IFAC Reports

of 21 adaptive algorithms are compared using analog simu- lated stable and unstable processes with various disturbances. Six combinations appear to be best using recursive least squares estimation. For stochastic disturbances, the maximum likelihood estimator should be used. Csaki et al. (Hungary) give a multivariable self-tuning regulator which they have used for control of cement blending and grinding. The application of a self-tuning regulator to large tanker auto- pilots is discussed by Kallstrom et al. (Sweden). Actual tests aboard a tanker were performed and showed excellent results under different loads, speed and weather conditions. Strejc (Czechoslovakia) presents a good survey on least squares and regression methods for identification. An interesting tutorial view of adaptive algorithms is presented by Tsypkin (U.S.S.R.). When one uses identification methods, an approxi- mation to the real system is obtained. The implications of this point of view for experimental design and model validation is discussed by Ljung (Sweden) and Van Overbrook (Sweden). They indicate that the use of the model must be taken into account. An approach to testing the model is given. By coincidence, two papers by Ljung (Sweden) and Landau (France) and Narendra and Valavani (U.S.A.) are concerned with the relationship between self-tuning and model adaptive controls. The convergence of either algorithm is shown to be governed by similar differential equations.

Theory. 33. Applications of Multilevel Structures, 43A. Multivariable Control Systems: General Aspects, 43B. Multivariable Control Systems: Control Design and 44. Large-Scale Systems

Most of these subjects will not be treated here. An area of considerable attention in recent years is the control of mul- tivariable systems. Extensions of the classical frequency do- main techniques have been developed. The paper by MacFarlane (U.K.) shows how the multivariable frequency techniques are related to the state space geometric approach of Wonham. This indicates that one can obtain the same

on the 7th Congress 367

information from either approach. One uses the approach that is most natural to the problem and the designer. Wong (U.S.A.) extends further the conditions under which linear quadratic regulators remain stable in the presence of actuator failures. It is shown that the choice of the cost criteria can have a decided effect on stability under failures.

Another theory area receiving considerable attention is that of large scale systems due to applicability to power networks and distributed computer systems. Siljak (U.S.A.) develops an approach for controlling large-scale systems which are com- posed of a number of overlapping subsystems. Local feedback controls can be designed ignoring the interconnections. Under conditions of weak coupling, the overall system is shown to be stable. Medanic (U.S.A.) has developed a new approach for model reduction to obtain low order models which closely approximate the higher order system. Through the use of a Generalized Hessenberg Representation a series of cascaded lower order systems is obtained. The series is truncated at the desired degree of model order.

Two rather preliminary papers by Meditch (U.S.A.) and Johnson (U.S.A.) apply control theory concepts to problems not usually treated. In the first paper Meditch develops a state-space model of a store and forward data communi- cations network. Using multivariable control theory, feedback policies are obtained to regulate the queue lengths throughout the network. Unfortunately it is a centralized control algor- ithm. Johnson's paper discusses feedback systems composed of both continuous and finite-state machines. Such systems occur whenever continuous processes are controlled by a computer. A new method of looking at such systems has been discovered which he claims may be able to provide better design algorithms.

Whether the concepts presented in these papers can be applied to real applications needs to be explored further.

H. A. SPANG IlI Associate Editor

IFAC Report

Report on the third IFAC Round Table Discussion Session (RT-15) on fuzzy decision making and applications

at the seventh IFAC World Congress

Summary--This report summarizes the main features of the Round Table Discussion Session (RT-15) that took place during the 7th IFAC World Congress.

In spite of another parallel round table on a more popular subject (next decade of control theory and application) and some other interesting regular sessions, it was a well attended session and was attended by nearly 50 delegates (a partial list is enclosed herewith). The subject matter was discussed by six panel members who presented their work also. Following the formal presentation of their work by the panel members, some interesting discussion emerged during the session.

I. Introduction THE NOTION of fuzziness has captured the interest of many researchers around the world because, potentially, it is cap- able of revolutionizing the nature of research in the area of man-machine systems and humanistic processes. This decade has seen an exponential growth in the development of fuzzy mathematics and its applications, providing a basis for new approaches to problems in engineering, management, social sciences, medicine, decision analysis, psychology and so- ciology, economics and many more fields.

Many formal and informal meetings were organized by Dr. M. M. Gupta in the past which provided a stimulating atmosphere for discussion of key problems and recent de- velopments at the forefront of the state-of-the-art of this fuzzy

~field. At this round table discussion on "Fuzzy decision

making and applications", many talented investigators pre- sented their views.

