Robust Lookup Table Controller Based on Piecewise Multi-linear Model for Nonlinear Systems with Parametric Uncertainty

This paper proposes a robust lookup table controller based on piecewise multi-linear model for nonlinear systems with parametric uncertainty. We construct a piecewise multi-linear model of a nonlinear system. The model is a nonlinear approximation and the model can be derived from fuzzy if-then rules with singleton consequents. The piecewise model can be expressed as a lookup table. The model dynamics is described by multi-linear interpolation of the lookup table elements. We design a robust piecewise multi-linear controller for the piecewise model via feedback linearization. The robust piecewise controller can be also expressed as a lookup table. We apply the robust lookup table controller to ball and beam system as a nonlinear system with parametric uncertainty. Examples are shown to confirm the feasibility of our proposals by computer simulations.