Search results for: Linear Multistep Method

Authors: Myeongjin Park, Ohmin Kwon, Juhyun Park, Sangmoon Lee

Abstract:

This paper proposes improved delay-dependent stability conditions of the linear time-delay systems of neutral type. The proposed methods employ a suitable Lyapunov-Krasovskii’s functional and a new form of the augmented system. New delay-dependent stability criteria for the systems are established in terms of Linear matrix inequalities (LMIs) which can be easily solved by various effective optimization algorithms. Numerical examples showed that the proposed method is effective and can provide less conservative results.

Keywords: Neutral systems, Time-delay, Stability, Lyapunovmethod, LMI.

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Authors: Tomoaki Hashimoto

Abstract:

Recently, feedback control systems using random dither quantizers have been proposed for linear discrete-time systems. However, the constraints imposed on state and control variables have not yet been taken into account for the design of feedback control systems with random dither quantization. Model predictive control is a kind of optimal feedback control in which control performance over a finite future is optimized with a performance index that has a moving initial and terminal time. An important advantage of model predictive control is its ability to handle constraints imposed on state and control variables. Based on the model predictive control approach, the objective of this paper is to present a control method that satisfies probabilistic state constraints for linear discrete-time feedback control systems with random dither quantization. In other words, this paper provides a method for solving the optimal control problems subject to probabilistic state constraints for linear discrete-time feedback control systems with random dither quantization.

Keywords: Optimal control, stochastic systems, discrete-time systems, probabilistic constraints, random dither quantization.

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Authors: N. H. Adenan, M. S. M. Noorani

Abstract:

River flow prediction is an essential tool to ensure proper management of water resources and the optimal distribution of water to consumers. This study presents an analysis and prediction by using nonlinear prediction method with monthly river flow data for Tanjung Tualang from 1976 to 2006. Nonlinear prediction method involves the reconstruction of phase space and local linear approximation approach. The reconstruction of phase space involves the reconstruction of one-dimension (the observed 287 months of data) in a multidimensional phase space to reveal the dynamics of the system. The revenue of phase space reconstruction is used to predict the next 72 months. A comparison of prediction performance based on correlation coefficient (CC) and root mean square error (RMSE) was employed to compare prediction performance for the nonlinear prediction method, ARIMA and SVM. Prediction performance comparisons show that the prediction results using the nonlinear prediction method are better than ARIMA and SVM. Therefore, the results of this study could be used to develop an efficient water management system to optimize the allocation of water resources.

Keywords: River flow, nonlinear prediction method, phase space, local linear approximation.

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Authors: Mehdi Ghayoumi

Abstract:

We have applied new accelerated algorithm for linear discriminate analysis (LDA) in face recognition with support vector machine. The new algorithm has the advantage of optimal selection of the step size. The gradient descent method and new algorithm has been implemented in software and evaluated on the Yale face database B. The eigenfaces of these approaches have been used to training a KNN. Recognition rate with new algorithm is compared with gradient.

Keywords: lda, adaptive, svm, face recognition.

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Authors: Mohana Sundaram Muthuvalu, Jumat Sulaiman

Abstract:

In this paper, application of the complexity reduction approach based on half- and quarter-sweep iteration concepts with Jacobi iterative method for solving composite trapezoidal (CT) algebraic equations is discussed. The performances of the methods for CT algebraic equations are comparatively studied by their application in solving linear Fredholm integral equations of the second kind. Furthermore, computational complexity analysis and numerical results for three test problems are also included in order to verify performance of the methods.

Keywords: Complexity reduction approach, Composite trapezoidal scheme, Jacobi method, Linear Fredholm integral equations

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Authors: I. Davies, O. L. C. Haas

Abstract:

In this paper, the problem of stability and stabilization for neutral delay-differential systems with infinite delay is investigated. Using Lyapunov method, new delay-independent sufficient condition for the stability of neutral systems with infinite delay is obtained in terms of linear matrix inequality (LMI). Memory-less state feedback controllers are then designed for the stabilization of the system using the feasible solution of the resulting LMI, which are easily solved using any optimization algorithms. Numerical examples are given to illustrate the results of the proposed methods.