2. General Discussion Dr. Gupta, the Chairman, in his opening remarks, pointed

out certain highlights of the round table discussion session including the challenges and criticisms that this new but growing field has faced and is facing. Some of his remarks are summarized here.

• . . scientists have long sought ways to use precision of mathematics to tame the imprecision of the real world phenomenon.

Many valued logic, topology and probability theory are a few but different attempts to give precision to imprecision or vagueness inherent in our real life.

The binary logic that we use in the computers is a two valued logic-- 'YES' or 'NO', 'TRUE' or 'FALSE', '1' or '0', 'WHITE' or 'BLACK', etc. It has a rigid two valued membership~ei ther it belongs to a TRUE group of to a FALSE group.

However, in the fuzzy set theory, we have the concept of graded membership, or grey membershi ly-as I call it, i.e. in the universe of discourse X, the membership function falls in the range [0, 1].

I admire the efforts and zest of Lotfi A. Zadeh (who unfortunately could not attend this meeting) to explore the manifold uses of the concept of graded membership.

368

l h i s field is young, and is facing an exponential growth. This is a third IFAC-discussion session (IFAC Hague (1973)), (IFAC Boston (1975)). A very successful one-day symposium was also organized at the 1977 IEEE-CDC Conference which was held in December, 1977 at New Orleans. Papers of this IEEE-CDC Conference have appeared in the Conference preprints and also some selected papers will appear in the Int. J. of Fuzzy Sets and Systems.'"

Also, Dr. Gupta summarized some of the recent work on the application of the theory in the area of industrial process control, pattern recognition, medical diagnosis and other decision making fields.

Following these opening remarks, panel members presented their recent work in the field: a summary of these pre- sentations is given here.

Dr. M. Peschel, Academy of Sciences q]' the G.D.R., Berlin: "Model reference [i*zzy identification method". Dr. Peschel made some interesting remarks on the development of appli- cations of the fuzzy theory, and gave a brief account of his own work in the fuzzy identification method using model reference adaptive approach. He reported some very interest- ing results on decomposition method and adaptive methods in optimization.

Projessor Huibert Kwakernaak, Twente University ol Technology, The Netherlands: "Fuzzy sets as an application of multi-valued logic". His presentation concerned with the fol- lowing: it helps to obtain a clearer understanding of fuzzy set theory to view a fuzzy set as a triple (X,,u,a). Here X is an ordinary set, while /z (the membership functionl is a map X -~[0,1]. The function a:X-+P assigns a statement a(x) to each element of X. P is a "universe of discourse" and consists of a collection of statements. For given x • X, the number l~(x) is the truth value of the statement a(x), i.e. p (x)= tla(x)), with t: P--+[0,1]. The truth function t follows certain rules from multi-valued logic, for example the well-known min max rule. In this view, a fuzzy set is an indexed set of statements together with the truth value for each member statement. The definition of the image of a fuzzy set under a given map, which is a central notion, now follows very naturally.

Dr. D. Willaeys, Laboratoire d'Automatique lndustrielle et Humaine, Valenciennes, France: "'Use of fuzzy discrete space for fi*zzy automatic control". He said that the theory of fuzzy sets has for some years now permitted a better grasp of certain systems in various fields, notably, in that of automatic process control. This type of automatic control may be envisaged for a class of systems which are difficult to modelize and identify, but which may be run nevertheless by a human operator after a learning phase. Fuzzy set theory, by formaliz- ing the subjective description that the human operator can give of the control strategy he applies to his process, or of the information he can get from the system itself, allows one to achieve a first approach to modelizing the process or to complete or confirm the results of objective analysis and measurements.

Such an approach, which uses the notions of fuzzy language, fuzzy algorithm and fuzzy automata, drives to some problems such as how to build a fuzzy control algorithm from a fuzzy model and also how to minimize the computer memory which will support the control algorithm. For the second point, the use of a fuzzy discrete space instead of a normal discrete space is a good solution to put into a mini- computer fuzzy sets defined on real space.

Dr. V. D. Dimitrov, International Institute of Control Sciences, U.S.S.R: "Fuzzy social choice." Dr. V. D. Dimitrov presented some of his work on fuzzy social choice (FSC). The problem of fuzzy choice arises when we come across si- tuations in which we have to take into account many criteria, goals and requirements, non-precisely known for us. Using the fuzzy set approach, this problem is formulated precisely and the following results are obtained and discussed:

(1) The fuzzy social choice (FSC) is compatible with the condition of positive responsiveness of the social choice function to the individual preferences.

