Robust Multi-Criteria Optimal Fuzzy Control of Continuous-Time Nonlinear Systems

This paper presents a novel fuzzy control design of continuous-time nonlinear systems with multiple performance criteria. The purpose behind this work is to improve the traditional fuzzy controller performance to satisfy several performance criteria simultaneously to secure quadratic optimality with inherent stability property together with dissipativity type of disturbance reduction. The Takagi– Sugeno fuzzy model is used in our control system design. By solving the linear matrix inequality at each time step, the control solution can be found to satisfy the mixed performance criteria. The effectiveness of the proposed technique is demonstrated by simulation of the control of the inverted pendulum system

On Nie-Tan operator and type-reduction of interval type-2 fuzzy sets

Type-reduction of type-2 fuzzy sets is considered to be a defuzzification bottleneck because of the computational complexity involved in the process of type-reduction. In this research, we prove that the closed-form Nie-Tan operator, which outputs the average of the upper and lower bounds of the footprint of uncertainty, is actually an accurate method for defuzzifing interval type-2 fuzzy sets

Fuzzy System Identification Based Upon a Novel Approach to Nonlinear Optimization

Fuzzy systems are often used to model the behavior of nonlinear dynamical systems in process control industries because the model is linguistic in nature, uses a natural-language rule set, and because they can be included in control laws that meet the design goals. However, because the rigorous study of fuzzy logic is relatively recent, there is a shortage of well-defined and understood mechanisms for the design of a fuzzy system. One of the greatest challenges in fuzzy modeling is to determine a suitable structure, parameters, and rules that minimize an appropriately chosen error between the fuzzy system, a mathematical model, and the target system. Numerous methods for establishing a suitable fuzzy system have been proposed, however, none are able to demonstrate the existence of a structure, parameters, or rule base that will minimize the error between the fuzzy and the target system. The piecewise linear approximator (PLA) is a mathematical construct that can be used to approximate an input-output data set with a series of connected line segments. The number of segments in the PLA is generally selected by the designer to meet a given error criteria. Increasing the number of segments will generally improve the approximation. If the location of the breakpoints between segments is known, it is a straightforward process to select the PLA parameters to minimize the error. However, if the location of the breakpoints is not known, a mechanism is required to determine their locations. While algorithms exist that will determine the location of the breakpoints, they do not minimize the error between data and the model. This work will develop theory that shows that an optimal solution to this nonlinear optimization problem exists and demonstrates how it can be applied to fuzzy modeling. This work also demonstrates that a fuzzy system restricted to a particular class of input membership functions, output membership functions, conjunction operator, and defuzzification technique is equivalent to a piecewise linear approximator (PLA). Furthermore, this work develops a new nonlinear optimization technique that minimizes the error between a PLA and an arbitrary one-dimensional set of input-output data and solves the optimal breakpoint problem. This nonlinear optimization technique minimizes the approximation error of several classes of nonlinear functions leading up to the generalized PLA. While direct application of this technique is computationally intensive, several paths are available for investigation that may ease this limitation. An algorithm is developed based on this optimization theory that is significantly more computationally tractable. Several potential applications of this work are discussed including the ability to model the nonlinear portions of Hammerstein and Wiener systems

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