**Title**:A Complete Method to Polynomial Differential
Invariant Generation for Hybrid Systems

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Speaker**:

**Abstract**:How to design correct hybrid systems is a grand challenge
in computer science and control theory. In this paper, by analyzing the Lie
derivatives of a polynomial at different orders along a given vector field,
we present a complete method for generating polynomial differential invariants
of a hybrid system in which all functions in the expression are or can be reduced
to polynomials. Completeness here means that for a given hybrid system, if there
exists a polynomial differential invariant in the form of the predefined template,
then our approach can indeed discover it. To the best of our knowledge, this
is the first complete approach to polynomial differential invariant generation.