Song-Shyong Chen

Robust static output-feedback stabilization for nonlinear discrete-time systems with time delay via fuzzy control approach

This paper addresses the problem of designing robust static output-feedback controllers for nonlinear discrete-time interval systems with time delays both in states and in control input. In the approach, we do not directly employ the Lyapunov approach, as do in most of traditional fuzzy control design approaches. Instead, sufficient conditions for guaranteeing the robust stability for the considered systems are derived in terms of the matrix spectral norm of the closed-loop fuzzy system. The stability conditions are further formulated into linear matrix inequalities so that the desired controller can be easily obtained by using the Matlab linear matrix inequality (LMI) toolbox. Finally, an example is provided to illustrate the effectiveness of the proposed approach.

Static output feedback stabilization for nonlinear interval time-delay systems via fuzzy control approach☆

Abstract This paper addresses the design problem of static output feedback controllers for nonlinear interval time-delay systems represented by the Takagi–Sugeno fuzzy model. Departing from traditional approaches, which are to find a common positive definite matrix for all rules, sufficient conditions to guarantee the robust stability for such fuzzy systems are derived in term of matrix measures of system matrices in the consequent parts of fuzzy rules. These conditions are further transformed into linear matrix inequalities. By solving linear matrix inequalities, a static output feedback controller that can stabilize the considered uncertain time-delay system can easily be obtained. Finally, an example is provided to illustrate the effectiveness of our approach.

Automatic recognition of frog calls using a multi-stage average spectrum

The automatic recognition of animal sounds is one of the powerful techniques for replacing the traditional ecological survey method that mainly depends on manpower, which is hence both costly and time consuming. This study developed an automatic frog call recognition system based on the combination of a pre-classification method of the syllable lengths and a multi-stage average spectrum (MSAS) method. In this system, the input frog syllables are first classified into one of the four groups determined by the pre-classification method according to syllable length. Then the proposed MSAS method is used to extract the standard feature template to analyze the time-varying features of each frog species and to recognize the input frog syllable by a template matching method. In all, 960 syllables recorded from 18 frog species are included in this study to evaluate the accuracy of the proposed frog call recognition system. The experimental results demonstrate that the proposed one-level (using the MSAS method only) and two-level (combining the syllable length pre-classification and MSAS methods) recognition methods can provide the best recognition accuracies of 91.9% and 94.3%, respectively, compared with other recognition methods based on dynamic time warping (DTW), spectral ensemble average voice prints (SEAV), k-nearest neighbor (kNN) and support vector machines (SVMs).

The Study on Direct Adaptive Fuzzy Controllers

Direct adaptive fuzzy controllers have been proposed and discussed in the literature. Even though such controllers have been proven to be effective, in our study, some phenomena are observed. In this paper, those problems of using adaptive fuzzy controllers for unknown nonlinear systems are reported. The role of a parameter matrix required in the Lyapunov equation is discussed. It can be found that even though the Lyapunov synthesis approach has already proven that the system is asymptotically stable, the parameter matrix still needs to be selected appropriately beside of the symmetric positive definite property. Another issue is that it can also be found in our simulations that this kind of adaptive fuzzy controllers does not converge to a fixed controller as assumed in the literature, but adaptively adjusts its parameters according to the errors. As a consequence, when the considered system has sensory noise, the system may gradually become unstable. Ways of restraining such an unbounded phenomenon are proposed. From our simulations, the proposed approaches can have nice performance.

LMI approach to static output feedback simultaneous stabilization of discrete-time interval systems with time delay

The simultaneous static output feedback stabilization problem for a collection of discrete-time interval systems with time delays is considered. A sufficient condition for the existence of static output feedback simultaneously stabilizing controllers is obtained in terms of matrix spectral norms. It is shown that this considered problem is solvable if a corresponding matrixs spectral norm assignment problem is solvable. Furthermore, we also show that the matrix spectral norm assignment problem is equivalent to a bilinear matrix inequality (BMI) problem. We then derive a sufficient condition for the BMI problem and the condition is a linear matrix inequality (LMI) feasibility problem, which can be solved easily. Finally, an example is provided to demonstrate the effectiveness of the proposed methodology.

