Linear Parameter Varying Models-Based Gain-Scheduling Control for Lane Keeping System With Parameter Reduction

Abstract

In this paper, a robust <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{2}$ </tex-math></inline-formula> controller based on Linear Parameter Varying (LPV) model with scheduling variable reduction is applied for a lane-keeping system. On a curved road section, varying longitudinal speed and roll motion lead to multiple parameter variations in the lateral vehicle dynamics. To trade-off between the complexity of the multiple scheduling variables and the accuracy of the LPV model, an order reducing method by Autoencoder (AE) is performed to obtain a reduced model and diminishes the conservatism of LPV-based controller design. Further, to ensure the continuous convex set membership of the reduced scheduling variables in online test scenarios, the Lipschitz constant of the offline trained neural network (NN) is tightly estimated by solving a Semidefinite Program (SDP). The convex set of local Linear Time-Invariant (LTI) controllers is designed according to the estimated Lipschitz bound of the trained NN. The LPV-based robust <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{2}$ </tex-math></inline-formula> feedback controller is then designed by solving a set of Linear Matrix Inequalities (LMIs). Numerical simulations with full vehicle dynamics from CarSim are given to demonstrate the performance of the proposed system on various test roads. The continuous finding of the reduced scheduling variable membership is guaranteed in the online tests, and the effectiveness of the proposed method is confirmed with the mean value of lateral offset error reduced by about 50% compared with LTI-based <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\mathcal {H}_{2}$ </tex-math></inline-formula> controllers.