A probabilistic algorithm to test local algebraic observability in polynomial time

摘要

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.