Nonlinear vehicle lateral dynamics estimation with unmeasurable premise variable Takagi-Sugeno approach

Abstract

This paper deals with the problem of observer design for vehicle lateral dynamics. The nonlinear model of this last is transformed into Takagi-Sugeno (T-S) formulation by using the sector nonlinearity transformation. The main contribution of this paper is the representation of the vehicle nonlinear model by a T-S model with minimal loss of information (almost exact T-S model). This inevitably leads to a model with unmeasurable premise variables which is more difficult to study compared to the classical T-S models where premise variables are assumed to be measurable even if this is not really true as their are often estimated. The second contribution of this paper is the observer design for estimating the lateral dynamics of the vehicle. Stability conditions are established using a Lyapunov method and the concept of Input-To-State Stability (ISS). These conditions are then expressed in terms of optimization problem subject to LMI constraints. Simulation results are provided to illustrate the proposed approach, where the observer is synthesized with a T-S model and then applied directly to the nonlinear model of the vehicle. Some aspects of the robustness of the observer, with respect to time varying longitudinal velocity and measurement noise, are discussed.