B. Kuipers and S. Ramamoorthy. 2002.
Qualitative modeling and heterogeneous control of global system
behavior.
In C. J. Tomlin and M. R. Greenstreet (Eds.), Hybrid
Systems: Computation and Control,
Lecture Notes in Computer Science 2289, Springer Verlag, 2002.
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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