Keywords: Infinite delays, Lyapunov method, linear matrix inequality, neutral systems, stability.

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Authors: Guangbin Wang, Ning Zhang, Fuping Tan

Abstract:

In this paper, we present parallel alternating two-stage methods for solving linear system Ax = b, where A is a monotone matrix or an H-matrix. And we give some convergence results of these methods for nonsingular linear system.

Keywords: Parallel, alternating two-stage, convergence, linear system.

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Authors: Faheem Ahmed, Fareed Ahmed, Yongheng Guo, Yong Yang

Abstract:

This paper deals with a high-order accurate Runge Kutta Discontinuous Galerkin (RKDG) method for the numerical solution of the wave equation, which is one of the simple case of a linear hyperbolic partial differential equation. Nodal DG method is used for a finite element space discretization in 'x' by discontinuous approximations. This method combines mainly two key ideas which are based on the finite volume and finite element methods. The physics of wave propagation being accounted for by means of Riemann problems and accuracy is obtained by means of high-order polynomial approximations within the elements. High order accurate Low Storage Explicit Runge Kutta (LSERK) method is used for temporal discretization in 't' that allows the method to be nonlinearly stable regardless of its accuracy. The resulting RKDG methods are stable and high-order accurate. The L1 ,L2 and L∞ error norm analysis shows that the scheme is highly accurate and effective. Hence, the method is well suited to achieve high order accurate solution for the scalar wave equation and other hyperbolic equations.

Keywords: Nodal Discontinuous Galerkin Method, RKDG, Scalar Wave Equation, LSERK

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Authors: Dursun M., Koc F., Ozbay H.

Abstract:

In this study, a double-sided linear switched reluctance motor (LSRM) drive was investigated as an alternative actuator for vertical linear transportation applications such as a linear elevator door, hospital and subway doors which move linearly and where accurate position control and rapid response is requested. A prototype sliding elevator door that is focused on a home elevator with LSRMs is designed. The motor has 6/4 poles, 3 phases, 8A, 24V, 250 W and 250 N pull forces. Air gap between rotor and translator poles of the designed motor and phase coil-s ideal inductance profile are obtained in compliance with the geometric dimensions. Operation and switching sections as motor and generator has been determined from the inductance profile.

Keywords: Linear switched reluctance motor, sliding door, elevator door, linear motor design.

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Authors: M. Pourgholi, V.J.Majd

Abstract:

This paper addresses parameter and state estimation problem in the presence of the perturbation of observer gain bounded input disturbances for the Lipschitz systems that are linear in unknown parameters and nonlinear in states. A new nonlinear adaptive resilient observer is designed, and its stability conditions based on Lyapunov technique are derived. The gain for this observer is derived systematically using linear matrix inequality approach. A numerical example is provided in which the nonlinear terms depend on unmeasured states. The simulation results are presented to show the effectiveness of the proposed method.

Keywords: Adaptive observer, linear matrix inequality, nonlinear systems, nonlinear observer, resilient observer, robust estimation.

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Authors: A. K. Al-Othman

Abstract:

This study presents a new approach based on Tanaka's fuzzy linear regression (FLP) algorithm to solve well-known power system economic load dispatch problem (ELD). Tanaka's fuzzy linear regression (FLP) formulation will be employed to compute the optimal solution of optimization problem after linearization. The unknowns are expressed as fuzzy numbers with a triangular membership function that has middle and spread value reflected on the unknowns. The proposed fuzzy model is formulated as a linear optimization problem, where the objective is to minimize the sum of the spread of the unknowns, subject to double inequality constraints. Linear programming technique is employed to obtain the middle and the symmetric spread for every unknown (power generation level). Simulation results of the proposed approach will be compared with those reported in literature.

Keywords: Economic Dispatch, Fuzzy Linear Regression (FLP)and Optimization.