(2) By the FSC the well-known Arrow's paradox disappears.

(3) By the FSC there exists a social choice function which respects the human rights of each society member.

I F A C R e p o r t s o n t h e 7 t h C o n g r e s s

Dr. A. Seill Laboratoire d'automatiquc et d'aaaly,w de., systemes, 7bulouse, France: "Classification by an artilicial skin using .luzzy correlation". He presented an application of the fuzzy correlation methods (Self and Aquilar-Martin, 1977 and to be published) to classify between different types of solid objects placed over a table. A noisy information is obtained from a planary distributed transducers called "artificial skin" (Stojiljkovik and Clot, 1977L The dimension of the object with respect to the skin is too large such that the skin must be moved using a logical control algorithm to go over the object. This algorithm depends on the skin peripheral infor- mation and has a memory which is necessary when there are several paths for the same object. The least squares method is used to adjust the axis of the object with that of the skin. Four step motors are used to serve the motion m three orthogonal directions in addition to the rotation.

The set of causes or criteria necessary for classification is chosen subjectively. The conditional fuzzy measures are calcu- lated recursively using the successive imprints given by the skin. Each conditional fuzzy measure o- (y/ixD represents the grade of membership of observed pattern to class (object) t~ in view of cause -':k. A set of groups is constructed where each group consists of one of the classes and its complement. Applying the fuzzy integral given by Sugeno (1974), the fuzzy correlations between the original class and its complement are calculated. The grade of importance of causes Ithe fuzzy densities) are adapted using a supervised learning model ira the sense that the fuzzy auto-correlation is greater than the fuzzy cross-correlation.

Using the previous property, after calculating the cor- relation between the observed pattern and the fuzzy densities of one of the group, it can be determined if this pattern belongs to the class in this group or not.

The algorithm is characterized by high rate of convergence and small computational effort. The stability of guaranteed even when there are large number of classes. Mathematical proof of convergence has previously been given by (Self and Aguilar-Martin. to be published }.

Rejerences Sell A. and J. Aguilar-Martin (1977). Classification by the

artificial hand using fuzzy correlation. 1st Symposium on Biophysics: theory and applications, Cairo, 18 20 October 1977.

Sell A. and J. Aguilar-Martin (1979). Multi-group classifi- cation using fuzzy correlations. Int. J. Fuzz)' Sets Systems, to be published.

Stojiljkovic, Z. and J. Clot (1977). Integrated behaviour of artificial skin. IEEE Trans. Biomed. Eng. 24, 39(~399.

Sugeno, M. (1974). Theory of Fuzzy Integral and its Applications, Ph.D. Thesis, Tokyo Institute of Technology.

During the general discussion that followed, there were several interesting issues raised by the participants of the discussion session. Many gave their experiences on both theoretical as well as experimental work. There was some discussion on fuzzy logic and probability logic. It was felt, however, that some more applications oriented work must emerge from these theories. Professor Terano discussed some of his work on theoretical and applications' oriented work in the fuzzy field.

Conclusions In spite of a t remendous amount of publications appearing

in the field, it was felt that there is a need for unification of various contents and the theoretical developments in the area. Also, there is a further need for good applications oriented work. It was felt, however, that the newly established journal ' International Journal of Fuzzy Sets and Systems' will help stimulate interest for good applications work. The discussion session ended with a desire to have such informal discussion sessions more often, perhaps preceded by some survey papers in the area.

ReJerences Gupta, M. M. (1975). IFAC report: round table discussion on

'the estimation and control in a fuzzy environment' . Automatica 2, 20%212.

I F A C R e p o r t s

Gupta, M. M. and E. H. Mamdani (1975). IFAC report on the second IFAC round table discussion on fuzzy automata and decision processes, held at the Sixth Triennial IFAC World Congress, Boston/Cambridge, August. Automatica 12, 241-296.

Gupta, M. M., G. N. Saridis and B. Gaines (1977). Fuzzy Automata and Decision Processes. Edited Volume, Elsevier North-Holland.

Gupta, M. M, R. K. Ragade, R. Yager (1977). 'Report of the IEEE Special Symposium on Fuzzy Set Theory and Applications', at the 1977 CDC, New Orleans, December 1978.

Proceedings of the 1977 IEEE Conference on Decision and Control Special Symposium on Fuzzy Set Theory and Applications, Vol. 2, pp. 1300-1450.

