System identification and optimization of fuzzy relation matrix models based on semi-tensor product

Abstract

Generally, in real-world engineering disciplines a dynamical system is nonlinear, having multi-input and multi-output (MIMO) variables, and high level parameter uncertainties. Although there are many approaches proposed in the literature for system modeling and optimization, it remains a challenging topic to derive the precise mathematical models to characterize complex, dynamic and globally described systems. If training data in a real-world system are available, artificial neural network theories can be applied for system parameter recognition and optimization. The objective of this work is to develop a new fuzzy formulation based on the semi-tensor product (STP) method to construct fuzzy logic models for MIMO systems in a matrix representation. It involves the following processing operations: fuzzy modeling, structure and parameters identification, system optimization, and adaptive control of closed-loop fuzzy systems based on the fuzzy relation matrix (FRM) models and STP algorithms. The related contributions are summarized below. [...]