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Authors: Pisit Boonsrimuang, Arjin Numsomran, Tawil Paungma, Hideo Kobayashi

Abstract:

One of the disadvantages of using OFDM is the larger peak to averaged power ratio (PAPR) in its time domain signal. The larger PAPR signal would course the fatal degradation of bit error rate performance (BER) due to the inter-modulation noise in the nonlinear channel. This paper proposes an improved DSI (Dummy Sequence Insertion) method, which can achieve the better PAPR and BER performances. The feature of proposed method is to optimize the phase of each dummy sub-carrier so as to reduce the PAPR performance by changing all predetermined phase coefficients in the time domain signal, which is calculated for data sub-carriers and dummy sub-carriers separately. To achieve the better PAPR performance, this paper also proposes to employ the time-frequency domain swapping algorithm for fine adjustment of phase coefficient of the dummy subcarriers, which can achieve the less complexity of processing and achieves the better PAPR and BER performances than those for the conventional DSI method. This paper presents various computer simulation results to verify the effectiveness of proposed method as comparing with the conventional methods in the non-linear channel.

Keywords: OFDM, PAPR, dummy sub-carriers, non-linear

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Authors: Jooho Hwang, Chang-Kyu Song, Chun-Hong Park

Abstract:

This paper describes a method to measure and compensate a 4 axes ultra-precision machine tool that generates micro patterns on the large surfaces. The grooving machine is usually used for making a micro mold for many electrical parts such as a light guide plate for LCD and fuel cells. The ultra precision machine tool has three linear axes and one rotational table. Shaping is usually used to generate micro patterns. In the case of 50 μm pitch and 25 μm height pyramid pattern machining with a 90° wedge angle bite, one of linear axis is used for long stroke motion for high cutting speed and other linear axis are used for feeding. The triangular patterns can be generated with many times of long stroke of one axis. Then 90° rotation of work piece is needed to make pyramid patterns with superposition of machined two triangular patterns. To make a two dimensional positioning error, straightness of two axes in out of plane, squareness between the each axis are important. Positioning errors, straightness and squarness were measured by laser interferometer system. Those were compensated and confirmed by ISO230-6. One of difficult problem to measure the error motions is squareness or parallelism of axis between the rotational table and linear axis. It was investigated by simultaneous moving of rotary table and XY axes. This compensation method is introduced in this paper.

Keywords: Ultra-precision machine tool, muti-axis errors, squraness, positioning errors.

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Authors: Rampal Singh, S. Balasundaram

Abstract:

In this paper, we study the application of Extreme Learning Machine (ELM) algorithm for single layered feedforward neural networks to non-linear chaotic time series problems. In this algorithm the input weights and the hidden layer bias are randomly chosen. The ELM formulation leads to solving a system of linear equations in terms of the unknown weights connecting the hidden layer to the output layer. The solution of this general system of linear equations will be obtained using Moore-Penrose generalized pseudo inverse. For the study of the application of the method we consider the time series generated by the Mackey Glass delay differential equation with different time delays, Santa Fe A and UCR heart beat rate ECG time series. For the choice of sigmoid, sin and hardlim activation functions the optimal values for the memory order and the number of hidden neurons which give the best prediction performance in terms of root mean square error are determined. It is observed that the results obtained are in close agreement with the exact solution of the problems considered which clearly shows that ELM is a very promising alternative method for time series prediction.

Keywords: Chaotic time series, Extreme learning machine, Generalization performance.

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Authors: Karima Siham Aoubid, Mohamed Boulemden

Abstract:

The development of the signal compression algorithms is having compressive progress. These algorithms are continuously improved by new tools and aim to reduce, an average, the number of bits necessary to the signal representation by means of minimizing the reconstruction error. The following article proposes the compression of Arabic speech signal by a hybrid method combining the wavelet transform and the linear prediction. The adopted approach rests, on one hand, on the original signal decomposition by ways of analysis filters, which is followed by the compression stage, and on the other hand, on the application of the order 5, as well as, the compression signal coefficients. The aim of this approach is the estimation of the predicted error, which will be coded and transmitted. The decoding operation is then used to reconstitute the original signal. Thus, the adequate choice of the bench of filters is useful to the transform in necessary to increase the compression rate and induce an impercevable distortion from an auditive point of view.

