New Nonlinear Takagi–Sugeno Vehicle Model for State and Road Curvature Estimation via a Nonlinear PMI Observer

The present article deals with an observer design for nonlinear vehicle lateral dynamics. The contributions of the article concern the nonconsideration of any force model and the consideration that the longitudinal velocity is time varying, which is more realistic than the assumption that it is constant. The vehicle model is then represented by an exact Takagi–Sugeno (TS) model via the sector nonlinearity transformation. A proportional multiple integral (PMI) observer based on the TS model is designed to estimate simultaneously the state vector and the unknown input (lateral forces and road curvature). The convergence conditions of the estimation error are expressed under LMI formulation using the Lyapunov theory, which guaranties a bounded error. Simulations are carried out for comparison between the conventional PI observer, the enhanced PI observer, and the PMI observer. Finally, experimental results are provided to illustrate the performances of the proposed PMI observer