System identification: theory for the user
System identification: theory for the user
Representation for the radical of a finitely generated differential ideal
ISSAC '95 Proceedings of the 1995 international symposium on Symbolic and algebraic computation
Fast Algorithms for Manipulating Formal Power Series
Journal of the ACM (JACM)
Factorization-free decomposition algorithms in differential algebra
Journal of Symbolic Computation - Special issue on symbolic computation in algebra, analysis and geometry
A Gröbner free alternative for polynomial system solving
Journal of Complexity
Kronecker's and Newton's approaches to solving: a first comparison
Journal of Complexity
A probabilistic algorithm to test local algebraic observability in polynomial time
Proceedings of the 2001 international symposium on Symbolic and algebraic computation
Fast computation of discrete invariants associated to a differential rational mapping
Journal of Symbolic Computation - Special issue: International symposium on symbolic and algebraic computation (ISSAC 2002)
Symbolic-numeric completion of differential systems by homotopy continuation
Proceedings of the 2005 international symposium on Symbolic and algebraic computation
On the complexity of the resolvent representation of some prime differential ideals
Journal of Complexity
Symbolic-numeric computation of implicit riquier bases for PDE
Proceedings of the 2007 international symposium on Symbolic and algebraic computation
Automatica (Journal of IFAC)
Differential Algebra and System Modeling in Cellular Biology
AB '08 Proceedings of the 3rd international conference on Algebraic Biology
Implicit Riquier Bases for PDAE and their semi-discretizations
Journal of Symbolic Computation
Brief paper: Structural identifiability analysis via symmetries of differential equations
Automatica (Journal of IFAC)
On the complexity of the resolvent representation of some prime differential ideals
Journal of Complexity
Brief paper: On analytic and algebraic observability of nonlinear delay systems
Automatica (Journal of IFAC)
The input-output relationship approach to structural identifiability analysis
Computer Methods and Programs in Biomedicine
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The following questions are often encountered in system and control theory. Given an algebraic model of a physical process, which variables can be, in theory, deduced from the input-output behaviour of an experiment? How many of the remaining variables should we assume to be known in order to determine all the others? These questions are parts of the local algebraic observability problem which is concerned with the existence of a non-trivial Lie subalgebra of model's symmetries letting the inputs and the outputs be invariant.We present a probabilistic seminumerical algorithm that proposes a solution to this problem in polynomial time. A bound for the necessary number of arithmetic operations on the rational field is presented. This bound is polynomial in the complexity of evaluation of the model and in the number of variables. Furthermore, we show that the size of the integers involved in the computations is polynomial in the number of variables and in the degree of the system. Last, we estimate the probability of success of our algorithm.