Model predictive control (MPC) is a popular technique for the development of active safety systems. However, its high computational cost prevents it from being implemented on lower-cost hardware. This paper presents a computationally efficient predictive controller for lane keeping assistance systems. The controller shares control with the driver, and applies a correction steering when there is a potential lane departure. Using the explicit feedback MPC, a multi-parametric nonlinear programming problem with a human-in-the-loop model and safety constraints is formulated. The cost function is chosen as the difference between the linear state feedback function to be determined and the resultant optimal control sequence of the MPC problem solved off-line given the current state. The piecewise linear feedback function is obtained by solving the parametric programming with an approximation approach. The effectiveness of the controller is evaluated through numerical simulations.
On Polyhedral Projection and Parametric Programming
