Adaptive mesh generation for singularly perturbed fourth-order ordinary differential equations

In this paper, we consider a singularly perturbed boundary-value problem for fourth-order ordinary differential equation (ODE) whose highest-order derivative is multiplied by a small perturbation parameter. To solve this ODE, we transform the differential equation into a coupled system of two singularly perturbed ODEs. The classical central difference scheme is used to discretize the system of ODEs on a nonuniform mesh which is generated by equidistribution of a positive monitor function. We have shown that the proposed technique provides first-order accuracy independent of the perturbation parameter. Numerical experiments are provided to validate the theoretical results.     

Controlling linear systems with nonlinear perturbations under sampled-data output feedback: digital redesign approach

This article develops a digital redesign (DR) technique for sampled-data observer-based output-feedback control of a continuous-time linear system with nonlinear perturbation. It is assumed that the nonlinear perturbation is a locally Lipschitz function. To deal with the discrete-time modelling error in nonlinear systems, as opposed to the previous approach, the DR problem is configured as a stabilisation one for error dynamics between the closed-loop system of nominal linear model under an analogue state-feedback controller and that of the linear system with the nonlinear perturbation under a sampled-data output-feedback controller. A constructive DR condition is formulated in the format of linear matrix inequalities. The stability of the actual sampled-data control system is guaranteed within the DR procedure. The effectiveness of the proposed DR methodology is demonstrated through a numerical simulation.     

Variable Structure Control of Robot Manipulators with Perturbation Estimator

The idea of perturbation compensation is incorporated in variable structure control (VSC) of robot manipulators to cancel the effects of system parametric uncertainties and external disturbances and hence alleviate control chattering. By using the dynamic response of the robot as characterized by the sliding function, a technique is proposed to deduce the system perturbation signal. For practical implementation, a perturbation estimator is introduced to approximate the system uncertainties. Estimates of the bounds on modelling errors and external disturbances are not required while signal measurement uncertainties can be accommodated. The suggested VSC law ensures that the robot control system reaches the sliding mode in finite time and with prescribed transient behaviour. Detailed computer simulation results are presented to demonstrate the effectiveness of this new approach.     

Stick slip and control in low-speed motion

Dimensional and perturbation analysis are applied to the problem of stick slip encountered during the motion of machines. The friction model studied is motivated by current tribological results and is appropriate for lubricated metal contacts. The friction model incorporates Coulomb, viscous, and Stribeck friction with frictional memory and rising static friction. Through dimensional analysis an exact model of the nonlinear system can be formed using five parameters rather than ten, greatly facilitating study and explicitly revealing the interaction of parameters. By converting the system of differential equations into a set of integrations, the perturbation technique makes approximate analysis possible where only numerical techniques had been available before. The analysis predicts the onset of stick slip as a function of plant and controller parameters; these results are compared with experimental data     

一类状态/输入受限的不确定非仿射非线性系统 鲁棒自适应backstepping控制

针对一类状态/输入受限的不确定严格反馈非仿射非线性系统跟踪控制问题,提出一种鲁棒自适应backstepping控制策略.在保证系统精度的前提下,对状态/输入受限的非仿射系统进行Taylor级数在线展开,得到其仿射形式;为保证系统复合扰动在线准确逼近,提出基于投影算子的递归扰动模糊神经网络干扰观测器(RPFNNDO);在考虑不确定系统存在状态受限和输入饱和等因素下,结合障碍Lyapunov函数、tanh函数及Nussbaum函数,利用backstepping方法设计控制器,并采用Lyapunov稳定理论分析闭环系统稳定性.应用于无人机航迹控制的仿真结果验证了所提方法的有效性.     

Fast LP method for the Schrödinger equation

The LP and CP methods are two versions of the piecewise perturbation methods to solve the Schrödinger equation. On each step the potential function is approximated by a constant (for CP) or by a linear function (for LP) and the deviation of the true potential from this approximation is treated by the perturbation theory.This paper is based on the idea that an LP algorithm can be made faster if expressed in a CP-like form. We obtain a version of order 12 whose two main ingredients are a new set of formulae for the computation of the zeroth-order solution which replaces the use of the Airy functions, and a convenient way of expressing the formulae for the perturbation corrections. Tests on a set of eigenvalue problems with a very big number of eigenvalues show that the proposed algorithm competes very well with a CP version of the same order and is by one order of magnitude faster than the LP algorithms existing in the literature. We also formulate a new technique for the step width adjustment and bring some new elements for a better understanding of the energy dependence of the error for the piecewise perturbation methods.     

Fuzzy age-dependent replacement policy and SPSA algorithm based-on fuzzy simulation

An increase in the performance of deteriorating systems can be achieved through the adoption of suitable maintenance policies. One of the most popular maintenance policies is the age-dependent replacement policy. In this paper, a fuzzy age-dependent replacement policy is considered in which the lifetimes of components are treated as fuzzy variables. To minimize the long-term expected cost per unit time, a programming model is formulated. Also, a theorem for optimal solution existence is proposed. In order to solve the proposed model, a fuzzy simulation technique is designed which estimates the expected value of the objective function. The simultaneous perturbation stochastic approximation (SPSA) algorithm is then used to determine a solution. Finally, a numerical example is presented to illustrate the effectiveness of this technique.     

