Search results for: Lipschitz nonlinear systems

Authors: Brahmi Brahim, Mohammad Habibur Rahman, Maarouf Saad, Cristóbal Ochoa Luna

Abstract:

A repetitive training movement is an efficient method to improve the ability and movement performance of stroke survivors and help them to recover their lost motor function and acquire new skills. The ETS-MARSE is seven degrees of freedom (DOF) exoskeleton robot developed to be worn on the lateral side of the right upper-extremity to assist and rehabilitate the patients with upper-extremity dysfunction resulting from stroke. Practically, rehabilitation activities are repetitive tasks, which make the assistive/robotic systems to suffer from repetitive/periodic uncertainties and external perturbations induced by the high-order dynamic model (seven DOF) and interaction with human muscle which impact on the tracking performance and even on the stability of the exoskeleton. To ensure the robustness and the stability of the robot, a new nonlinear backstepping control was implemented with designed tests performed by healthy subjects. In order to limit and to reject the periodic/repetitive disturbances, an iterative estimator was integrated into the control of the system. The estimator does not need the precise dynamic model of the exoskeleton. Experimental results confirm the robustness and accuracy of the controller performance to deal with the external perturbation, and the effectiveness of the iterative estimator to reject the repetitive/periodic disturbances.

Keywords: Backstepping control, iterative control, rehabilitation, ETS-MARSE.

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Authors: Hassen M. Ouakad

Abstract:

In this paper, the influence of van der Waals, as well as electrostatic forces on the structural behavior of MEMS and NEMS actuators, has been investigated using of a Euler-Bernoulli beam continuous model. In the proposed nonlinear model, the electrostatic fringing-fields and the mid-plane stretching (geometric nonlinearity) effects have been considered. The nonlinear integro-differential equation governing the static structural behavior of the actuator has been derived. An original Galerkin-based reduced-order model has been developed to avoid problems arising from the nonlinearities in the differential equation. The obtained reduced-order model equations have been solved numerically using the Newton-Raphson method. The basic design parameters such as the pull-in parameters (voltage and deflection at pull-in), as well as the detachment length due to the van der Waals force of some investigated micro- and nano-actuators have been calculated. The obtained numerical results have been compared with some other existing methods (finite-elements method and finite-difference method) and the comparison showed good agreement among all assumed numerical techniques.

Keywords: MEMS, NEMS, fringing-fields, mid-plane stretching, Galerkin method.

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Authors: A. Pashkevich, A. Klimchik, D. Chablat

Abstract:

The paper focuses on the enhanced stiffness modeling of robotic manipulators by taking into account influence of the external force/torque acting upon the end point. It implements the virtual joint technique that describes the compliance of manipulator elements by a set of localized six-dimensional springs separated by rigid links and perfect joints. In contrast to the conventional formulation, which is valid for the unloaded mode and small displacements, the proposed approach implicitly assumes that the loading leads to the non-negligible changes of the manipulator posture and corresponding amendment of the Jacobian. The developed numerical technique allows computing the static equilibrium and relevant force/torque reaction of the manipulator for any given displacement of the end-effector. This enables designer detecting essentially nonlinear effects in elastic behavior of manipulator, similar to the buckling of beam elements. It is also proposed the linearization procedure that is based on the inversion of the dedicated matrix composed of the stiffness parameters of the virtual springs and the Jacobians/Hessians of the active and passive joints. The developed technique is illustrated by an application example that deals with the stiffness analysis of a parallel manipulator of the Orthoglide family

Keywords: Robotic manipulators, Stiffness model, Loaded mode, Nonlinear effects, Buckling, Orthoglide manipulator

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Authors: Mingyu Xie, Mietek Brdys

Abstract:

The paper develops a Non-Linear Model Predictive Control (NMPC) of water quality in Drinking Water Distribution Systems (DWDS) based on the advanced non-linear quality dynamics model including disinfections by-products (DBPs). A special attention is paid to the analysis of an impact of the flow trajectories prescribed by an upper control level of the recently developed two-time scale architecture of an integrated quality and quantity control in DWDS. The new quality controller is to operate within this architecture in the fast time scale as the lower level quality controller. The controller performance is validated by a comprehensive simulation study based on an example case study DWDS.

