Nonlinear Stability Analysis of Vehicle Side-Slip Dynamics using SOS Programming

This paper proposes a convex polynomial optimization method based on sum of squares (SOS) programming techniques for estimating the region of attraction (RoA) of a vehicle tire side-slip dynamics. The paper first derives a dynamic model of a four-wheels tire side-slip which takes into account the nonlinear lateral force characteristic of the tires. In order to accommodate the use of SOS programming techniques, a polynomial approximation model of the tire slip dynamics is then derived. An SOS program which implements Lyapunov's second method for stability analysis is then proposed to estimate the RoA of a stable equilibrium point in the derived approximate polynomial tire slip model. Simulation results from the implementation of the proposed RoA estimation method is reported to illustrate the good performance of the proposed method.