Model-based fuzzy control for two trailers problem: stability analysis and design via linear matrix inequalities

We design a backward movement control system for a vehicle with two trailers via a model-based fuzzy control technique. A Takagi-Sugeno fuzzy model is constructed to describe the nonlinear dynamics of the vehicle. The so-called parallel distributed compensation is employed to determine a control rule structure of a fuzzy controller from the fuzzy model of the vehicle. The parameters of the fuzzy controller are obtained via the linear matrix inequality (LMI) based design with respect to the decay rate, constraint on the control input and constraint on the output. Simulation and experimental results show that the fuzzy controller designed effectively achieves the backward movement control of the articulated vehicle without using the jack-knife phenomenon.