Jiang Y. - A Review of Fuzzy Logic and Neural Network Based Intelligent Control Design for Discrete-Time Systems

1Key Lab of Autonomous Systems and Networked Control (MOE), School of Automation Science and Engineering, South China University of Technology, Guangzhou 510640, China
2Zienkiewicz Centre for Computational Engineering, Swansea University, Swansea SA1 8EN, UK
3State Key Lab of Intelligent Control and Decision of Complex Systems, Beijing Institute of Technology, Beijing 100081, China

Received 5 November 2015; Accepted 29 December 2015

Academic Editor: Juan R. Torregrosa

Copyright 2016 Yiming Jiang 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.

Over the last few decades, the intelligent control methods such as fuzzy logic control (FLC) and neural network (NN) control have been successfully used in various applications. The rapid development of digital computer based control systems requires control signals to be calculated in a digital or discrete-time form. In this background, the intelligent control methods developed for discrete-time systems have drawn great attentions. This survey aims to present a summary of the state of the art of the design of FLC and NN-based intelligent control for discrete-time systems. For discrete-time FLC systems, numerous remarkable design approaches are introduced and a series of efficient methods to deal with the robustness, stability, and time delay of FLC discrete-time systems are recommended. Techniques for NN-based intelligent control for discrete-time systems, such as adaptive methods and adaptive dynamic programming approaches, are also reviewed. Overall, this paper is devoted to make a brief summary for recent progresses in FLC and NN-based intelligent control design for discrete-time systems as well as to present our thoughts and considerations of recent trends and potential research directions in this area.

It is well known that control design is critical to the performance of the closed-loop system response, while an accurate system model is usually necessary for a high quality control design. But there are inevitable uncertainties during modeling of any practical systems. These modeling uncertainties may result in poor performance and may even lead to instability of the closed-loop systems. To improve control performance, many control strategies have been developed to consider these uncertainties in the control design stage. As one of the major control approaches, adaptive control has been developed for more than half a century with intense research activities involving rigorous problem formulation, stability analysis, robustness design, performance analysis, and applications [].

Early progress of adaptive control focused on identification and closed-loop system analysis of linear systems. Self-tuning regulator and model reference adaptive control are two typical adaptive controllers based on different design philosophies, and they have attracted renown scholars such as strm and Wittenmark [].

Besides linear systems, discrete-time adaptive control has also been developed for various different classes of nonlinear systems, such as nonlinear systems with linear growth rate [], which is quantitatively characterized by fundamental limitations of feedback mechanism in terms of certain introduced uncertainty measure.

In addition to the progress from linear systems to the nonlinear systems, rigorous stability analysis of the closed-loop adaptive system has also been well established [].

The concept of fuzzy set was initially proposed by Zadeh []. And later, a stable adaptive fuzzy controller was successfully designed for a class of nonlinear systems. In this approach, the adaptive law was constructed to update the parameters of the FL controller during the adaptation procedure while it was not necessary to have the accurate mathematical model of the system. From then on, fuzzy control has attracted ever increasing research interest, since it is able to provide an effective solution to control complex and uncertain plants by employing the knowledge of specific experts for the controller design.

NN is inspired by biological neuronal systems witch consist of a number of simple processing neurons interconnected to each other. McCulloch and Pitts introduced an idea to study the computational abilities of networks composed of simple models of neurons in the 1940s [].

Nowadays, most of the control algorithms are realized by digital computers, and thus the desired control signals are calculated in a digital manner. Digital control systems have advantages such as easy to build, less sensitive to environment variation, flexible to change, and less expensive. A model based digital controller is designed in discrete-time form and operated in continuous-time with analogy signals. Since the data are generally processed at discrete-time instants, it is necessary for us to build the system model in discrete-time for ease of control design [].

Yet in the past decades, many significant progresses of FLC and NN control for nonlinear systems were in continuous-time form and there is considerable lag in the development for nonlinear discrete-time systems []. Therefore, in order to design discrete-time fuzzy or NN controllers and implement them into digital control systems, they deserve in-depth investigation for fuzzy control and NN control of nonlinear discrete-time systems.

The remainder of this paper is organized as follows. In Section a brief conclusion is given.

Nowadays, techniques for FLC have developed rapidly, especially in modeling complex nonlinear systems. Since Wang first proved that the linear combinations of a series of fuzzy basis functions are universal approximators of any nonlinear systems, the universal approximation property of the fuzzy logic systems has been extensively studied []. The combination of adaptive control and fuzzy logic system allows adaptive laws to update parameters of the FL controller during the adaptation procedure while adaptive fuzzy control provides an efficient method to model complex nonlinear systems. In practice, the difficulty of design a fuzzy controller lies in the fact that there are usually various requirement imposed on the systems to ensure stability and performance, while most of complex control systems today are using digital computers to calculate the control signals in a digital form. Hence, the continuous-time methods could not be directly applied to most practical systems. The modeling/control for discrete-time systems is crucial to take the controllers into real plants. Thus, it is significant to study the discrete-time fuzzy systems as well as their molding and control. To this end, researchers have paid efforts to develop the discrete-time FLC. A typical procedure of the multiple-input multiple-output (MIMO) fuuzy logic system (FLS) approximating an unknown function is comprised of three primary components as follows [].

(1) Fuzzification. Take as the input of the fuzzy system, and is the estimation of the output. Both the input and the output are fuzzified into fuzzy linguistic terms with fuzzy membership function.

(2) Fuzzy Rules. The collection of the fuzzy MIMO IF-THEN rules are designed to comprise the knowledge base for constructing the FLS. Using prior expert knowledge, the fuzzy rules can be obtained as where and are the premise variables consisting of and , respectively; and are the linguistic variables of the fuzzy sets; .