Singular perturbation approach to trajectory tracking of flexible robot with joint elasticity

The control problem of a robot manipulator with flexures both in the links and joints was investigated using the singular perturbation technique. Owing to the combined efects of the link and joint jlexibilities, the dynamics of this type of manipulator become more complex and under-actuated leading to a challenging control task. The singular perturbation being a successful technique for solving control problems with under-actuation was exploited to obtain simpler subsystems with two-time-scale separation, thus enabling easier design of subcontrollers. Furthermore, simultaneous tracking and suppression of vibration of the link andjoint of the manipulator is possible by application of the composite controller, i.e. the superposition of both subcontrol actions. In the first instance, the design of a composite controller was based on a computed torque control for slow dynamics and linear-quadratic fast control. Later, to obtain an improved control performance under model uncertainty, the composite control action was achieved using the radial basis function neural network for the slow control and a linear-quadratic fast control. It was confirmed through numerical simulations that the proposed singular perturbation controllers suppress the joint and link vibrations of the manipulator satisfactorily while a perfect trajectory tracking was achieved.     

A Robust Control Law with Estimated Perturbation Compensation for Robot Manipulators

By considering the dynamic response of a robot manipulator as characterized by the sliding function, a technique is proposed to estimate the perturbation in the robot control system. Perturbation compensation is then incorporated in the design of a robust control law to cancel the effects of system parametric uncertainties and external disturbances. A normalized power rate component is introduced to replace the discontinuous control that is usually associated with variable structure system. The suggested robust control law ensures that the robot control system reaches an user specified neighbourhood of the sliding manifold in finite time and with prescribed transient behaviour. Explicit estimates of the bounds on modelling errors and external disturbances are not required while signal measurement uncertainties can be accommodated. Furthermore, using the equivalent control concept, a very simple expression is derived to estimate the system perturbation signal. Detailed computer simulation results are presented to demonstrate the effectiveness of the proposed control law.     

Design and development of new control technique for standalone PV system

A Sub-Maximum Power Point Tracking (S-MPPT) algorithm improves the performance of Photo Voltaic (PV) systems. This S-MPPT is used in single-phase PV system to test the tracking accuracy and its impact on the consistency of the whole system. Single phase PV Deadbeat Scheduler is proposed in this paper. The Deadbeat scheduler is a linear system. It initializes each initial state of the system to zero in shortest time possible. A single phase PV structure configuration is proposed to decrease the partial shading effect by changing the parameters of S-MPPT control algorithm. Thus, voltage sensor based S-MPPT algorithm through voltage reference control technique with the help of controller is developed for minimizing the tracking time and steady state oscillations. Selection of the objective function to mitigate the drawbacks associated with voltage sensor based algorithm for a decrease in solar irradiance are also demonstrated. The proposed MPPT algorithm with the designed controller is tested for a step change in irradiance from 270 to 480 W/m2 with a perturbation time of 20 ms and ∆V = 0.5 V (perturbation of voltage). From the simulation results, the proposed method with S-MPPT plus deadbeat control algorithm is compared with other existing algorithms.     

An efficient algorithm for 3D hand gesture recognition using combined neural classifiers

Gestures are the dynamic movements of hands within a certain time interval, which are of practical importance in many areas, such as human–computer interaction, computer vision, and computer graphics. The human hand gesture can provide a free and natural alternative to today’s cumbersome interface devices so as to improve the efficiency and effectiveness of human–computer interaction. This paper presents a neural-based combined classifier for 3D gesture recognition. The combined classifier is based on varying the parameters related to both the design and training of neural network classifier. The boosting algorithm is used to make perturbation of the training set employing the Multi-Layer Perceptron as base classifier. The final decision of the ensemble of classifiers is based on the majority voting rule. Experiments performed on 3D gesture database show the robustness of the proposed technique.     

A novel segmentation model for medical images with intensity inhomogeneity based on adaptive perturbation

In medical field, it remains challenging to accurately segment medical images due to low contrast, complex noises and intensity inhomogeneity. To overcome these obstacles, this paper provides a novel edge-based active contour model (ACM) for medical image segmentation. Specifically, an accurate regularization approach is presented to maintain the level set function with a signed distance property, which guarantees the stability of the evolution curve and the accuracy of the numerical computation. More significantly, an adaptive perturbation is integrated into the framework of the edge-based ACM. The perturbation technique can balance the stability of curve evolution and the accuracy of segmentation, which is key for segmenting medical images with intensity inhomogeneity. A number of experiments on both artificial and real medical images demonstrate that the proposed segmentation model outperforms state-of-the-art methods in terms of robustness to noise and segmentation accuracy.

