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The purpose of this paper is to investigate the analytical solution of a hyperbolic partial differential equation (PDE) and its application.

The change of variables and the method of successive approximations are introduced. The Volterra transformation and boundary control scheme are adopted in the analysis of the reaction-diffusion system.

A detailed and complete calculation process of the analytical solution of hyperbolic PDE (1)-(3) is given. Based on the Volterra transformation, a reaction-diffusion system is controlled by boundary control.

The introduced approach is interesting for the solution of hyperbolic PDE and boundary control of the reaction-diffusion system.

Generally, the motion range of the micro scale operation is within several hundreds of microns, and the conventional joints cannot satisfy the requirements due to manufacturing and assembling errors, hysteresis and backlash in the joints. The paper aims to discuss these issues.

The following issues should be considered: a micromanipulation stage should be designed using a small-dimensional scale driven by the small size of piezoelectric actuator and the components can be replaced due to fatigue failure caused by repeated cyclic loading. This paper proposes a modular design of a flexure-based 2-DOF precision stage made using aluminum (T6-7075) material and Acrylonitrile Butadiene Styrene plastic material. The piezoelectric actuator is adopted to drive the stage for the fast response and large output force. To compensate the stroke of piezoelectric actuator, a bridge-type amplifier is designed with optimized structure.

The simulation results validate the advantages of modular positioning stage fabricated by two different materials.

The stage can be used in micro scale precision’s applications. If it will be used in nanoscale precision, then some sensors in nanoscale of measurement should be used.

The designed stage can be used in biomedical engineering, such as cell injection testing, etc.

The designed stage will be used in micro/nanoengineering field, such as micro/nanomanufacturing or assembly, manipulation of cell, etc., which will push forward high technology to a higher level.

Two kinds of materials have been selected to make the positioning stage, which are seldomly found in literature on compliant mechanism field. A modular design concept is proposed for the positioning stage design.

The purpose of this paper is to present a novel algorithm for image inpainting, which has been widely used for removing unwanted objects from images or reconstructing damaged photographs.

An image piecewise inpainting technique based on radial basis function (RBF) is used to transform the 2D image inpainting problem into 3D implicit surface reconstruction problem. And a RBF center reduction method is proposed. By RBF resampling, the algorithm can nicely fix the damaged image or remove specific objects.

Experimental results show that the proposed algorithms can prevent the edge blur caused by the isotropic character of RBF, and effectively reduce the RBF centers without a loss in accuracy.

The proposed inpainting approach is interesting for its combination of RBF method and region segmentation that can handle the restoring of high‐variation areas.

The purpose of this paper is to study the control and synchronization of the hyperchaotic finance system.

A single controller scheme is introduced. The Routh-Hurwitz criteria and the structure of solution of first-order linear differential equations are adopted in analysis of control and synchronization.

Two single controllers are designed and added to the new hyperchaotic finance system. The stability of the hyperchaotic finance system at its zero equilibrium point is guaranteed by applying the appropriate single controller signal based on Routh-Hurwitz criteria. Another effective controller is also designed for the global asymptotic synchronization on the hyperchaotic finance system based on the structure of solution of first-order linear differential equations. Numerical simulations are demonstrated to verify the effectiveness of the proposed single controller scheme.

The introduced approach is interesting for control and synchronization the hyperchaotic finance system.

The purpose of this paper is to examine a new idea of vibration control which minimizes joint‐torques and suppresses vibration of the flexible redundant manipulator.

Using the kinematics redundancy feature of the flexible redundant manipulator, the self‐motion in the joint space can be properly chosen to both suppress vibration and minimize joint‐torques.

The study shows that the flexible redundant manipulator still has the second optimization feature on the premise of vibration suppression. The second optimization feature can be used to minimize joint‐torques on the premise of vibration suppression.

To a flexible redundant manipulator, its joint‐torques and vibration can be reduced simultaneously via its kinematics redundancy feature.

The method and algorithm discussed in the paper can be used to minimize joint‐torques and suppress vibration for the flexible redundant manipulator.

The paper contributes to the study on improving dynamic performance of the flexible redundant manipulator via its kinematics redundancy feature. The second optimization capability of the flexible redundant manipulator is discovered and used to both minimize joint‐torques and suppress vibration.