Keywords: Model predictive control, hierarchical control structure, genetic algorithm, water quality with DBPs objectives.

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Authors: Nicolò Vaiana, Filip C. Filippou, Giorgio Serino

Abstract:

In order to reduce numerical computations in the nonlinear dynamic analysis of seismically base-isolated structures, a Mixed Explicit-Implicit time integration Method (MEIM) has been proposed. Adopting the explicit conditionally stable central difference method to compute the nonlinear response of the base isolation system, and the implicit unconditionally stable Newmark’s constant average acceleration method to determine the superstructure linear response, the proposed MEIM, which is conditionally stable due to the use of the central difference method, allows to avoid the iterative procedure generally required by conventional monolithic solution approaches within each time step of the analysis. The main aim of this paper is to investigate the stability and computational efficiency of the MEIM when employed to perform the nonlinear time history analysis of base-isolated structures with sliding bearings. Indeed, in this case, the critical time step could become smaller than the one used to define accurately the earthquake excitation due to the very high initial stiffness values of such devices. The numerical results obtained from nonlinear dynamic analyses of a base-isolated structure with a friction pendulum bearing system, performed by using the proposed MEIM, are compared to those obtained adopting a conventional monolithic solution approach, i.e. the implicit unconditionally stable Newmark’s constant acceleration method employed in conjunction with the iterative pseudo-force procedure. According to the numerical results, in the presented numerical application, the MEIM does not have stability problems being the critical time step larger than the ground acceleration one despite of the high initial stiffness of the friction pendulum bearings. In addition, compared to the conventional monolithic solution approach, the proposed algorithm preserves its computational efficiency even when it is adopted to perform the nonlinear dynamic analysis using a smaller time step.

Keywords: Base isolation, computational efficiency, mixed explicit-implicit method, partitioned solution approach, stability.

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Authors: William Anderson, Kyle Kobold, Oleg Yakimenko

Abstract:

Green microgrids using mostly renewable energy (RE) for generation, are complex systems with inherent nonlinear dynamics. Among a variety of different optimization tools there are only a few ones that adequately consider this complexity. This paper evaluates applicability of two somewhat similar optimization tools tailored for standalone RE microgrids and also assesses a machine learning tool for performance prediction that can enhance the reliability of any chosen optimization tool. It shows that one of these microgrid optimization tools has certain advantages over another and presents a detailed routine of preparing input data to simulate RE microgrid behavior. The paper also shows how neural-network-based predictive modeling can be used to validate and forecast solar power generation based on weather time series data, which improves the overall quality of standalone RE microgrid analysis.

Keywords: Microgrid, renewable energy, complex systems, optimization, predictive modeling, neural networks.

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Authors: Farnaz G. Nezami, Mir B. Aryanezhad, Seyed J. Sadjadi

Abstract:

In this paper a nonlinear model is presented to demonstrate the relation between production and marketing departments. By introducing some functions such as pricing cost and market share loss functions it will be tried to show some aspects of market modelling which has not been regarded before. The proposed model will be a constrained signomial geometric programming model. For model solving, after variables- modifications an iterative technique based on the concept of geometric mean will be introduced to solve the resulting non-standard posynomial model which can be applied to a wide variety of models in non-standard posynomial geometric programming form. At the end a numerical analysis will be presented to accredit the validity of the mentioned model.

Keywords: Geometric programming, marketing, nonlinear optimization, production.

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

Abstract:

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, sparse-view reconstruction, L1 −L2 minimization, non-convex, difference of convex functions.

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Authors: K. P. Csányi, L. T. Kóczy, D. Tikk

Abstract:

This paper indicate the importance of telecommunications supervision systems (TSS), integrating heterogeneous TSS into single system thru umbrella systems, introduces the structure, features, requirements of TSS and TSS related intelligent solutions.

