Sum of squares approach for ground vehicle lateral control under tire saturation forces

Abstract

This work presents the stability analysis and design of a lateral controller for a nonlinear ground vehicle applying the concept of polynomial sum of squares relaxations. The system is approximated by a polynomial vector field that describes the lateral vehicle dynamics. The resulting polynomial system falls on a class of non-affine in input system, which makes the control synthesis more involved. This issue is circumvented by an input-affine approximation, simplifying the stability analysis and the design procedure of a polynomial state-feedback controller able to enlarge the region of attraction (RoA). We also compare the estimated region of attraction with the standard LQR optimal controller.