Unknown Input Observers for Simultaneous Estimation of Vehicle Dynamics and Driver Torque: Theoretical Design and Hardware Experiments

This article investigates a new observer design method to estimate simultaneously both the vehicle dynamics and the unknown driver's torque. To take into account the time-varying nature of the longitudinal speed, the vehicle system is transformed into a polytopic linear parameter-varying (LPV) model with a reduced level of numerical complexity. Based on Lyapunov stability arguments, we prove that the estimation errors of the system state and of the unknown input (UI) are norm-bounded, which can be made arbitrarily small by minimizing a guaranteed $\mathcal {L}_{\infty }-$gain performance. The design of the LPV UI observer is reformulated as an linear matrix inequality-based optimization which can be effectively solved via semidefinite programming. Extensive hardware experiments are carried out under various driving test scenarios to confirm the effectiveness of the proposed observer design. In particular, a comparative study is performed with a widely adopted observer to emphasize the practical interests of the new estimation solution.