Invariant subspaces and sensor placement for observability in Continuous Timed Petri Nets

Enrique Aguayo-Lara,Javier Ruiz-Leon,Antonio Ramirez-Trevino

doi:10.1109/case.2011.6042525

Abstract

This work deals with the problem of sensor placement for observability in Continuous Timed Petri Nets (ContPN) with infinite server semantics. ContPN are represented by a family of linear systems F = Σ 1 = (A 1 , B 1 , S 1 ), ..., Σ n = (A n , B n , S n ) switching between them. The observability in ContPN requires the observability of each linear system Σ k and the distinguishability of each pair of systems Σ k , Σ j . Thus this work uses the well known result that a system Σ k is observable iff the maximum A k -invariant subspace contained in the kernel of S k is the null space to build output functions S k in such a way that the ContPN becomes observable. This work characterizes the A k -invariant subspaces associated to nonzero eigenvalues from the ContPN incidence matrix and the others A k -invariant subspaces from the ContPN structure. Using this information an output matrix S = S 1 = ... = S n is computed in such a way that no A k -invariant subspace is contained in the kernel of S. From the construction of S we can guarantee that every pair of systems is distinguishable from each other. Thus the ContPN becomes observable.

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