Symbolic Reachability Computation for Families of Linear Vector Fields

نویسندگان

Gerardo Lafferriere

George J. Pappas

Sergio Yovine

چکیده

Symbolic Reachability Computation for Families of Linear Vector Fields Gerardo Lafferriere Department of Mathematical Sciences Portland State University, P.O. Box 751, Portland, OR 97207-0751. [email protected] George J. Pappas Department of Electrical Engineering University of Pennsylvania, 200 South 33rd Street, Philadelphia, PA 19104. [email protected] Sergio Yovine VERIMAG Centre Equation, 2 Ave Vignate, 38610 Gi eres, France. [email protected] (Received 25 April 2001) The control paradigm of physical processes being supervised by digital programs has lead to the development of a theory of hybrid systems combining nite state automata with di erential equations. One of the most important problems in the veri cation of hybrid systems is the reachability problem. Even though the computation of reachable spaces for nite state machines is well developed, computing the reachable space of a di erential equation is di cult. In this paper, we present the rst known families of linear di erential equations with a decidable reachability problem. This is achieved by posing the reachability computation as a quanti er elimination problem in the decidable theory of the reals. We illustrate the applicability of our approach by performing computations using the packages Redlog and Qepcad. Such symbolic computations can be incorporated in computer-aided veri cation tools for purely discrete systems, resulting in veri cation tools for hybrid systems with linear di erential equations.

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