Abstract
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.
Highlights
Dynamic control is one of the most crucial tasks for autonomous driving vehicle (Chen et al, 2020)
We focus on discrete vehicle dynamic control
To find an upper bound of J∞(k), a Lyapunov-Krasovskii function (LKF) candidate related to time-varying delay is designed as follows: V(x(k)) = V1(x(k)) + V2(x(k)) + V3(x(k))
Summary
Dynamic control is one of the most crucial tasks for autonomous driving vehicle (Chen et al, 2020). Most of existing LMIs or BMIs based robust MPC vehicle control papers only consider the model uncertainties. Few matrix inequalities based robust MPC papers consider both model uncertainties and external disturbances of vehicle. To suppress the influence of model uncertainties, external disturbances, and time-varying delay on vehicle dynamic state tracking performance, we design a matrix inequalities based robust MPC controller. A robust MPC controller is designed to 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. H ST SR when the expression has the format Q + S + ST, we simplify it to Q + S + ∗
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