Keywords: Telecommunication, telecommunication supervisionsystems, umbrella systems

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Authors: Anupma Bansal, R. K. Gupta

Abstract:

In this paper, we study a new modified Novikov equation for its classical and nonclassical symmetries and use the symmetries to reduce it to a nonlinear ordinary differential equation (ODE). With the aid of solutions of the nonlinear ODE by using the modified (G/G)-expansion method proposed recently, multiple exact traveling wave solutions are obtained and the traveling wave solutions are expressed by the hyperbolic functions, trigonometric functions and rational functions.

Keywords: New Modified Novikov Equation, Lie Classical Method, Nonclassical Method, Modified (G'/G)-Expansion Method, Traveling Wave Solutions.

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Authors: Chuanyun Gu

Abstract:

By using fixed point theorems for a class of generalized concave and convex operators, the positive solution of nonlinear fractional differential equation with integral boundary conditions is studied, where n ≥ 3 is an integer, μ is a parameter and 0 ≤ μ < α. Its existence and uniqueness is proved, and an iterative scheme is constructed to approximate it. Finally, two examples are given to illustrate our results.

Keywords: Fractional differential equation, positive solution, existence and uniqueness, fixed point theorem, generalized concave and convex operator, integral boundary conditions.

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Authors: Ikbal Zammouri, Béchir Ayeb

Abstract:

In this paper, we propose a new method to describe fractal shapes using parametric l-systems. First we introduce scaling factors in the production rules of the parametric l-systems grammars. Then we decorticate these grammars with scaling factors using turtle algebra to show the mathematical relation between l-systems and iterated function systems (IFS). We demonstrate that with specific values of the scaling factors, we find the exact relationship established by Prusinkiewicz and Hammel between l-systems and IFS.

Keywords: Fractal shapes, IFS, parametric l-systems, turtlealgebra.

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Authors: Joe Imae, Kenjiro Shinagawa, Tomoaki Kobayashi, Guisheng Zhai

Abstract:

We propose a new approach on how to obtain the approximate solutions of Hamilton-Jacobi (HJ) equations. The process of the approximation consists of two steps. The first step is to transform the HJ equations into the virtual time based HJ equations (VT-HJ) by introducing a new idea of ‘virtual-time’. The second step is to construct the approximate solutions of the HJ equations through a computationally iterative procedure based on the VT-HJ equations. It should be noted that the approximate feedback solutions evolve by themselves as the virtual-time goes by. Finally, we demonstrate the effectiveness of our approximation approach by means of simulations with linear and nonlinear control problems.

Keywords: Nonlinear Control, Optimal Control, Hamilton-Jacobi Equation, Virtual-Time

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Authors: Ramesh K. Sunkaria

Abstract:

The linear methods of heart rate variability analysis such as non-parametric (e.g. fast Fourier transform analysis) and parametric methods (e.g. autoregressive modeling) has become an established non-invasive tool for marking the cardiac health, but their sensitivity and specificity were found to be lower than expected with positive predictive value <30%. This may be due to considering the RR-interval series as stationary and re-sampling them prior to their use for analysis, whereas actually it is not. This paper reviews the non-linear methods of HRV analysis such as correlation dimension, largest Lyupnov exponent, power law slope, fractal analysis, detrended fluctuation analysis, complexity measure etc. which are currently becoming popular as these uses the actual RR-interval series. These methods are expected to highly accurate cardiac health prognosis.

Keywords: chaos, nonlinear dynamics, sample entropy, approximate entropy, detrended fluctuation analysis.

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Authors: Mohamed M. Mousa, Aidarkhan Kaltayev Shahwar F. Ragab

Abstract:

In this paper, a new dependable algorithm based on an adaptation of the standard variational iteration method (VIM) is used for analyzing the transition from steady convection to chaos for lowto-intermediate Rayleigh numbers convection in porous media. The solution trajectories show the transition from steady convection to chaos that occurs at a slightly subcritical value of Rayleigh number, the critical value being associated with the loss of linear stability of the steady convection solution. The VIM is treated as an algorithm in a sequence of intervals for finding accurate approximate solutions to the considered model and other dynamical systems. We shall call this technique as the piecewise VIM. Numerical comparisons between the piecewise VIM and the classical fourth-order Runge–Kutta (RK4) numerical solutions reveal that the proposed technique is a promising tool for the nonlinear chaotic and nonchaotic systems.

