.83 (95% CI 1.06, 3.15)), independent of age, gender, smoking status, alcohol intake, BMI, SBP, triglycerides, fatty liver, ALT, AST, and fasting plasma glucose. Further analysis revealed a positive curvilinear association between GGT and incident diabetes mellitus, with a saturation effect predicted at 24 IU/L. When serum GGT level was less than 24 IU/L, the risk of developing diabetes mellitus increased significantly with an increase in serum GGT levels (HR 1.04 (1.02, 1.07), P=0.0017). Besides, the association was more significant in nonsmoking participants than ex- or current-smokers (P for interaction = 0.0378). Conclusion. Serum GGT level was a significant predictor of subsequent risk of diabetes mellitus, which increased by 4% for every 1 IU/L increase in GGT when GGT was less than 24 IU/L.

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Józefczyk, Jerzy, and Mirosław Ławrynowicz. "Heuristic algorithms for the Internet shopping optimization problem with price sensitivity discounts." Kybernetes 47, no. 4 (2018): 831–52. http://dx.doi.org/10.1108/k-07-2017-0264.

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Purpose Rapid advancements in internet technology have made it possible to develop electronic commerce in general and internet shopping in particular. Easy access to a vast number of existing internet stores enables buyers to customize their shopping processes to minimize the total purchase cost. This paper aims to investigate a novel internet shopping problem, which consists of the diversification of a given list of products to buy among many stores and to use discounts offered by the stores. Design/methodology/approach The adequate discrete optimization problem referred to as internet shopping optimization problem with price sensitivity discounts (ISOPwD) is investigated, which turned out to be strongly nondeterministic polynomial (NS)-hard. Two heuristic solution algorithms have been derived using the tabu search (TS) and the simulated annealing (SA) metaheuristics for having a solution in a reasonable time. The algorithms have been assessed via computational experiments, and they have been compared with another algorithm known from the literature that has been elaborated for a simpler version of ISOPwD. Findings The conducted evaluation has shown the advantage of both heuristic algorithms on the algorithm known from the literature. Moreover, the TS-based algorithm outperformed the other one in terms of the total cost incurred by customers and the computational time. Research limitations/implications The special primary piecewise linear discounting function is only taken into account. Other possible discounts connected, for example, with bundles of products and (or) coupons are not considered. Practical implications The elaborated algorithms can be recommended for internet shopping providers who want to introduce the ability to search a cost-optimized set of products in their databases or for applications that combine offers from various online retailers, e.g. internet price comparison services and auction sites. Originality/value The novelty of considered ISOPwD, in comparison with similar problems discussed in the literature, deals with an arbitrary number of purchased products, the possibility to buy an identical product in different stores and the consideration of the weight, the amount and the availability of goods as parameters of ISOPwD.

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