Nowadays, automotive engines are controlled by electronic control units (ECUs), and the engine idle speed performance is significantly affected by the setup of control parameters in the ECU. The engine ECU tune‐up is done empirically through tests on a dynamometer (dyno). In this way, a lot of time, fuel and human resources are consumed, while the optimal control parameters may not be obtained. The purpose of this paper is to propose a novel ECU setup optimization approach for engine idle speed control.

In the first phase of the approach, Latin hypercube sampling (LHS) and a multi‐input/output least squares support vector machine (LS‐SVM) is proposed to build up an engine idle speed model based on dyno test data, and then a genetic algorithm (GA) is applied to obtain optimal ECU setting automatically subject to various user‐defined constraints.

The study shows that the predicted results using the estimated model from LS‐SVM are in good agreement with the actual test results. Moreover, the optimization results show a significant improvement on idle speed performance in a test engine.

As the methodology is generic it can be applied to different vehicle control optimization problems.

The research is the first attempt to integrate a couple of paradigms (LHS, multi‐input/output LS‐SVM and GA) into a general framework for constrained multivariable optimization problems under insufficient system information. The proposed multi‐input/output LS‐SVM for modelling of multi‐input/output systems is original, because the traditional LS‐SVM modelling approach is suitable for multi‐input, but single output systems. Finally, this is the first use of the novel integrated framework for automotive engine idle‐speed control optimization.

The purpose of this paper is to present a neural network approach to control performance assessment.

The performance index under study is based on the minimum variance control benchmark, a radial basis function network (RBFN) is used as the pre‐whitening filter to estimate the white noise sequence, and a stable filtering and correlation analysis method is adopted to calculate the performance index by estimating innovations sequence using the RBFN pre‐whitening filter. The new approach is compared with the auto‐regressive moving average model and the Laguerre model methods, for both linear and nonlinear cases.

Simulation results show that the RBFN approach works satisfactorily for both linear and nonlinear examples. In particular, the proposed scheme shows merits in assessing controller performance for nonlinear systems and surpasses the Laguerre model method in parameter selection.

A RBFN approach is proposed for control performance assessment. This new approach, in comparison with some well‐known methods, provides satisfactory performance and potentials for both linear and nonlinear cases.

The purpose of this paper is to develop a mathematical framework to address some algorithmic features of approximate dynamic programming (ADP) by using an average cost formulation based on the concepts of differential costs and performance gradients. Under such a framework, a modified value iteration algorithm is developed that is easy to implement, in the mean time it can address a class of partially observable Markov decision processes (POMDP).

Gradient‐based policy iteration (GBPI) is a top‐down, system‐theoretic approach to dynamic optimization with performance guarantees. In this paper, a bottom‐up, algorithmic view is provided to complement the original high‐level development of GBPI. A modified value iteration is introduced, which can provide solutions to the same type of POMDP problems dealt with by GBPI. Numerical simulations are conducted to include a queuing problem and a maze problem to illustrate and verify features of the proposed algorithms as compared to GBPI.

The direct connection between GBPI and policy iteration is shown under a Markov decision process formulation. As such, additional analytical insights were gained on GBPI. Furthermore, motivated by this analytical framework, the authors propose a modified value iteration as an alternative to addressing the same POMDP problem handled by GBPI.

Several important insights are gained from the analytical framework, which motivate the development of both algorithms. Built on this paradigm, new ADP learning algorithms can be developed, in this case, the modified value iteration, to address a broader class of problems, the POMDP. In addition, it is now possible to provide ADP algorithms with a gradient perspective. Inspired by the fundamental understanding of learning and optimization problems under the gradient‐based framework, additional new insight may be developed for bottom‐up type of algorithms with performance guarantees.

The purpose of this paper is to provide a review of the issues related to cluster analysis, one of the most important and primitive activities of human beings, and of the advances made in recent years.

The paper investigates the clustering algorithms rooted in machine learning, computer science, statistics, and computational intelligence.

The paper reviews the basic issues of cluster analysis and discusses the recent advances of clustering algorithms in scalability, robustness, visualization, irregular cluster shape detection, and so on.

The paper presents a comprehensive and systematic survey of cluster analysis and emphasizes its recent efforts in order to meet the challenges caused by the glut of complicated data from a wide variety of communities.