A control sequence generator for fuzzy gain schedulers

The generation of the sequence of control inputs along a given state trajectory for a nonlinear system is described. A nonlinear system is linearized at predefined points in the product space of the states and control inputs and then approximated by local linear fuzzy models. Based on this approximation the system is controlled by a set of local linear Takagi-Sugeno fuzzy controllers. The local control laws designed for the error system incorporate both the desired and the actual state as well as the corresponding control input. Normally, the desired state is defined by the user but the related control input cannot always be calculated in a unique way especially for a non-square system. The proposed method generates the desired control inputs on the basis of the states and its derivatives using inverse fuzzy models of the system. In an optimization loop the control inputs are corrected by the analytical forward model of the nonlinear system