Distributed LPV State-Feedback Control Under Control Input Saturation

Developed in this note is a scheduled state-feedback controller synthesis method for discrete-time Linear Parameter Varying (LPV) systems subjected to control input saturation constraints. The static state-feedback gain is scheduled with an exact replica of the parameter matrix. The saturation effect is modeled by introducing time-varying parameters as functions of the control inputs, which are also used to schedule the controller. The synthesis method is then specialized to distributed state-feedback by imposing a particular structure on the feedback gain matrix. An explicit formula is also derived for the computation of the distributed control input from a nonlinear equation. The viability of the proposed method is tested in a simulation environment, for a ramp meter traffic flow control problem.