Switched LQR/H∞ steering vehicle control to detect critical driving situations

Abstract

This paper proposes a switching steering vehicle control designed using the linear quadratic regulator (LQR) problem, the Linear Matrix Inequality (LMI) framework and the H∞ norm. The proposed switched control law comprises two levels: the first level is a switched Proportional–Integral-Derivative controller of lateral deviation (PIDy) and the second is a switched Proportional-Derivative controller of yaw angle (PDψ). These two levels are used to ensure an accurate tracking of the vehicle's lateral deviation y and yaw angle ψ. This control strategy makes use of a common Lyapunov function design method used for the stability analysis of switched continuous-time systems. Sufficient conditions for global convergence of the switched control law are presented and proved under arbitrary switching signals. All these conditions are expressed in terms of LMIs. The switched steering control was developed for an application seeking to identify approximately the maximum achievable speed in a bend. This application requires a steering control for simulating a realistic nonlinear four-wheel vehicle model and for performing a speed extrapolation test to evaluate the physical limits of a vehicle in a bend. This study includes the performance tests using experimental data from the Peugeot 307 prototype vehicle developed by IFSTTAR Laboratory.