Adaptive fuzzy control for differentially flat MIMO nonlinear dynamical systems

摘要

The paper proposes flatness-based adaptive fuzzy control for uncertain MIMO nonlinear dynamical systems. The considered control scheme based on differential flatness theory extends the class of systems in which indirect adaptive fuzzy control can be applied. To conclude if a dynamical system is differentially flat, the following should be examined: (i) the existence of the flat output, which is a variable that can be written as a function of the system's state variables (ii) the system's state variables and the input can be written as functions of the flat output and its derivatives. Nonlinear systems satisfying the differential flatness property can be written in the Brunovsky (canonical) 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 benchmark nonlinear multi-input multi-output dynamical systems, such as robotic manipulators.