Observability of Nonlinear Dynamical Systems over Finite Fields
CoRR(2024)
Abstract
This paper discusses the observability of nonlinear Dynamical Systems over
Finite Fields (DSFF) through the Koopman operator framework. In this work,
given a nonlinear DSFF, we construct a linear system of the smallest dimension,
called the Linear Output Realization (LOR), which can generate all the output
sequences of the original nonlinear system through proper choices of initial
conditions (of the associated LOR). We provide necessary and sufficient
conditions for the observability of a nonlinear system and establish that the
maximum number of outputs sufficient for computing the initial condition is
precisely equal to the dimension of the LOR. Further, when the system is not
known to be observable, we provide necessary and sufficient conditions for the
unique reconstruction of initial conditions for specific output sequences.
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