An Interval-based Approximation Method for Discrete Changes in Hybrid cc

Hybrid cc is a constraint-based programming language aimed for simple modeling and rigorous simulation of hybrid systems. The existing implementation of Hybrid cc uses intervals to handle partially specified models. Although the implementation solves nonlinear equations and ordinary differential equations (ODEs) based on interval arithmetic, discrete changes are not properly computed with intervals. We propose a method for enclosing every solution of a hybrid system with a set of boxes. Our method computes continuous state changes by solving ODEs with initial time and values expressed by intervals. Then the method detects and encloses every state that will cause a discrete change. We devise algorithms for pruning and splitting intervals to obtain tight enclosures. The experimental results show the efficiency of the algorithms.