Using Analytic CLP to Model and Analyze Hybrid Systems

Timothy J. Hickey and David K. Wittenberg

We use CLP(F), anAnalytic Constraint Logic Programming (ACLP) language, to model hybrid systems. ACLP languages combine intervals, constraints, and ODEs (Ordinary Differential Equations) in a clean and natural way. CLP(F) provides an implementation of an ACLP language based on interval arithmetic. The semantics of CLP(F) rigorously handle non-linear ODEs and round-off error. The ODEs describing a hybrid system need only a minor change of syntax to become a CLP(F) program. This simple transformation from a physical description of a hybrid system to a program which can be used to provide a proof of safety properties of the system bridges the gap between practical tools and formal models, and allows one to easily prove statements about realworld systems. The combination of interval arithmetic with ACLP makes it easy to pose and answer many sorts of queries about a system. For example, “At what point does the system change from one state to another?”, or “What control settings result in a cycle with period t?”

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