Application of an auto-tuning neuron to sliding mode control

This paper presents a control strategy that incorporates an auto-tuning neuron into the sliding mode control (SMC) in order to eliminate the high control activity and chattering due to the SMC. The main difference between the auto-tuning neuron and the general one is that a modified hyperbolic tangent function with adjustable parameters is employed. In this proposed control structure, an auto-tuning neuron is then used as the neural controller without any connection weights.. The control law will be switched from the sliding control to the neural control, when the state trajectory of system enters in some boundary layer. In this way, the chattering phenomenon will not occur. The results of numerical simulations are provided to show the control performance of our proposed method.     

Global exponential stabilization for a class of uncertain nonlinearsystems with control constraint

In this paper, the global exponential stabilization for a class of uncertain nonlinear systems with control constraint is investigated. A bounded and continuous feedback control is constructed, under which the global exponential convergence for such systems can be guaranteed. A numerical example is also provided to illustrate the use of our main result     

Study on Huber Fractal Image Compression

In this paper, a new similarity measure for fractal image compression (FIC) is introduced. In the proposed Huber fractal image compression (HFIC), the linear Huber regression technique from robust statistics is embedded into the encoding procedure of the fractal image compression. When the original image is corrupted by noises, we argue that the fractal image compression scheme should be insensitive to those noises presented in the corrupted image. This leads to a new concept of robust fractal image compression. The proposed HFIC is one of our attempts toward the design of robust fractal image compression. The main disadvantage of HFIC is the high computational cost. To overcome this drawback, particle swarm optimization (PSO) technique is utilized to reduce the searching time. Simulation results show that the proposed HFIC is robust against outliers in the image. Also, the PSO method can effectively reduce the encoding time while retaining the quality of the retrieved image.     

PCA image coding with iterative clustering

Cluster analysis divides the data into groups of individuals that are homogeneous and separated from other groups. In consideration of the homogeneity, principal component analysis is usually used to reduce the redundancy of storages inside each cluster through the projection of data based on the principal components. Such data reduction is applied in this paper to images to achieve image compression. Moreover, genetic algorithm is employed in this study to determine the optimal number of components that preserve most of the information of the original data. Based on this mechanism, we develop an iterative clustering method for image coding. The proposed method effectively removes the coding redundancy and increases the number of principal components in some clusters in order to improve the reconstructed effect of certain clusters with complex structures. Consequently, the retrieved image has high quality and good visual effect.     

New algebraic criteria for absolute stability of nonlinear systems

In this paper, new and simple algebraic criteria are derived via elementary proofs to provide easy sufficient conditions for the standard absolute stability problems of nonlinear systems, i.e. Lur'e problems. These criteria are equivalent to the famous graphical circle criteria and Popov criterion. By means of the Sturm theorem and the Euclidean division algorithm, a Routh-Hurwitz-like Sturm criterion is obtained. No graphical technique is needed. Only basic numerical manipulations are involved in the new criteria.     

NXOR- or XOR-based robust template decomposition for cellular neural networks implementing an arbitrary Boolean function via support vector classifiers

Robust template design for cellular neural networks (CNNs) implementing an arbitrary Boolean function is currently an active research area. If the given Boolean function is linearly separable, a single robust uncoupled CNN can be designed preferably as a maximal margin classifier to implement the Boolean function. On the other hand, if the linearly separable Boolean function has a small geometric margin or the Boolean function is not linearly separable, a popular approach is to find a sequence of robust uncoupled CNNs implementing the given Boolean function. In the past research works using this approach, the control template parameters and thresholds are usually restricted to assume only a given finite set of integers. In this study, we try to remove this unnecessary restriction. NXOR- or XOR-based decomposition algorithm utilizing the soft margin and maximal margin support vector classifiers is proposed to design a sequence of robust templates implementing an arbitrary Boolean function. Several illustrative examples are simulated to demonstrate the efficiency of the proposed method by comparing our results with those produced by other decomposition methods with restricted weights.

     

Three-parameter sequential minimal optimization for support vector machines

The well-known sequential minimal optimization (SMO) algorithm is the most commonly used algorithm for numerical solutions of the support vector learning problems. At each iteration in the traditional SMO algorithm, also called 2PSMO algorithm in this paper, it jointly optimizes only two chosen parameters. The two parameters are selected either heuristically or randomly, whilst the optimization with respect to the two chosen parameters is performed analytically. The 2PSMO algorithm is naturally generalized to the three-parameter sequential minimal optimization (3PSMO) algorithm in this paper. At each iteration of this new algorithm, it jointly optimizes three chosen parameters. As in 2PSMO algorithm, the three parameters are selected either heuristically or randomly, whilst the optimization with respect to the three chosen parameters is performed analytically. Consequently, the main difference between these two algorithms is that the optimization is performed at each iteration of the 2PSMO algorithm on a line segment, whilst that of the 3PSMO algorithm on a two-dimensional region consisting of infinitely many line segments. This implies that the maximum can be attained more efficiently by 3PSMO algorithm. Main updating formulae of both algorithms for each support vector learning problem are presented. To assess the efficiency of the 3PSMO algorithm compared with the 2PSMO algorithm, 14 benchmark datasets, 7 for classification and 7 for regression, will be tested and numerical performances are compared. Simulation results demonstrate that the 3PSMO outperforms the 2PSMO algorithm significantly in both executing time and computation complexity.     

A self-tuning PID control for a class of nonlinear systems based on the Lyapunov approach

In this paper, we will propose a self-tuning method for a class of nonlinear PID control systems based on Lyapunov approach. The three PID control gains are adjustable parameters and will be updated online with a stable adaptation mechanism such that the PID control law tracks certain feedback linearization control, which is previously designed. The stability of closed-loop nonlinear PID control system is analyzed and guaranteed by introducing a supervisory control and a modified adaptation law with projection. Finally, a tracking control of an inverted pendulum system is illustrated to demonstrate the control performance by using the proposed method.     

Global stabilizability for a class of uncertain systems with multiple time-varying delays via linear control

In this paper, global uniform asymptotic stabilizability for a class of uncertain systems with multiple time-varying delays is considered. Some less conservative criteria for global uniform asymptotic stabilizability of such systems via linear control is provided. A numerical example is given to illustrate our main results.