Analysis of braking dynamics using parameter-dependent polynomial Control Lyapunov Functions

The paper presents a Sum-of-Squares programming based method for the analysis of the nonlinear characteristics of braking dynamics. The goal of the analysis is the determination of the maximum braking torque by which the stability of the system is guaranteed and wheel skidding is avoided. The longitudinal wheel dynamics is modeled as a parameter-dependent polynomial system, which depends on the tire force characteristics and the vertical tire load. The formulation of the Sum-of-Squares optimization process using the parameter-dependent polynomial Control Lyapunov Function for the computation of the maximum braking torque is proposed. The results of the nonlinear analysis can be applied to the analysis and synthesis of braking systems. The efficiency of the optimization process is demonstrated through simulation examples.