Fuzzy control design for switched nonlinear systems

Recently, many researchers have devoted themselves to the study of methods of designing controllers for switched nonlinear systems with the use of the switched Takagi-Sugeno (T-S) fuzzy model. The main feature of switched T-S fuzzy models is that they characterize the local dynamics of each fuzzy rule by a linear model. The appeal of the switched T-S fuzzy model in control design is that the stability and performance characteristics of a system can be verified by using a Lyapunov function approach. Nevertheless, it should be noted that in a switched T-S fuzzy model, the consequence could be any functions. In this study, we attempt to study the control design problem of switched T-S fuzzy models, which have nonlinear consequence functions. The paper presents a novel switching fuzzy control design approach based on control Lyapunov function. The proposed approach can design stable controllers for a switched T-S fuzzy model of which the consequents are affine nonlinear state dynamic equations. The proposed switching fuzzy controller guarantees the stability of the closed loop switched systems. The Sontagpsilas formula developed for affine nonlinear control systems is employed to construct a switching T-S fuzzy controller. Based on a control Lyapunov function approach, we derive a sufficient condition to ensure the stability of the closed loop switched fuzzy systems. Two examples are given to show the advantage of the presented method.

Hybrid robust LS-SVMR with outliers for MIMO system

In this study, a hybrid robust LS-SVMR approach is proposed to deal with training data sets with outliers dor MIMO system. The proposed approach consists of two stages of strategies. The first stage is for data preprocessing and a support vector regression is used to filter out outliers. Then, the training data set except for outliers, called as the reduced training data set, is directly used in training the non-robust least squares support vector machines for regression (LS-SVMR) for MIMO system in the second stage. Consequently, the learning mechanism of the proposed approach is much easier than the weighted LS-SVMR approach. Based on the simulation results, the performance of the proposed approach with non-robust LS-SVMR is superior to the weighted LS-SVMR approach for MIMO system when the outliers exist.

On the analysis of direct adaptive fuzzy controllers

The control problem of using adaptive fuzzy controllers for nonlinear unstable systems is reported. In this study, how the parameter matrix P required in the Lyapunov equation for guaranteeing the system stability can affect the system performance is discussed. It can be found that even though the Lyapunov synthesis approach has already proven that the system is asymptotically stable, the parameter matrix P still needs to be selected appropriately besides the symmetric positive definite property. In our simulations, it can also be found that this kind of controller does not converge to a fixed controller, but adaptively adjusts its parameters according to the errors. As a consequence, when the considered system has a sensory noise, the system may gradually become unstable. Ways of restraining such an unbounded phenomenon are proposed in the paper.

Lmi approach to simultaneous output-feedback stabilization for discrete-time interval systems

Abstract In this paper, the simultaneous static output feedback stabilization problem for a collection of discrete‐time interval systems is considered. A sufficient condition for the existence of static output feedback simultaneously stabilizing controllers is obtained. It is shown that this problem is solvable if a matrixs spectral norm assignment problem is solvable. We proved that the admissible solution set of the matrixs spectral norm assignment problem is convex. Then, the matrixs spectral norm assignment problem is shown to be equivalent to a linear matrix inequality (LMI) feasibility problem. Finally, an example is provided to illustrate the proposed methodology.

Networked control systems design via fuzzy logic method

This paper addresses the problem of designing robust static output-feedback controllers for nonlinear network based controller design for the given T-S fuzzy model. The effects of both network-induced delays and data packet dropout will be investigated. Based on an integral inequality and a matrix inequality, a delay-dependent sufficient condition for the existence of a network-based controller is formulated in terms of a linear matrix inequality by adjusting effective parameter matrices. In the approach, we do not directly employ the Lyapunov approach, as do in most of traditional fuzzy control design approaches. Instead, sufficient conditions for guaranteeing the robust stability for the considered networked systems are derived in terms of the matrix spectral norm of the closed-loop fuzzy system. The sufficient conditions are further formulated into linear matrix inequalities so that the desired controller can be easily obtained by using the Matlab LMI toolbox. An illustrative numerical example is also given to show the effectiveness of the proposed design method.