Linear time‐varying model predictive control and its application to active steering systems: Stability analysis and experimental validation

Abstract A model predictive control (MPC) approach for controlling an active front steering (AFS) system in an autonomous vehicle is presented. At each time step a trajectory is assumed to be known over a finite horizon, and an MPC controller computes the front steering angle in order to best follow the desired trajectory on slippery roads at the highest possible entry speed. We start from the results presented in ( Int. J. Veh. Auton. Syst. 2005; 3 (2–4):265–291; IEEE Trans. Contr. Syst. Technol. 2007; 15 (3)) and formulate the MPC problem based on successive online linearization of the nonlinear vehicle model (linear time‐varying (LTV) MPC). We present a sufficient stability condition for such LTV MPC scheme. The condition is derived for a general class of nonlinear discrete time systems and results into an additional convex constraint to be included in the LTV MPC design. For the AFS control problem, we compare the proposed LTV MPC scheme with the LTV MPC scheme in ( IEEE Trans. Contr. Syst. Technol. 2007; 15 (3)) where stability has been enforced with an ad hoc constraint. Simulation and experimental tests up to 17 m/s on icy roads show the effectiveness of the LTV MPC formulation. Copyright © 2007 John Wiley & Sons, Ltd.