Multivariable Fuzzy Sliding Mode Control by Using a Simplex of Control Vectors

  • Giorgio Bartolini
  • Antonella Ferrrara
Part of the International Series on Microprocessor-Based and Intelligent Systems Engineering book series (ISCA, volume 11)


Since the basic work by Zadeh in the late sixties xc12, xc13, fuzzy logic has been intensively applied in the area of control system theory and design, in order to set up control environments which do not require the pecise knowledge of the mathematical model of the process to be controlled (see, for instance, xc3, xc8 and the references therein cited).

Indeed, fuzzy logic, enabling the definition of sets and membership functions of a certain elemenst to given sets by using natural language, appears to be suitable to deal with all those practical situations in which a certain level of uncertainty in the description of the system under study has to be taken into account.

The design of a fuzzy controller consists of a fixed number of steps. The aim of the controller is that of relating the relevant variables, such as input or error signals, usually described in a crisp way, to the cotnrol action. The first step is therefore devoted to the convension of the crisp input variables to the fuzzy form by associating with them the corresponding linguistic values.

The core of the controller is represented by a set of linguistic rule. These latter are evaluated according to the compositional rule of inference, producing a fuzzy output which, once transformed into a crisp variables, enables the generation of the suitable control action.

In spite of the wide variety og applications of fuzzy controllers to industrial processes, a certain number of problems, mainly related to the efficient design of the look-up table containing the fuzzy ruels, still remain to be overcome. A noteworthly attempt in this direction is constituted by the possibility of combining a controller design procedure based on fuzzy logic with a less qualitative design approach, such as that inspired to the variable structure systems theory, recently outlined in the literature xc7.

A variable structure controller (VSC) enables the definition of a suitable sliding manifold on which the state trajectories of the controlled system are kept, from a certain time instant onwards, in spite of the uncertainties assumed on the process in questions xc10, xc11. The sliding manifold coincides with the intersection of the discontinuity surfaces associated with the various control signals on the plan- t. As a consequence, the overall control strategy, once the state trajectory of the controlled systems lies on the sliding manifold becomes discontinuous.


Membership Function Fuzzy Logic Control Vector Fuzzy Controller State Trajectory 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.


Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.


  1. [1]
    Baida, S. V., and D. B. Izosimov 1985, Vector method of design of sliding motion and simplex algorithms, Automation and Remote Control, 46, 830–837.Google Scholar
  2. [2]
    Bartolini, G., and T. Zolezzi 1985, Variable structure non linear in the control law, IEEE Transaction on Automatic Control, 30, 681–684.CrossRefGoogle Scholar
  3. [3]
    Chang, S., and L. A. Zadeh 1972, On fuzzy mapping and control, IEEE Transaction on Sys., Man, Cyber., 2, 30–34.MATHGoogle Scholar
  4. [4]
    DeCarlo, R. A., Zak, S. H., and G. P. Mattews 1988, Variable structure control of non linear multivariable systems: a tutorial, Proceedings of the IEEE, 76, 212–232.CrossRefGoogle Scholar
  5. [5]
    Guzzella, L., and H. P. Geering 1990, Variable structure controllers for robots, in Deterministic Control of Uncertain Systems, A. S. I. Zinober Editor, Peter Peregrinus, London.Google Scholar
  6. [6]
    Isidori, A. 1985, Non linear control systems, Springer-Verlag, Berlin.Google Scholar
  7. [7]
    Kung, C. C., and S. C. Lin 1992, A fuzzy sliding mode controller design, Proc. IEEE Int. Conf. on Systems Engineering, Kobe, Japan, 608–611.Google Scholar
  8. [8]
    Lee, C. C. 1990, Fuzzy logic in control systems: fuzzy logic controller, IEEE Transaction on Sys., Man, Cyber., 20, 404–435.MATHCrossRefGoogle Scholar
  9. [9]
    Slotine, J. J. E., and W. Li 1991, Applied non linear control, Prentice-Hall, Englewood Cliff, N.J..Google Scholar
  10. [10]
    Utkin, V. I. 1978, Sliding modes and their application in variable structure systems, MIR Publishers, Moscow.MATHGoogle Scholar
  11. [11]
    Utkin, V. I. 1992, Sliding modes in control and optimization, Springer-Verlag, Berlin.MATHGoogle Scholar
  12. [12]
    Zadeh, L. A. 1965, Fuzzy sets, Informat. Control, 8, 338–353.MATHCrossRefGoogle Scholar
  13. [13]
    Zadeh, L. A. 1968, Fuzzy algorithms, Informat. Control, 12, 94–102.MATHCrossRefGoogle Scholar
  14. [14]
    Zinober, A. S. I. (editor) 1990, Deterministic Control of Uncertain Systems, Peter Peregrinus, London.MATHGoogle Scholar

Copyright information

© Kluwer Academic Publishers 1994

Authors and Affiliations

  • Giorgio Bartolini
    • 1
  • Antonella Ferrrara
    • 1
  1. 1.Department of Communication, Computer and System SciencesUniversity of GenovaGenovaItaly

Personalised recommendations