A new algorithm for on-line relational identification of nonlinear dynamic systems

Fuzzy relations can model nonlinear dynamic systems since they are universal approximators and can perform nonlinear mappings. A model which takes into account input-output relations is more suited for identification of complex nonlinear processes. The fuzzy relation R describes the existing relation between input-output variables treated as fuzzy sets. This relation must be modified when a time-variant system online identification is performed. For each convenient set of sampling periods, a time-invariant fuzzy relation R can be found. A new online identification algorithm for fuzzy model systems, based on a simplified max-min relational equation, is proposed, where online gravity-center adjustment and variable universe of discourse concepts are applied. This last concept intends to avoid predicted signal saturation. The fuzzy algorithm is tested in two numerical examples, the traditional gas-furnace experimental data-set and a bilinear system. Its performance for different situations is discussed and compared with other published results