Fuzzy and Neuro Control

Introduction

Fuzzy systems and Neural Networks have been recognized as attractive alternatives to the classical control schemes for the low-cost and facilitated design of the control laws of partially known, nonlinear and complex processes. Having intensively contributed to their developments, IRIDIA is today recognized as a leading European research laboratory in the field of intelligent control.

Fuzzy Control

Fuzzy systems present a nice duality: On one hand, they are knowledge-based software environments constructed from a collection of linguistic IF-THEN rules, and on the other hand, they realize nonlinear mappings which have interesting mathematical properties like "low-order interpolation" and "universal function approximation". Fuzzy systems have been recognized as an attractive alternative to classical control schemes for the low-cost and facilitated design of the control laws of partially known, nonlinear and complex processes. Their intrinsic linguistic nature makes easier the exploitation and integration of qualitative knowledge of the control laws, constraints and objectives. Moreover, fuzzy systems can readily be grounded in distributed and parallel computer architecture in order to allow real- time performance.
Japan and other Asian countries have became leaders in the market of fuzzy controllers but the large majority of them have been developed for the control of very low dimensional processes whereas real challenges appear for the control of high dimensional, strongly coupled and hard to model processes. For such processes, the design of fuzzy control systems remains a time-consuming activity involving knowledge acquisition and tuning of a large number of parameters. The lack of analytical results regarding the stability of "handicraft" fuzzy controllers is such as to render their industrial usefulness at least questionable. In consequence, these last years IRIDIA has been placing a special emphasis on four different issues related to the design of fuzzy controllers for MIMO processes: the ability to control complex multivariable systems for which precise mathematical models are not available, the links with traditional control schemes for MIMO processes, the adaptive capabilities, and finally the stability and robustness.
The possibility of adaptation allows to alleviate the design effort by automatically tuning the parameters with respect to a given performance criterion. The robustness of the fuzzy controller ensures the stability of the overall system in the presence of imperfect modelling or external disturbances (noise). The existence of a fuzzy model makes possible the derivation of control laws either based on the inversion of the fuzzy model or using the model based predictive control scheme.

The resulting theoretically well-founded fuzzy control systems are being applied for real- world applications:

• In collaboration with SIEMENS AUTOMATIVE, vehicle suspension control and powertrain management.
• In collaboration with Honeywell Europe, control and calibration of paper machine

IRIDIA has been part of the FALCON EEC Basic Research Esprit working group. FALCON was the first European, cooperative, and apparently successful response to the important Japanese scientific and industrial efforts dedicated to the development of fuzzy controllers. FALCON was an initiating investigation aiming at a better comprehension of the field, at a better characterization of fuzzy controllers located somewhere between fuzzy logic and process control theories. In this project IRIDIA was in charge of the learning and adaptation parts of fuzzy controllers as well as the neuro-fuzzy developments. There is currently a natural pursuit of such effort by tackling more complex MIMO processes and getting more deeply into the connections between classical control theory and fuzzy control.

IRIDIA is one of the founding nodes of ERUDIT which is an open Network of Excellence for uncertainty modeling and fuzzy technology in the European Union. The main objective of this network is to establish a European infrastructure to enable coordination of research, training, and technology transfer activities in the above mentioned areas. The presence of IRIDIA in ERUDIT appears very helpful for the communication and the exploitation of the fuzzy controllers results in the industrial world.

Neurocontrol

The use of neural networks in control applications has recently experienced rapid growth. The basic objective of control is to provide the appropriate input signal to a given physical process in order to obtain a desired output. In control theory, the physical process to be controlled is referred to as a plant. If the input signal supplied to the plant is generated by a neural network based controller, the case can be termed "neural control" or briefly "neurocontrol". Neurocontrol is part of the much broader concept of "intelligent control".

The intelligent control paradigm emerged quite naturally from the field of conventional control. As control methods have found their way into practice, they have opened the door to a wide spectrum of complex applications. Such complex systems are characterized by poor models, high dimentionality of the decision space, high noise levels, multiple performance criteria, complex behavior, etc. We can broadly classify the difficulties that arise in these systems into three categories for which established methods are insufficient. The first is computational complexity, the second is the presence of nonlinear processes with many degrees of freedom, and the third is uncertainty (presence of noise, disturbances, etc.). The greater the ability to deal with these difficulties, the more intelligent is the control system.

Because many living systems do implement some sort of intelligent control, it has been natural to look into computational paradigms used by nature. Artificial neural networks represent such a biologically inspired paradigm. At the present time, neural networks represent an important paradigm for classifying patterns, or generating signals to control their environment. The main reasons for this are:

• Neural networks can be trained. This means that, given a set of input-output patterns (called the training set), the connection weights of the neural network can be adapted in order to approximate, according to some predefined criterion, the input-output patterns provided in the training set. After training, the neural network can be used to predict a new output patterns, based on the input pattern only. The adaptation law that allows to adjust the connection weights is called the learning algorithm. This is of course reminiscent of the adaptive control strategy.
• Neural networks can approximate nonlinear functions. Multi-layer neural networks (units or neurons are organized in layers: the input layer, the hidden layers, and the output layer) are special architectures for which powerful learning algorithms exist. Once the connection weights have been trained, the neural network approximates the input-output mapping provided by the training set. It has been shown that a multi-layer neural network is a "universal approximator". Mathematically speaking, it means that a multi-layer neural network can approximate any continuous nonlinear function, provided that there is a sufficient number of hidden units in the hidden layers.
• Neural networks can be trained in noise. For instance, a neural network trained with a least mean square criterion approximates the conditional expectation of the output pattern, given the input pattern. There exists robust learning algorithms that guarantee convergence in the presence of uncertainties.
• Neural networks can easily be implemented on parallel hardware for fast computation. Indeed, they realize, by nature, a parallel processing of information.

These properties clearly indicate that neural networks exhibit some intelligent behavior, and are good candidate models for the control of nonlinear processes, for which no perfect mathematical model is available.

IRIDIA laboratory has been working in the field of neurocontrol since 1988. Several control design methods have been developed and compared, including the design of robust adaptive neurocontrol schemes that ensure tracking of the desired output signal, and optimal neurocontrol that provides optimal stabilization with respect to a predefined performance criterion (in collaboration with Jean-Michel Renders). IRIDIA is today recognized as a leading European research laboratory in the field of intelligent control.

Selected references

Saerens, M., Renders, J.-M. & H. Bersini :

"Neurocontrollers based on backpropagation algorithm".
In IEEE Press Book on Intelligent Control Systems - Gupta M. & N. Sinha (eds.) - IEEE Computer Society Press, 1995.

Renders J-M., M. Saerens and H. Bersini :

Adaptive Neurocontrol of a Certain Class of MIMO Discrete-Time Processes Based on Stability Theory - In Neural Network
Engineering in Dynamic Control Systems - K.J. Hunt, G.R. Irwin and K. Warwick (Eds) - Advances in Industrial Control - Springer, 1995.

H. Bersini and V. Gorrini :

An Empirical Analysis of One Type of Direct Adaptive Fuzzy Control.
In Fuzzy Logic and Intelligent Systems (Theory and Applications) - Hua Li and M. Gupta (Eds.) - Kluwer Academic Publisher, 1995.

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