Integrating Projections

摘要

This paper describes three techniques for reachability analysis for systems modeled by ordinary differential equations (ODEs). First, linear models with regions modeled by convex polyhedra are considered, and an exact algorithm is presented. Next, non-convex polyhedra are considered, and techniques are presented for representing a polyhedron by its projection onto two-dimensional subspaces. This approach yieds a compact representation, and allows efficient algorithms from computational geometry to be employed. Within this context, an approximation technique for reducing non-linear ODE models to linear nonhomogeneous models is presented. This reduction provides a sound basis for applying methods for linear systems analysis to non-linear systems.