Keywords: Compression, linear prediction analysis, multiresolution analysis, speech signal.

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Authors: M. Saravi, F. Ashrafi, S.R. Mirrajei

Abstract:

As we know, most differential equations concerning physical phenomenon could not be solved by analytical method. Even if we use Series Method, some times we need an appropriate change of variable, and even when we can, their closed form solution may be so complicated that using it to obtain an image or to examine the structure of the system is impossible. For example, if we consider Schrodinger equation, i.e., We come to a three-term recursion relations, which work with it takes, at least, a little bit time to get a series solution[6]. For this reason we use a change of variable such as or when we consider the orbital angular momentum[1], it will be necessary to solve. As we can observe, working with this equation is tedious. In this paper, after introducing Clenshaw method, which is a kind of Spectral method, we try to solve some of such equations.

Keywords: Chebyshev polynomials, Clenshaw method, ODEs, Spectral methods

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Authors: Chao Yi, Cunyue Lu, Lingwei Quan

Abstract:

Piezoelectric linear motors have the characteristics of great electromagnetic compatibility, high positioning accuracy, compact structure and no deceleration mechanism, which make it promising to applicate in micro-miniature precision drive systems. However, most piezoelectric motors are employed by flexible clamping, which has insufficient rigidity and is difficult to use in rapid positioning. Another problem is that this clamping method seriously affects the vibration efficiency of the vibrating unit. In order to solve these problems, this paper proposes a piezoelectric stack linear motor based on double-end rigid clamping. First, a piezoelectric linear motor with a length of only 35.5 mm is designed. This motor is mainly composed of a motor stator, a driving foot, a ceramic friction strip, a linear guide, a pre-tightening mechanism and a base. This structure is much simpler and smaller than most similar motors, and it is easy to assemble as well as to realize precise control. In addition, the properties of piezoelectric stack are reviewed and in order to obtain the elliptic motion trajectory of the driving head, a driving scheme of the longitudinal-shear composite stack is innovatively proposed. Finally, impedance analysis and speed performance testing were performed on the piezoelectric linear motor prototype. The motor can measure speed up to 25.5 mm/s under the excitation of signal voltage of 120 V and frequency of 390 Hz. The result shows that the proposed piezoelectric stacked linear motor obtains great performance. It can run smoothly in a large speed range, which is suitable for various precision control in medical images, aerospace, precision machinery and many other fields.

Keywords: Elliptical trajectory, linear motor, piezoelectric stack, rigid clamping.

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Authors: A. G. Sifalakis, E. P. Papadopoulou, Y. G. Saridakis

Abstract:

A generalized Dirichlet to Neumann map is one of the main aspects characterizing a recently introduced method for analyzing linear elliptic PDEs, through which it became possible to couple known and unknown components of the solution on the boundary of the domain without solving on its interior. For its numerical solution, a well conditioned quadratically convergent sine-Collocation method was developed, which yielded a linear system of equations with the diagonal blocks of its associated coefficient matrix being point diagonal. This structural property, among others, initiated interest for the employment of iterative methods for its solution. In this work we present a conclusive numerical study for the behavior of classical (Jacobi and Gauss-Seidel) and Krylov subspace (GMRES and Bi-CGSTAB) iterative methods when they are applied for the solution of the Dirichlet to Neumann map associated with the Laplace-s equation on regular polygons with the same boundary conditions on all edges.

Keywords: Elliptic PDEs, Dirichlet to Neumann Map, Global Relation, Collocation, Iterative Methods, Jacobi, Gauss-Seidel, GMRES, Bi-CGSTAB.

