Static and Dynamic Abstraction Solves the Problem of Chatter in Qualitative Simulation

Daniel J. Clancy, Benjamin Kuipers

One of the major factors hindering the use of qualitative simulation techniques to reason a,bout the behavior of complex dynamical systems is intractable branching due to a phenomenon called chatter. This paper presents two general abstraction techniques that solve the problem of chatter. Eliminating the problem of chatter significantly extends the range of models that can be tractably simulated using qualitative simulation. Chatter occurs when a variable’s direction of change is constrained only by continuity within a region of the state space. This results in intractable, potentially infinite branching within the behavioral description due to irrelevant distinctions in the direction of change. While a number of techniques have been proposed to eliminate chatter, none of them provide a general solution that can eliminate all instances of chatter. Chatter box abstraction and dynamic chatter abstraction provide two such solutions to this problem. Both solutions eliminate chatter by abstracting the chattering region of the state space into a single qualitative state with an abstract direction of change. The algorithms differ in the manner in which they identify the chattering region of the state space.

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