MIMO fuzzy adaptive control systems based on fuzzy semi-tensor product

Based on fuzzy semi-tensor product (STP) algorithms and fuzzy relation matrix (FRM) models, the design of an adaptive fuzzy controller was proposed in this paper for the multivariable nonlinear systems with uncertainty. The controlled multi-input-and-multi-output (MIMO) plants were expressed and processed first by FRM models and fuzzy STP operations, and then the indirect adaptive fuzzy control laws were designed. The tracking property of the FRM models was proved for the control objective of MIMO systems. The effectiveness of the novel matrix expression was verified by simulations of the tracking control on a two-link rigid robot manipulator. Results in simulation tests show that the proposed design of adaptive FRM control is efficient for nonlinear multivariables. Therefore, the proposed indirect fuzzy adaptive controllers can be extended to general matrix expression for MIMO nonlinear systems with fuzzy STP algorithms and FRM models and online approximate unknown parameters, according to required accuracy.