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Authors: T. Sakamoto, N. Hori

Abstract:

A multi-rate discrete-time model, whose response agrees exactly with that of a continuous-time original at all sampling instants for any sampling periods, is developed for a linear system, which is assumed to have multiple real eigenvalues. The sampling rates can be chosen arbitrarily and individually, so that their ratios can even be irrational. The state space model is obtained as a combination of a linear diagonal state equation and a nonlinear output equation. Unlike the usual lifted model, the order of the proposed model is the same as the number of sampling rates, which is less than or equal to the order of the original continuous-time system. The method is based on a nonlinear variable transformation, which can be considered as a generalization of linear similarity transformation, which cannot be applied to systems with multiple eigenvalues in general. An example and its simulation result show that the proposed multi-rate model gives exact responses at all sampling instants.

Keywords: Multi-rate discretization, linear systems, triangularization, similarity transformation, diagonalization, exponential transformation, multiple eigenvalues

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Authors: H. Abaali

Abstract:

The power buck converter is the most widely used DC/DC converter topology. They have a very large application area such as DC motor drives, photovoltaic power system which require fast transient responses and high efficiency over a wide range of load current. This work proposes, the modelling of DC/DC power buck converter using state-space averaging method and the current-mode control using a proportional-integral controller. The efficiency of the proposed model and control loop are evaluated with operating point changes. The simulation results proved the effectiveness of the linear model of DC/DC power buck converter.

Keywords: DC/DC power buck converter, Linear current control, State-space averaging method.

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Authors: Shao-Tzu Huang, Chen-Chien Hsu, Wei-Yen Wang

Abstract:

Matching high dimensional features between images is computationally expensive for exhaustive search approaches in computer vision. Although the dimension of the feature can be degraded by simplifying the prior knowledge of homography, matching accuracy may degrade as a tradeoff. In this paper, we present a feature matching method based on k-means algorithm that reduces the matching cost and matches the features between images instead of using a simplified geometric assumption. Experimental results show that the proposed method outperforms the previous linear exhaustive search approaches in terms of the inlier ratio of matched pairs.

Keywords: Feature matching, k-means clustering, scale invariant feature transform, linear exhaustive search.

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Authors: H. Nikzad, S. Yoshitomi

Abstract:

In this paper, an optimization procedure is applied for 3D Reinforced concrete building structure with shear wall.  In the optimization problem, cross sections of beams, columns and shear wall dimensions are considered as design variables and the optimal cross sections can be derived to minimize the total cost of the structure. As for final design application, the most suitable sections are selected to satisfy ACI 318-14 code provision based on static linear analysis. The validity of the method is examined through numerical example of 15 storied 3D RC building with shear wall.  This optimization method is expected to assist in providing a useful reference in design early stage, and to be an effective and powerful tool for structural design of RC shear wall structures.

Keywords: Structural optimization, linear static analysis, ETABS, MATLAB, RC moment frame, RC shear wall structures.

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

Abstract:

Standard Hammerstein-Wiener models consist of a linear subsystem sandwiched by two memoryless nonlinearities. The problem of identifying Hammerstein-Wiener systems is addressed in the presence of linear subsystem of structure totally unknown and polynomial input and output nonlinearities. Presently, the system nonlinearities are allowed to be noninvertible. The system identification problem is dealt by developing a two-stage frequency identification method. First, the parameters of system nonlinearities are identified. In the second stage, a frequency approach is designed to estimate the linear subsystem frequency gain. All involved estimators are proved to be consistent.

Keywords: Nonlinear system identification, Hammerstein systems, Wiener systems, frequency identification.

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Authors: M. Zarebnia, R. Parvaz

Abstract:

In this paper the Kuramoto-Sivashinsky equation is solved numerically by collocation method. The solution is approximated as a linear combination of septic B-spline functions. Applying the Von-Neumann stability analysis technique, we show that the method is unconditionally stable. The method is applied on some test examples, and the numerical results have been compared with the exact solutions. The global relative error and L∞ in the solutions show the efficiency of the method computationally.

Keywords: Kuramoto-Sivashinsky equation, Septic B-spline, Collocation method, Finite difference.