Keywords: Variational iteration method, free convection, Chaos, Lorenz equations.

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

Abstract:

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: Miloš Šeda, Tomáš Březina

Abstract:

In this paper, we focus on the use of knowledge bases in two different application areas – control of systems with unknown or strongly nonlinear models (i.e. hardly controllable by the classical methods), and robot motion planning in eight directions. The first one deals with fuzzy logic and the paper presents approaches for setting and aggregating the rules of a knowledge base. Te second one is concentrated on a case-based reasoning strategy for finding the path in a planar scene with obstacles.

Keywords: fuzzy controller, fuzzification, rule base, inference, defuzzification, genetic algorithm, neural network, case-based reasoning

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Authors: Ö. Tolga Altınöz

Abstract:

The adaptive backstepping controller for inverted pendulum is designed by using the general motion control model. Backstepping is a novel nonlinear control technique based on the Lyapunov design approach, used when higher derivatives of parameter estimation appear. For easy parameter adaptation, the mathematical model of the inverted pendulum converted into the motion control model. This conversion is performed by taking functions of unknown parameters and dynamics of the system. By using motion control model equations, inverted pendulum is simulated without any information about not only parameters but also measurable dynamics. Also these results are compare with the adaptive backstepping controller which extended with integral action that given from [1].

Keywords: Adaptive backstepping, inverted pendulum, nonlinear adaptive control.

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Authors: L. Bikulciene, E. Venskaityte, G. Jarusevicius

Abstract:

Nonstationary and nonlinear signals generated by living complex systems defy traditional mechanistic approaches, which are based on homeostasis. Previous our studies have shown that the evaluation of the interactions of physiological signals by using special analysis methods is suitable for observation of physiological processes. It is demonstrated the possibility of using deep physiological model, based on the interpretation of the changes of the human body’s functional states combined with an application of the analytical method based on matrix theory for the physiological signals analysis, which was applied on high risk cardiac patients. It is shown that evaluation of cardiac signals interactions show peculiar for each individual functional changes at the onset of hemodynamic restoration procedure. Therefore, we suggest that the alterations of functional state of the body, after patients overcome surgery can be complemented by the data received from the suggested approach of the evaluation of functional variables’ interactions.

Keywords: Cardiac diseases, Complex systems theory, ECG analysis, matrix analysis.

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Authors: Mansoor Ahsan, Suhail Akhtar, Adnan Ali, Farrukh Mazhar, Muddssar Khalid

Abstract:

In the present era of aviation technology, autonomous navigation and control have emerged as a prime area of active research. Owing to the tremendous developments in the field, autonomous controls have led today’s engineers to claim that future of aerospace vehicle is unmanned. Development of guidance and navigation algorithms for an unmanned aerial vehicle (UAV) is an extremely challenging task, which requires efforts to meet strict, and at times, conflicting goals of guidance and control. In this paper, aircraft altitude and heading controllers and an efficient algorithm for self-governing navigation using MATLAB® mapping toolbox is presented which also enables loitering of a fixed wing UAV over a specified area. For this purpose, a nonlinear mathematical model of a UAV is used. The nonlinear model is linearized around a stable trim point and decoupled for controller design. The linear controllers are tested on the nonlinear aircraft model and navigation algorithm is subsequently developed for for autonomous flight of the UAV. The results are presented for trajectory controllers and waypoint based navigation. Our investigation reveals that MATLAB® mapping toolbox can be exploited to successfully deliver an efficient algorithm for autonomous aerial navigation for a UAV.

Keywords: Navigation, trajectory-control, unmanned aerial vehicle, PID-control, MATLAB® mapping toolbox.

