$\mathcal {H}_{2}$ Optimal Sliding Hyperplane Design of Discrete-Time Integral Sliding-Mode Control for Automated Driving Vehicles

This article proposes the optimal discrete-time integral sliding-mode control for unmatched external signal compensation in a lane-keeping system on curved roads. Since curved roads appear as an external signal in a lateral vehicle motion model, improving the tracking performance with external signal compensation is necessary. To tackle the problem, we solve the optimization problem of obtaining the optimal sliding surface that minimizes the $\mathcal {H}_{2}$ norm of the transfer matrix from the external signal to the system state of interest. As a result, robust performance in the sense of $\mathcal {H}_{2}$ is guaranteed in the proposed framework. We provide a theorem to prove the $\mathcal {H}_{2}$ performance and present the design process. The proposed method is applied to lateral vehicle control to validate the effectiveness via numerical simulation and real-world experiments. A comparative study confirmed that the tracking performance of the proposed algorithm outperforms those of other methods on curved roads.