Adaptive fuzzy control of MIMO dynamical systems using differential flatness theory

The paper proposes adaptive fuzzy control for uncertain MIMO nonlinear dynamical systems using the differential flatness theory. Through the considered control scheme the paper defines an extended class of systems in which indirect adaptive fuzzy control can be applied. Nonlinear systems satisfying the differential flatness property can be written in the Brunovsky form via a transformation of their state variables and control inputs. The resulting control signal is shown to contain nonlinear elements, which in case of unknown system parameters can be calculated using neuro-fuzzy approximators. Using Lyapunov stability analysis it is shown that one can compute an adaptation law for the neuro-fuzzy approximators which assures stability of the closed loop. The performance of the proposed flatness-based adaptive fuzzy control scheme is tested through simulation experiments on the MIMO model of a robotic manipulator.