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Authors: Soyoon Bak, Sunyoung Bu, Philsu Kim

Abstract:

In this paper, a backward semi-Lagrangian scheme combined with the second-order backward difference formula is designed to calculate the numerical solutions of nonlinear advection-diffusion equations. The primary aims of this paper are to remove any iteration process and to get an efficient algorithm with the convergence order of accuracy 2 in time. In order to achieve these objects, we use the second-order central finite difference and the B-spline approximations of degree 2 and 3 in order to approximate the diffusion term and the spatial discretization, respectively. For the temporal discretization, the second order backward difference formula is applied. To calculate the numerical solution of the starting point of the characteristic curves, we use the error correction methodology developed by the authors recently. The proposed algorithm turns out to be completely iteration free, which resolves the main weakness of the conventional backward semi-Lagrangian method. Also, the adaptability of the proposed method is indicated by numerical simulations for Burgers’ equations. Throughout these numerical simulations, it is shown that the numerical results is in good agreement with the analytic solution and the present scheme offer better accuracy in comparison with other existing numerical schemes.

Keywords: Semi-Lagrangian method, Iteration free method, Nonlinear advection-diffusion equation.

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Authors: Kourosh Parand, Jamal Amani Rad

Abstract:

In this paper, Exp-function method is used for some exact solitary solutions of the generalized Pochhammer-Chree equation. It has been shown that the Exp-function method, with the help of symbolic computation, provides a very effective and powerful mathematical tool for solving nonlinear partial differential equations. As a result, some exact solitary solutions are obtained. It is shown that the Exp-function method is direct, effective, succinct and can be used for many other nonlinear partial differential equations.

Keywords: Exp-function method, generalized Pochhammer- Chree equation, solitary wave solution, ODE's.

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Authors: B. Ghosh, H. Sahoo, K. K. Mondal

Abstract:

Propagation of arbitrary amplitude nonlinear Alfven waves has been investigated in low but finite β electron-positron-ion plasma including full ion dynamics. Using Sagdeev pseudopotential method an energy integral equation has been derived. The Sagdeev potential has been calculated for different plasma parameters and it has been shown that inclusion of ion parallel motion along the magnetic field changes the nature of slow shear Alfven wave solitons from dip type to hump type. The effects of positron concentration, plasma-β and obliqueness of the wave propagation on the solitary wave structure have also been examined.

Keywords: Alfven waves, Sagdeev potential, Solitary waves.

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Authors: E. Assareh, M.A. Behrang, M. Ghalambaz, A.R. Noghrehabadi, A. Ghanbarzadeh

Abstract:

In this paper, a new approach is introduced to solve Blasius equation using parameter identification of a nonlinear function which is used as approximation function. Bees Algorithm (BA) is applied in order to find the adjustable parameters of approximation function regarding minimizing a fitness function including these parameters (i.e. adjustable parameters). These parameters are determined how the approximation function has to satisfy the boundary conditions. In order to demonstrate the presented method, the obtained results are compared with another numerical method. Present method can be easily extended to solve a wide range of problems.

Keywords: Bees Algorithm (BA); Approximate Solutions; Blasius Differential Equation.

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Authors: Jagannath Aryal, Don Kulasiri, Dishi Liu

Abstract:

This paper describes the optimization of a complex dairy farm simulation model using two quite different methods of optimization, the Genetic algorithm (GA) and the Lipschitz Branch-and-Bound (LBB) algorithm. These techniques have been used to improve an agricultural system model developed by Dexcel Limited, New Zealand, which describes a detailed representation of pastoral dairying scenarios and contains an 8-dimensional parameter space. The model incorporates the sub-models of pasture growth and animal metabolism, which are themselves complex in many cases. Each evaluation of the objective function, a composite 'Farm Performance Index (FPI)', requires simulation of at least a one-year period of farm operation with a daily time-step, and is therefore computationally expensive. The problem of visualization of the objective function (response surface) in high-dimensional spaces is also considered in the context of the farm optimization problem. Adaptations of the sammon mapping and parallel coordinates visualization are described which help visualize some important properties of the model-s output topography. From this study, it is found that GA requires fewer function evaluations in optimization than the LBB algorithm.

