Matrix Inequalities Based Robust Model Predictive Control for Vehicle Considering Model Uncertainties, External Disturbances, and Time-Varying Delay

In this paper, we design a robust model predictive control (MPC) controller for vehicle subjected to bounded model uncertainties, norm-bounded external disturbances and bounded time-varying delay. A Lyapunov-Razumikhin function (LRF) is adopted to ensure that the vehicle system state enters in a robust positively invariant (RPI) set under the control law. A quadratic cost function is selected as the stage cost function, which yields the upper bound of the infinite horizon cost function. A Lyapunov-Krasovskii function (LKF) candidate related to time-varying delay is designed to obtain the upper bound of the infinite horizon cost function and minimize it at each step by using matrix inequalities technology. Then the robust MPC state feedback control law is obtained at each step. Simulation results show that the proposed vehicle dynamic controller can steer vehicle states into a very small region near the reference tracking signal even in the presence of external disturbances, model uncertainties and time-varying delay. The source code can be downloaded on https://github.com/wenjunliu999.