     

RBF网络的鲁棒最小二乘学习算法

首先,针对径向基函数(RBF)神经网络参数学习中最小二乘法(LS)难以获得较高鲁棒性的问题,假定训练数据扰动上界可知,并基于鲁棒最小二乘原理,提出一种RBF网的最优鲁棒参数学习算法;然后分析指出,扰动上界可依据训练数据集自适应学习估计;最后通过实验分析结果表明了所提算法具有较高的参数鲁棒学习能力.与LS相似,新算法无额外参数,易于实际应用.     

基于交错Buck变换器的光伏系统MPPT控制

具有最大功率点跟踪(MPPT)功能的控制器常采用单相Buck变换器,输出功率稳定性差;鉴于此,提出将交错并联技术应用于Buck变换器,并以两相交错并联Buck变换器为例进行研究,减小输出电压、电流纹波,提高了输出功率稳定性,有利于实现MPPT控制;然后针对固定步长扰动观察法跟踪速度与精度之间的矛盾,研究了一种自适应变步长的算法,MATLAB仿真结果表明,改进算法具有较好的跟踪速度和稳态性能。     

Singular perturbation for the dynamic interaction measure

The singular perturbation technique is used for the dynamic extension of the RGA (relative gain array) based on the state-space model. The dynamic interaction measure derived serves as a means of pairing input and output variables for the systems having substantially different time scales.     

Parameter convergence in adaptive extremum-seeking control

This paper addresses the problem of parameter convergence in adaptive extremum-seeking control design. An alternate version of the popular persistence of excitation condition is proposed for a class of nonlinear systems with parametric uncertainties. The condition is translated to an asymptotic sufficient richness condition on the reference set-point. Since the desired optimal set-point is not known a priori in this type of problem, the proposed method includes a technique for generating perturbation signal that satisfies this condition in closed-loop. This demonstrates its superiority in terms of parameter convergence. The method guarantees parameter convergence with minimal but sufficient level of perturbation. The effectiveness of the proposed method is illustrated with a simulation example.     

An adaptive control strategy for mechanical manipulators

This paper focuses on the study of an adaptive perturbation control which tracks a desired time-based trajectory as close as possible for all times over a wide range of manipulator motion and payloads. The proposed adaptive control is based on the linearized perturbation equations in the vicinity of a nominal trajectory. The controlled system is characterized by feedforward and feedback components which can be computed separately and simultaneously. The feedforward component computes the nominal torques from the Newton-Euler equations of motion to compensate all the interaction forces among the various joints. The feedback component consisting of recursive least-square identification and an optimal adaptive self-tuning control algorithm for the linearized system computes the perturbation torques which reduce the position and velocity errors of the manipulator along the nominal trajectory. A computer simulation study was conducted to evaluate the performance of the proposed adaptive control.     

Homotopy perturbation transform method for nonlinear equations using He’s polynomials

In this paper, a combined form of the Laplace transform method with the homotopy perturbation method is proposed to solve nonlinear equations. This method is called the homotopy perturbation transform method (HPTM). The nonlinear terms can be easily handled by the use of He’s polynomials. The proposed scheme finds the solution without any discretization or restrictive assumptions and avoids the round-off errors. The fact that the proposed technique solves nonlinear problems without using Adomian’s polynomials can be considered as a clear advantage of this algorithm over the decomposition method.     

一种在3D手势交互中模拟鼠标的方法

针对当下3D手势交互在执行2D交互任务时用户体验不佳,提出了一种模拟鼠标2D交互方式的3D手势交互技术。根据ISO9241-9标准,设计多方向点选实验,用于比较该3D手势交互技术、一般3D手势交互技术和日常鼠标这三种交互技术在执行典型2D交互任务时的标准吞吐量、指向-选择时间和错误率。以调查问卷的方式评估该交互技术的主观舒适性。结果显示,与一般的手势交互相比,在不降低吞吐率的情况下,该交互技术在执行2D交互任务时可以获得更高的准确率以及更好的舒适度体验。     

On the exponential synchronization of stochastic impulsive chaotic delayed neural networks

In this paper, the exponential synchronization of stochastic impulsive chaotic delayed neural networks is investigated. Based on the Lyapunov function method, time-varying delay feedback control technique and the efficient modified Halanay inequality for stochastic differential equations, several sufficient conditions are presented to guarantee the exponential synchronization in mean square between two identical chaotic delayed neural networks with stochastic and impulsive perturbations. These conditions are expressed in terms of linear matrix inequalities (LMIs), which can easily be checked by utilizing the numerically efficient Matlab LMI toolbox. Comparing with the existing works that consider single perturbation (stochastic or impulsive one), the proposed method can provide a more general framework for the synchronization of multi-perturbation chaotic systems, which is favorable for practical application in secure communication. Finally, numerical simulations verify the effectiveness of the proposed method.