A partial list of participants Genser, R.

OBB, GD/IK, Vienna, Austria. Gupta, M. M.

University of Saskatchewan, Saskatoon, Canada. Ju-Wei, Jai

Inst. of Automation, Academia Sinica, Peking, China. Yang, C. C.

Inst. of Control Eng., Peking, China. Vitek, V.

Vyzkummy 6stav energetidy, Praha 7, Partzanska 7a, Czechoslovakia.

Larsen, P. Martin Electric Power Eng. Dept., Build 325, Tech. Univ. of Denmark, DK 2800 Lyngby, Denmark.

Pedersen, S. Tokkesdal F. F. Smidth & Co. A/S, Processtech, Dept., 77 Vigerslevalle, DK 2500 Valby, Denmark.

Seid, B. Badische Aniliu u. Soda Fabrik (67), Ludwigshaten, F.R.G.

Holmberg, Andrea Systems Theory Lab., Helsinki University of Tech., SF- 02150, Espoo 15, Finland.

Eerola, Annele Jaakko Poyry Engineering, PL 16, 00401 Helsinki 40, Finland.

Kohre, Jan Uer-Control of Akavatalo, Helsinki 52, Finland.

Korhonen, Juhani Jaakko Poyry Engineering, PL 16, 00401 Helsinki 40, Finland.

o n t h e 7 t h C o n g r e s s 369

Silvennoiren, Risto Tampere University of Technology, P.O. Box 527, SF- 33101, Tampere 10, Finland.

Seif, Abdel-Monem Laas, 7 av-du Colonel-Roche, 31400 Toulouse, France.

Vidal, S. University of Lille, France.

Willaeys, D. Laboratoire d'Automotique l'industrielle et Humaine, University of Valenciennes, France.

Wernstedt, Jurgen Department of Automatic Control, Tech. Univ. Ilmemau, G.D.R.

Peschel, M. Acad. of Sci. of the G.D.R., 1199 Rodowek Chaussees, Berlin, G.D.R.

Hatvany, T. Computer & Automation Institute, Hung. Ac. Sci., 1502 Budapest POB 63, Hungary.

Terano, T. Tokyo Inst. of Tech., Systems Science Dept., 152 Tokyo, Japan.

Kwakernaak, H. Twente Univ. of Tech., P.O. Box 217, En Schede, The Netherlands.

Ewart, D. G. British Aerospace, Dynamics Group, Site B, Stevenage, U.K.

Etschmaier, M. M. Dept. of Industrial Engineering, Univ. of Pittsburgh, Pittsburgh, Pa. 15261, U.S.A.

Martin, C. Lyndon 6 John St., Newark Valley, New York, N.Y. 13811, U.S.A.

Dimitrov, V. International Inst. of Control Sciences, 29 Ryleeva Str., 119034 Moscow, U.S.S.R.

Ryabinin, I. A. 199151, Leningrad, Nalichnaya 36~2-53, U.S.S.R.

Tavast, R. Inst. of Cybernetics, Academy of Sciences, Estowan SSR, Talliun 200104, U.S.S.R.

Saridis, G. N. Purdue University, U.S.A.

MADAN M. GUPTA Chairman and Organizer

Systems Science Control Research Laboratory University of Saskatchewan

Saskatoon, Saskatchewan, Canada S7N OWO

IFAC Report

Comments on Round Tables

THE 7th IFAC Congress was remarkable for the breadth of applications presented in various technical sessions. I think this is a mark of the maturing of IFAC and a very positive sign indeed. I believe that the round tables were generally quite successful. The one big difficulty with the round table discussions at the Congress was that they were not conducted around a round table. The theater-style environment in which the round tables took place is not optimal for that type of meeting format. Future Congress and Symposium organizers should be strongly encouraged to use a round table geometry

when organizing such sessions. The more relaxed interaction between participants and members of the audience gave the impression, and indeed resulted in, a useful working session kind of environment rather than the formal stand-up lecture with slides format. Let us indeed continue with round table discussions, but let us find round tables around which to have these discussions.

S. J. KAHNE Associate Editor

-x IFAC Report

Comments on the 7th IFAC Congress

THE CONGRESS program lacked a good deal in the latest control problems and trends, especially with respect to con- sidering control as a means for solving, social, economical,

industrial environmental, energy, etc. problems facing the world community. In fact the "link between science and applications of automatic control", the congress theme, was a