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Authors: M. Sasajima, T. Yamaguchi, Y. Koike, A. Hara

Abstract:

This paper describes vibration analysis using the finite element method for a small earphone, especially for the diaphragm shape with a low-rigidity. The viscoelastic diaphragm is supported by multiple nonlinear concentrated springs with linear hysteresis damping. The restoring forces of the nonlinear springs have cubic nonlinearity. The finite elements for the nonlinear springs with hysteresis are expressed and are connected to the diaphragm that is modeled by linear solid finite elements in consideration of a complex modulus of elasticity. Further, the discretized equations in physical coordinates are transformed into the nonlinear ordinary coupled equations using normal coordinates corresponding to the linear natural modes. We computed the nonlinear stationary and non-stationary responses due to the internal resonance between modes with large amplitude in the nonlinear springs and elastic modes in the diaphragm. The non-stationary motions are confirmed as the chaos due to the maximum Lyapunov exponents with a positive number. From the time histories of the deformation distribution in the chaotic vibration, we identified nonlinear modal couplings.

Keywords: Nonlinear Vibration, Finite Element Method, Chaos , Small Earphone.

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Authors: Ping He, Heng-You Lan, Gong-Quan Tan

Abstract:

The multidelays linear control systems described by difference differential equations are often studied in modern control theory. In this paper, the delay-independent stabilization algebraic criteria and the theorem of delay-independent stabilization for linear systems with multiple time-delays are established by using the Lyapunov functional and the Riccati algebra matrix equation in the matrix theory. An illustrative example and the simulation result, show that the approach to linear systems with multiple time-delays is effective.

Keywords: Linear system, Delay-independent stabilization, Lyapunovfunctional, Riccati algebra matrix equation.

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Authors: H. Nasiraghdam, A. Jalilian

Abstract:

DSTATCOM is one of the equipments for voltage sag mitigation in power systems. In this paper a new control method for balanced and unbalanced voltage sag mitigation using DSTATCOM is proposed. The control system has two loops in order to regulate compensator current and load voltage. Delayed signal cancellation has been used for sequence separation. The compensator should protect sensitive loads against different types of voltage sag. Performance of the proposed method is investigated under different types of voltage sags for linear and nonlinear loads. Simulation results show appropriate operation of the proposed control system.

Keywords: Custom power, power quality, voltage sagmitigation, current vector control.

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Authors: Dibyendu Ghoshal, Pinaki Pratim Acharjya

Abstract:

Image segmentation process based on mathematical morphology has been studied in the paper. It has been established from the first principles of the morphological process, the entire segmentation is although a nonlinear signal processing task, the constituent wise, the intermediate steps are linear, bilinear and conformal transformation and they give rise to a non linear affect in a cumulative manner.

Keywords: Image segmentation, linear transform, bilinear transform, conformal transform, mathematical morphology.

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Authors: Peyman Sindareh Esfahani, Jeffery Kurt Pieper

Abstract:

In this paper, the problem of robust model predictive control (MPC) for discrete-time linear systems in linear fractional transformation form with structured uncertainty and norm-bounded disturbance is investigated. The problem of minimization of the cost function for MPC design is converted to minimization of the worst case of the cost function. Then, this problem is reduced to minimization of an upper bound of the cost function subject to a terminal inequality satisfying the l₂-norm of the closed loop system. The characteristic of the linear fractional transformation system is taken into account, and by using some mathematical tools, the robust predictive controller design problem is turned into a linear matrix inequality minimization problem. Afterwards, a formulation which includes an integrator to improve the performance of the proposed robust model predictive controller in steady state condition is studied. The validity of the approaches is illustrated through a robust control benchmark problem.

Keywords: Linear fractional transformation, linear matrix inequality, robust model predictive control, state feedback control.

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Authors: H. N. Agiza, M. A. Sohaly, M. A. Elfouly

Abstract:

Parkinson's disease (PD) is a heterogeneous disorder with common age of onset, symptoms, and progression levels. In this paper we will solve analytically the PD model as a non-linear delay differential equation using the steps method. The step method transforms a system of delay differential equations (DDEs) into systems of ordinary differential equations (ODEs). On some numerical examples, the analytical solution will be difficult. So we will approximate the analytical solution using Picard method and Taylor method to ODEs.

Keywords: Parkinson's disease, Step method, delay differential equation, simulation.

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