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Currently, a large number of clustering algorithms are available for data mining. But it will be difficult for people who to a large extent know little about data mining to select an appropriate clustering algorithm. In order to solve this problem, in this paper, we first comprehensively analyze a number of clustering algorithms, then summarize their evaluation criteria and apply the so-called fuzzy...
This paper deals with Takagi-Sugeno (T-S) systems stabilization based on a static output feedback (SOF) non-PDC control law. To investigate SOF stabilization, the closed loop dynamics is written using a descriptor redundancy formulation. This approach allows avoiding appearance of crossing terms between the controller's and the T-S system's matrices. Thus, based on a fuzzy Lyapunov candidate function...
This paper presents a sum of squares (SOS, for brevity) approach to polynomial fuzzy observer design for polynomial fuzzy systems. First, we briefly summarize previous results with respect to a polynomial fuzzy system and controller that are more general representation of the well-known Takagi-Sugeno (T-S) fuzzy system and controller, respectively. Secondly, we propose a polynomial fuzzy observer...
This paper proposes novel stability conditions of nonlinear systems in Takagi-Sugeno's form. This problem has been studied over twenty years with many sufficient conditions. Recently, asymptotically necessary and sufficient conditions are obtained, which are preferred with respect to common quadratic Lyapunov function. This paper considers general forms of homogeneously polynomially nonquadratic Lyapunov...
Based on analytical structure of fuzzy controller, a new kind of membership function with difference-interval factor is designed by the research of relationship between membership function and output of fuzzy controller, and used in a typical 2-dimensional fuzzy controller. With the mathematical structures, the stability conditions for fuzzy control systems have been obtained. Finally, a simulation...
In recent years, using controllable series device (CSD) such as controllable series capacitors (CSCs) has been considered to improve transient stability and damp power oscillations. These devices can be useful if they have suitable input signals and control strategy. In this paper base on Lyapunov theory mixed with fuzzy control system (FLC) a useful controller has been developed for damping the electromagnetic...
This paper deals with the problem of optimizing a fuzzy self-tuning PID controller for robot manipulators. Fuzzy PID controllers have been developed and applied in many fields in the last fifteen years. However, there is no systematic method to design Membership Functions (MFs) for these controllers. We propose a simple method based on Genetic Algorithms (GA) to find optimal input and output MFs of...
According to the characteristics of long time-delays, large inertia and time-variation in the dissolved oxygen control method of sewage treatment, one fuzzy-Smith control model on dissolved oxygen control is presented in this paper. This model has the merits of a high robustness in fuzzy controller and a compensation for time delay in Smith predictor. After simulation experiment, the result is shown...
This paper presents stability analysis of polynomial fuzzy control systems using sum-of-squares (SOS) approach. To take continuous form of membership functions into the stability analysis, based on the Lyapunov stability theory, stability conditions in the form of fuzzy summations are derived where each term contains product of polynomial fuzzy model and polynomial fuzzy controller membership functions...
In our earlier study, the property of L2-gain robust control is incorporated into the direct adaptive fuzzy control design with the use of the compensative controller. The tracking control performance is guaranteed. In the study, we further employ the L2-gain property to improve the adaptive law design. Due to the L2-gain control property, the approximate error of the fuzzy system is estimable, and...
This paper investigates the stability and stabilization problem of fuzzy large-scale systems in which the system is composed of a number of Takagi-Sugeno fuzzy subsystems with interconnection. Instead of fuzzy parallel distributed compensation (PDC) design, nonlinear state feedback controllers are used in the stabilization of the overall large-scale system. Based on Lyapunov criterion, some conditions...
In this paper we present a fuzzy self-tuning algorithm to select the Proportional, Integral and Derivative gains of a PID controller according to the actual state of a robotic manipulator. The stability via Lyapunov theory for the closed loop control system is also analyzed and shown that is locally asymptotically stable for a class of gain matrices depending on the manipulator states. This feature...
In this paper, an interval type-2 fuzzy kinematic control (IT2-FKC) combined with an interval type-2 adaptive fuzzy sliding-mode dynamic control (IT2-AFSMDC) are proposed for controlling the trajectory-tracking of a nonholonomic wheeled mobile robot (WMR). Firstly, an interval type-2 fuzzy logic controller designed for the kinematic model of the WMR is introduced, and then the IT2-AFSMDC is developed...
A new stability condition in terms of LMIs is studied in this paper. Based on a premise-dependent Lyapunov function and multiconvexity, we release the conservatism that commonly exists in the common P approach. Comparison studies for common P and non-common P methods are demonstrated, showing relaxation is achieved via the proposed approach.
This paper presents relaxed stability conditions for Takagi-Sugeno fuzzy-model-based (FMB) control systems. Similar to many previous approaches, stability conditions are represented in the form of multi-dimensional fuzzy summation. To investigate the system stability, the inequalities of p-dimensional fuzzy summation are expanded to n-dimensional fuzzy summation (n ges p). Then the boundary and regional...
This paper presents a nonlinear identification and indirect control algorithm based on a self-structuring fuzzy system (SFS) with guaranteed stability. The overall controller consists of two parts: the indirect adaptive controller based on the self-structuring fuzzy system (IACSFS) is the dominant controller which maintains the closed-loop stability when the fuzzy system is a good approximation of...
This paper investigates the stability and stabilization problem for fuzzy impulsive controller in which the fuzzy system is presented by Takagi-Sugeno model. Based on Lyapunov criterion, some conditions are derived under which the whole fuzzy impulsive controller is stabilized asymptotically and exponentially in term of some matrix inequalities. Finally, a chaotic example is given to illustrate the...
This paper presents the stability analysis of polynomial fuzzy-model-based control systems, formed by a polynomial fuzzy model and a fuzzy controller connected in a closed loop, using sum-of-squares (SOS) approach. Based on the Lyapunov stability theory, the stability analysis is generalized by bringing the membership functions as polynomial variables to the stability analysis for relaxation of SOS-based...
This paper presents switching fuzzy model construction based on optimal dividing planes. In our previous papers, we proposed the switching fuzzy model with arbitrary dividing planes. However, dividing planes have been selected by controller designers before constructing the switching fuzzy model. Unfortunately, it is difficult to find suitable dividing planes for complicated nonlinear systems. Moreover,...
In this paper, we present a new approach for the stability analysis of continuous-time recurrent fuzzy systems (CTRFS). The approach is based on the representation of a CTRFS as a switched polynomial system, for which a Lyapunov function is constructed in a two step procedure. Both steps are based on semidefinite programming. The applicability is shown by an ecological system formulated as a rule...
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