Aggregated Bisimulation and Identification of Finite-Valued Networks

We propose a method that combines aggregation and bisimulation to approximate large finite-valued networks by smaller models. With the algebraic state-space representation of a quotient system under observational equivalence, the aggregated bisimulation is performed by partitioning a network into blocks and replacing the dynamics of each block by that of its quotient system. If the aggregation is not a bisimulation, these quotient systems can be further replaced by probabilistic networks based on the relative frequency of transitions, which contain full information about the input–output dynamics. As an inverse problem of aggregation, simulated identification of finite-valued networks is studied. We give an upper bound on the minimal number of nodes required to identify a system, and design an online algorithm to reproduce the internal state dynamics from given input–output sequences. The results are illustrated with numerical examples.