Analysis, filtering, and control for Takagi-Sugeno fuzzy models in networked systems

Copyright © 2015 Sunjie Zhang et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.The fuzzy logic theory has been proven to be effective in dealing with various nonlinear systems and has a great success in industry applications. Among different kinds of models for fuzzy systems, the so-called Takagi-Sugeno (T-S) fuzzy model has been quite popular due to its convenient and simple dynamic structure as well as its capability of approximating any smooth nonlinear function to any specified accuracy within any compact set. In terms of such a model, the performance analysis and the design of controllers and filters play important roles in the research of fuzzy systems. In this paper, we aim to survey some recent advances on the T-S fuzzy control and filtering problems with various network-induced phenomena. The network-induced phenomena under consideration mainly include communication delays, packet dropouts, signal quantization, and randomly occurring uncertainties (ROUs). With such network-induced phenomena, the developments on T-S fuzzy control and filtering issues are reviewed in detail. In addition, some latest results on this topic are highlighted. In the end, conclusions are drawn and some possible future research directions are pointed out.This work was supported in part by the National Natural Science Foundation of China under Grants 61134009, 61329301, 11301118 and 61174136, the Natural Science Foundation of Jiangsu Province of China under Grant BK20130017, the Fundamental Research Funds for the Central Universities of China under Grant CUSF-DH-D-2013061, the Royal Society of the U.K., and the Alexander von Humboldt Foundation of Germany

An integral sliding-mode parallel control approach for general nonlinear systems via piecewise affine linear models

The fundamental problem of stabilizing a general nonaffine continuous-time nonlinear system is investigated via piecewise affine linear models (PALMs) in this article. A novel integral sliding-mode parallel control (ISMPC) approach is developed, where an uncertain piecewise affine system (PWA) is constructed to model a nonaffine continuous-time nonlinear system equivalently on a compact region containing the origin. A piecewise sliding-mode parallel controller is designed to globally stabilize the PALM and, consequently, to semiglobally stabilize the original nonlinear system. The proposed scheme enjoys three favorable features: (i) some restrictions on the system input channel are eliminated, thus the developed method is more relaxed compared with the published approaches; (ii) it is convenient to be used to deal with both matched and unmatched uncertainties of the system; and (iii) the proposed piecewise parallel controller generates smooth control signals even around the boundaries between different subspaces, which makes the developed control strategy more implementable and reliable. Moreover, we provide discussions about the universality analysis of the developed control strategy for two kinds of typical nonlinear systems. Simulation results from two numerical examples further demonstrate the performance of the developed control approach

Event-triggered proportional-derivative control for nonlinear network systems with a novel event-triggering scheme: Differential of triggered state consideration

This article proposes event-triggered proportional-derivative control for a class of nonlinear network control systems. For derivative action of the proposed proportional-derivative control, a novel event-triggering scheme is devised together with the control that considers a differential of a triggered state. The class of the nonlinear network systems is represented as a Lur'e system to consider various nonlinear cases. Time varying transmission delay is considered which can be defined by lower and upper delay bounds. The proposed proportional-derivative control is designed by Lyapunov-Krasovskii stability analysis, and the design condition is presented by linear matrix inequalities. The proposed event-triggered proportional-derivative control and event-triggering condition are verified with numerical simulation. ? 2017 The Author(s).111Ysciescopu

Spatiotemporal Fuzzy-Observer-based Feedback Control for Networked Parabolic PDE Systems

Assisted by the Takagi-Sugeno (T-S) fuzzy model- based nonlinear control technique, nonlinear spatiotemporal feedback compensators are proposed in this article for exponential stabilization of parabolic partial differential dynamic systems with measurement outputs transmitted over a communication network. More specifically, an approximate T-S fuzzy partial differential equation (PDE) model with C∞-smooth membership functions is constructed to describe the complex spatiotemporal dynamics of the nonlinear partial differential systems, and its approximation capability is analyzed via the uniform approximation theorem on a real separable Hilbert space. A spatiotemporally asynchronous sampled-data measurement output equation is proposed to model the transmission process of networked measurement outputs. By the approximate T-S fuzzy PDE model, fuzzy-observer-based nonlinear continuous-time and sampled- data feedback compensators are constructed via the spatiotemporally asynchronous sampled-data measurement outputs. Given that sufficient conditions presented in terms of linear matrix inequalities are satisfied, the suggested fuzzy compensators can exponentially stabilize the nonlinear system in the Lyapunov sense. Simulation results are presented to show the effectiveness and merit of the suggested spatiotemporal fuzzy compensators

Filter Design for Positive T-S Fuzzy Continuous-Time Systems with Time Delay Using Piecewise-Linear Membership Functions

The file attached to this record is the author's final peer reviewed version. The Publisher's final version can be found by following the DOI link.This work focuses on the filtering problem and stability analysis for positive Takagi-Sugeno (T-S) fuzzy systems with time delay under L1-induced performance. Due to the importance of estimation of system states but the few filter design results on positive nonlinear systems, it is an attractive and meaningful topic well worth studying. In order to fully exploit and take advantage of the positivity of positive T-S fuzzy systems, many commonly used methods, for instance free-weighting matrix approach and similarity transformation are probably not suitable for positive systems. To address the hard-nut-to-crack problem, an auxiliary variable is introduced so that the augmentation approach can be employed to carry out the positivity and stability analysis of filtering error systems. In addition, another obstacle that cannot be ignored is the existence of non-convex terms in the stability and positivity conditions. For getting around this barrier, some iterative linear matrix inequality (ILMI) algorithms have been proposed in the literature. However, considering the weakness that these methods cannot guarantee the convergence to a numerical solution and the iterative process is exhaustive, we present an effective matrix decoupling method to convert the nonconvex conditions into convex ones in this paper. Furthermore, a linear co-positive Lyapunov function which incorporates the positivity of system states and time delay at the same time is chosen so that the positivity characteristic of filtering error systems can be captured further. However, because of plenty of valuable information of membership functions (MFs) being ignored, hence, the obtained results are conservative. For the sake of relaxing the conservativeness, the advanced piecewise-linear membership functions (PLMFs) approximate method is utilized to facilitate the stability and positivity analysis. Therefore, the relaxed stability and positivity conditions which are cast as sum of squares (SOS) are obtained and can be solved numerically. Finally, the effectiveness of the designed fuzzy filtering strategy with satisfying L1-induced performance are demonstrated by a simulation example

Suboptimal Event-Triggered Consensus of Multiagent Systems

In this paper the suboptimal event-triggered consensus problem of Multiagent systems is investigated. Using the combinational measurement approach, each agent only updates its control input at its own event time instants. Thus the total number of events and the amount of controller updates can be significantly reduced in practice. Then, based on the observation of increasing the consensus rate and reducing the number of triggering events, we have proposed the time-average cost of the agent system and developed a suboptimal approach to determine the triggering condition. The effectiveness of the proposed strategy is illustrated by numerical examples