Qualitative Modeling and Heterogeneous Control of Global System Behavior

  • Benjamin Kuipers
  • Subramanian Ramamoorthy
Conference paper
Part of the Lecture Notes in Computer Science book series (LNCS, volume 2289)

Abstract

Multiple model approaches to the control of complex dynamical systems are attractive because the local models can be simple and intuitive, and global behavior can be analyzed in terms of transitions among local operating regions. In this paper, we argue that the use of qualitative models further improves the strengths of the multiple model approach by allowing each local model to describe a large class of useful non-linear dynamical systems. In addition, reasoning with qualitative models naturally identifies weak sufficient conditions adequate to prove qualitative properties such as stability. We demonstrate our approach by building a global controller for the free pendulum. We specify and validate local controllers by matching their structures to simple generic qualitative models. This process identifies qualitative constraints on the controller designs, sufficient to guarantee the desired local properties and to determine the possible transitions between local regions. This, in turn, allows the continuous phase portrait to be abstracted to a simple transition graph. The degrees of freedom in the design that are unconstrained by the qualitative description remain available for optimization by the designer for any other purpose.

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References

  1. 1.
    Murray-Smith, R., Johansen, T.A.: Multiple Model Approaches to Modelling and Control. Taylor and Francis, UK (1997)Google Scholar
  2. 2.
    Kuipers, B.J.: Qualitative Reasoning:Modeling and Simulation with Incomplete Knowledge. MIT Press, Cambridge, MA (1994)Google Scholar
  3. 3.
    Shults, B., Kuipers, B.: Proving properties of continuous systems: qualitative simulation and temporal logic. Artificial Intelligence 92 (1997) 91–129MATHCrossRefMathSciNetGoogle Scholar
  4. 4.
    Alur, R., Courcoubetis, C., Halbwachs, N., Henzinger, T.A., Ho, P.H., Nicollin, X., Olivero, A., Sifakis, J., Yovine, S.: The algorithmic analysis of hybrid systems. Theoretical Computer Science 138 (1995) 3–34MATHCrossRefMathSciNetGoogle Scholar
  5. 5.
    Varaiya, P.: A question about hierarchical systems. In Djaferis, T., Schick, I., eds.: System Theory: Modeling, Analysis and Control. Kluwer (2000)Google Scholar
  6. 6.
    Guckenheimer, J., Holmes, P.: Nonlinear Oscillations, Dynamical Systems, and Bifurcations of Vector Fields. Springer-Verlag, Berlin (1983)MATHGoogle Scholar
  7. 7.
    Kuipers, B.: Qualitative simulation. Artificial Intelligence 29 (1986) 289–338MATHCrossRefMathSciNetGoogle Scholar
  8. 8.
    Kuipers, B.J., Åström, K.: The composition and validation of heterogeneous control laws. Automatica 30 (1994) 233–249MATHCrossRefGoogle Scholar
  9. 9.
    Slotine, J.J., Li, W.: Applied Nonlinear Control. Prentice Hall, Englewood Cliffs NJ (1991)Google Scholar
  10. 10.
    Friedland, B.: Advanced Control System Design. Prentice-Hall (1996)Google Scholar

Copyright information

© Springer-Verlag Berlin Heidelberg 2002

Authors and Affiliations

  • Benjamin Kuipers
    • 1
  • Subramanian Ramamoorthy
    • 2
  1. 1.Computer Science DepartmentUniversity of Texas at AustinAustinUSA
  2. 2.Electrical and Computer Engineering DepartmentUniversity of Texas at AustinAustinUSA

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