Keywords: Genetic Algorithm, Linux Cluster, LipschitzBranch-and-Bound, Optimization

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Authors: A. Nuric, S. Nuric, L. Kricak, I. Lapandic, R. Husagic

Abstract:

This paper describes topic of computer simulation with regard to the ground movement above an underground mine. Simulation made with software package ADINA for nonlinear elastic-plastic analysis with finite elements method. The one of representative profiles from Mine 'Stara Jama' in Zenica has been investigated. A collection and selection of both geo-mechanical data and geometric parameters of the mine was necessary for performing these simulations. Results of estimation have been compared with measured values (vertical displacement of surface), and then simulation performed with assumed dynamic and dimensions of excavation, over a period of time. Results are presented with bitmaps and charts.

Keywords: Computer, finite element method, mine, nonlinear analysis, numerical modeling, simulation, subsidence.

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Authors: Saman M. Siddiqui, Fang Jiancheng

Abstract:

Robust nonlinear integrated navigation of GPS and low cost MEMS is a hot topic of research these days. A robust filter is required to cope up with the problem of unpredictable discontinuities and colored noises associated with low cost sensors. H∞ filter is previously used in Extended Kalman filter and Unscented Kalman filter frame. Unscented Kalman filter has a problem of Cholesky matrix factorization at each step which is a very unstable operation. To avoid this problem in this research H∞ filter is designed in Square root Unscented filter framework and found 50% more robust towards increased level of colored noises.

Keywords: H∞ filter, MEMS, GPS, Nonlinear system, robust system, Square root unscented filter.

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Authors: B. X. Tchomeni, A. A. Alugongo, L. M. Masu

Abstract:

An analytical 4-DOF nonlinear model of a de Laval rotor-stator system based on Energy Principles has been used theoretically and experimentally to investigate fault symptoms in a rotating system. The faults, namely rotor-stator-rub, crack and unbalance are modeled as excitations on the rotor shaft. Mayes steering function is used to simulate the breathing behaviour of the crack. The fault analysis technique is based on waveform signal, orbits and Fast Fourier Transform (FFT) derived from simulated and real measured signals. Simulated and experimental results manifest considerable mutual resemblance of elliptic-shaped orbits and FFT for a same range of test data.

Keywords: A breathing crack, fault, FFT, nonlinear, orbit, rotorstator rub, vibration analysis.

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Authors: Nina Øystad-Larsen, Miran Cemalovic, Amir M. Kaynia

Abstract:

The nonlinear static and dynamic analysis procedures presented in EN 1998-1 for the structural response of a RC wall-frame building are assessed. The structure is designed according to the guidelines for high ductility (DCH) in 1998-1. The finite element packages SeismoStruct and OpenSees are utilized and evaluated. The structural response remains nearly in the elastic range even though the building was designed for high ductility. The overstrength is a result of oversized and heavily reinforced members, with emphasis on the lower storey walls. Nonlinear response history analysis in the software packages give virtually identical results for displacements.

Keywords: Behaviour factor, Dual system, OpenSEES, Overstrength, SeismoStruct.

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Authors: Zixin Liu, Jian Yu, Daoyun Xu

Abstract:

This paper aims to establish a delayed dynamical relationship between payoffs of players in a zero-sum game. By introducing Markovian chain and time delay in the network model, a delayed game network model with sector bounds and slope bounds restriction nonlinear function is first proposed. As a result, a direct dynamical relationship between payoffs of players in a zero-sum game can be illustrated through a delayed singular system. Combined with Finsler-s Lemma and Lyapunov stable theory, a sufficient condition guaranteeing the unique existence and stability of zero-sum game-s Nash equilibrium is derived. One numerical example is presented to illustrate the validity of the main result.

Keywords: Game networks, zero-sum game, delayed singular system, nonlinear perturbation, time delay.

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