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TitleGenerating invariants for non-linear hybrid systems by linear algebraic methods.
Author(s) Nadir Matringe, Arnaldo Vieira Moura, Rachid Rebiha
TypeBook, Chapter in Book, Conference Proceeding
AbstractWe describe powerful computational methods, relying on linear algebraic methods, for generating ideals for non-linear invariants of algebraic hybrid systems. We show that the preconditions for discrete transitions and the Lie-derivatives for continuous evolution can be viewed as morphisms and so can be suitably represented by matrices. We reduce the non-trivial invariant generation problem to the computation of the associated eigenspaces by encoding the new consecution requirements as specific morphisms represented by matrices. More specifically, we establish very general sufficient conditions that show the existence and allow the computation of invariant ideals. Our methods also embody a strategy to estimate degree bounds, leading to the discovery of rich classes of inductive, i.e. provable, invariants. Our approach avoids first-order quantifier elimination, Grobner basis computation or direct system resolution, thereby circumventing difficulties met by other recent techniques.
URL http://link.springer.com/chapter/10.1007%2F978-3-642-15769-1_23
PublisherBerlin: Springer
Translation No
Refereed No