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.

Publication:

IEEE TRANSACTIONS ON AUTOMATIC CONTROL

http://dx.doi.org/10.1109/TAC.2024.3509334

Author:

Zhengping Ji

the Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science and School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100190, China

e-mail: jizhengping@amss.ac.cn

Xiao Zhang

Department of Applied Mathematics, Hong Kong Polytechnic University, Hong Kong SAR 999077, China

e-mail: xiaozhang@amss.ac.cn

Daizhan Cheng

Key Laboratory of Systems and Control, Academy of Mathematics and Systems Science, Chinese Academy of Sciences, Beijing 100190, China

e-mail: dcheng@iss.ac.cn