Nonlinear automotive actuator analysis based on sum of squares programming

The paper analyses the maximum Controlled Invariant Sets of vehicle actuators. In the calculation of the shape of the sets a nonlinear polynomial Sum-of-Squares (SOS) programming method is applied. The aim of the analysis is to identify the similarities and differences between the different actuator interventions and provide a theoretical basis for their coordination. The maximum Controlled Invariant Sets of the steering and the brake control systems are analyzed at various velocities and road conditions. In the analysis the nonlinear characteristics of the lateral tire force are considered with a polynomial approximation. The results of the analysis are illustrated through a simulation example.