Morphisms for Non-trivial Non-linear Invariant Generation for Algebraic Hybrid Systems

We present a new method that addresses the various deficiencies of the state-ofthe-art non-linear invariant generation methods for hybrid systems. Present approaches for non-linear invariant generation are limited to linear systems, or they relay on non scalable methods which have high complexity. Moreover, for hybrid systems with discrete transitions, differential rules, and local conditions that are described by multivariate polynomial or fractional systems, no applicable method is known that lends itself to non-trivial non-linear invariants generation. We demonstrate a powerful computational complete method to solve this problem. By identifying suitable endomorphisms for each consecution condition, we reduce the problem to the intersection between specific eigenspaces and initial semi-affine/algebraic constraints. Our approach avoids first-order quantifier elimination, Grobner bases computation or direct resolution of the systems, hereby circumventing difficulties met by other recent techniques.