基于分段多项式李雅普诺夫函数的模糊系统的稳定性分析

本文采用最大型分段多项式李雅普诺夫函数研究了多项式模糊系统的闭环稳定性问题.首先,本文设计了与分段李雅普诺夫函数对应的切换模糊控制器,提出了多项式模糊模型稳定的平方和条件,同时证明了最大型分段多项式李雅普诺夫函数在函数切换点的稳定性.然后,设计了相应的路径跟踪优化算法,对本文非凸的稳定条件进行迭代求解.最后,通过两个算例进行仿真与比较,说明并验证了本文所提出结论的可行有效性.     

Intelligent control of a stepping motor drive using an adaptive neuro–fuzzy inference system

Stepping motors are widely used in robotics and in the numerical control of machine tools where they have to perform high-precision positioning operations. However, the variations of the mechanical configuration of the drive, which are common to these two applications, can lead to a loss of synchronism for high stepping rates. Moreover, the classical open-loop speed control is weak and a closed-loop control becomes necessary. In this paper, fuzzy logic is applied to control the speed of a stepping motor drive with feedback. A neuro-fuzzy hybrid approach is used to design the fuzzy rule base of the intelligent system for control. In particular, we used the ANFIS methodology to build a Sugeno fuzzy model for controlling the stepping motor drive. An advanced test bed is used in order to evaluate the tracking properties and the robustness capacities of the fuzzy logic controller.     

Stability analysis of discrete-time switched systems: a switched homogeneous Lyapunov function method

This paper addresses the stability issue of discrete-time switched systems with guaranteed dwell-time. The approach of switched homogeneous Lyapunov function of higher order is formally proposed. By means of this approach, a necessary and sufficient condition is established to check the exponential stability of the considered system. With the observation that switching signal is actually arbitrary if the dwell time is one sample time, a necessary and sufficient condition is also presented to verify the exponential stability of switched systems under arbitrary switching signals. Using the augmented argument, a necessary and sufficient exponential stability criterion is given for discrete-time switched systems with delays. A numerical example is provided to show the advantages of the theoretical results.     

Stability analysis for discrete‐time fuzzy system by utilizing homogeneous polynomial matrix function

The purpose of this paper is to investigate the stability of nonlinear systems represented by a Takagi‐Sugeno discrete‐time fuzzy model. The homogeneous polynomial matrix function (HPMF) is developed to obtain new stabilization conditions. Applying the HPMF to the non‐parallel distributed compensation (non‐PDC) law and non‐quadratic Lyapunov function, some new stabilization conditions are obtained by the following two means: (a) utilizing the popular idea of introducing additional variables for some fixed degree of the HPMF; and (b) increasing the degree of the HPMF. It is shown that the conditions obtained with approach (a) are less conservative than some sufficient stability conditions available in the literature to date. It is also shown that as the degree of HPMF increases the conditions obtained under (b) become less conservative. An example is provided to illustrate how the proposed approaches compare with other techniques available in the literature. Copyright © 2009 John Wiley and Sons Asia Pte Ltd and Chinese Automatic Control Society     

Stability and stabilization of continuous‐time switched systems: A multiple discontinuous convex Lyapunov function approach

In this paper, the problems of stability and stabilization are considered for a class of switched linear systems with slow switching and fast switching. A multiple convex Lyapunov function and a multiple discontinuous convex Lyapunov function are first introduced, under which the extended stability and stabilization results are derived with a mode‐dependent average dwell time switching strategy, where slow switching and fast switching are exerted on stable and unstable subsystems, respectively. These two types of Lyapunov functions are established in a constructive manner by virtue of a set of time‐varying functions. By using our proposed approaches, larger stability regions of system parameters are identified, and tighter bounds can be obtained for the mode‐dependent average dwell time. New mode‐dependent and time‐varying controllers are constructed for a class of switched control systems with stabilizable and unstabilizable subsystems as well. All the stability and stabilization conditions can be given in terms of strict linear matrix inequalities (LMIs), which can be checked easily by using recently developed algorithms in solving LMIs. Finally, two numerical examples are provided to show the effectiveness of the obtained results compared with the existing results.     

Modelling the nonlinear dynamic behaviour of a boiler‐turbine system using a radial basis function neural network

Building an appropriate mathematical model that describes the system behaviour with a certain degree of satisfaction is quite challenging owing to the uncertain and volatile nature of thermodynamic constants and geometric parameters. In this paper, we present a technique to approximate and validate the dynamic behaviour of the Aström–Bell boiler‐turbine power plant based on an RBFNN over a large operating range. The proposed RBFNN is applied to solve the parametric identification problem for nonlinear and complex systems using an optimiser based on a hybrid genetic algorithm. This optimiser is composed of the gradient descent optimiser and a genetic algorithm for fast convergence. Two simulations were performed to show the effectiveness of the proposed technique under different situations with several boiler‐turbine input variables. The optimal structure and parameters of the obtained RBFNN‐based model emulates well the dynamic behaviour of the Aström–Bell boiler‐turbine system. Copyright © 2013 John Wiley & Sons, Ltd.