A self-tuning fuzzy controller for a class of multi-input multi-output nonlinear systems

This paper presents a systematic design procedure of a multivariable fuzzy controller for a general Multi-Input Multi-Output (MIMO) nonlinear system with an input–output monotonic relationship or a piecewise monotonic relationship for each input–output pair. Firstly, the system is modeled as a Fuzzy Basis Function Network (FBFN) and its Relative Gain Array (RGA) is calculated based on the obtained fuzzy model. The proposed multivariable fuzzy controller is constructed with two orthogonal fuzzy control engines. The horizontal fuzzy control engine for each system input–output pair has a hierarchical structure to update the control parameters online and compensate for unknown system variations. The perpendicular fuzzy control engine is designed based on the system RGA to eliminate the multivariable interaction effect. The resultant closed-loop fuzzy control system is proved to be passive stable as long as the augmented open-loop system is input–output passive. Two sets of simulation examples demonstrate that the proposed fuzzy control strategy can be a promising way in controlling multivariable nonlinear systems with unknown system uncertainties and time-varying parameters.