Constructing a Symmetric Tsallis Divergence as a System Identification Criterion

摘要

In spite of the system identification, as (in accordance to L. Ljung (2010)) a science and art of constructing mathematical models via sample data, is a polyhedral process, selecting an identification criterion within an identification problem statement is a constituent part requiring both accounting its adequacy to the data available and practical suitability of implementation. The paper presents an approach to the identification of input/output mappings of stochastic systems in accordance to information-theoretic criteria that are derived by constructing a symmetric divergence measure based on Tsallis entropy of an arbitrary order. Meanwhile, a parameterized description of the system under study is utilized combined with a corresponding technique of estimation of the mutual information constructed by use of Tsallis entropy. This leads, finally, to a problem of the finite dimensional optimization to be solved by a suitable technique.