Differential flatness conditions, with illustrations using symbolic computations | Francois Olivier

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Lecture: Differential flatness conditions, with illustrations using symbolic computations. Speaker: Francois Olivier, Ecole Polytechnique, France. Bio: François Ollivier obtained his PhD in mathematics at École polytechnique in 1990. He is Researcher with the National Center for Scientific Research since 1991. He works in the field of symbolic computation and differential algebra on problems related to control theory. He belongs to the Algebraic modeling team of the Computer science laboratory at Polytechnique. He contributed to algorithms for testing identifiability and observability, test subalgebra, subfield or differential subfield membership and for computing characteristic sets of differential ideals. His recent works are related to Jacobi's bound. He was involved in the SCIEnce project (Symbolic Computation Infrastructure for Europe), the LEDA project (Logistic of Differential Algebraic Equations) and theMath AmSud Simca project (Implicit Systems, Modeling and Automated Control). Abstract: Necessary conditions for flatness as well as some sufficient conditions are exposed and developed. We show that some necessary condition reduces to testing the homogeneous Nullstellensatz, viz. deciding if some projective variety is nonempty, which is known as a "good case" for algebraic algorithms. If a system satisfies the necessary conditions, then its flat outputs will be common first integrals of a finite family of vector fields. It is shown that the existence of rational first integrals of a given degree can be tested and how to compute them (joint work with G. Chèze). The theoretical algorithms will be illustrated by symbolic computations.

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