Modeling and identification of parallel nonlinear systems: structural classification and parameter estimation methods

Structural classification and parameter estimation (SCPE) methods are used for studying single-input single-output (SISO) parallel linear-nonlinear-linear (LNL), linear-nonlinear (LN), and nonlinear-linear (NL) system models from input-output (I-O) measurements. The uniqueness of the I-O mappings of some model structures is discussed. The uniqueness of I-O mappings of different models tells us in what conditions given model structures can be differentiated from one another. Parameter uniqueness of the I-O mapping of a given structural model is also discussed, which tells us in what conditions a given model´s parameters can be uniquely estimated from I-O measurements. These methods are then generalized so that they can be used to study single-input multi-output (SIMO), multi-input single-output (MISO), as well as multi-input multi-output (MIMO) nonlinear system models. Parameter estimation of the two-input single-output nonlinear system model, which was left unsolved previously, can now be obtained using the newly derived algorithms. Applications of SCPE methods for modeling visual cortical neurons, system fault detection, modeling and identification of communication networks, biological systems, and natural and artificial neural networks are also discussed. The feasibility of these methods is demonstrated using simulated examples. SCPE methods presented in this paper can be further developed to study more complicated block-structured models, and will therefore have future potential for modeling and identifying highly complex multi-input multi-output nonlinear systems