Observer Design for Parameter Varying Differentiable Nonlinear Systems, with Application to Slip Angle Estimation

This technical note develops observer design techniques in a unified framework for both time invariant and parameter varying Lipschitz nonlinear systems that are differentiable w.r.t. state variables. First, a new sufficient condition for asymptotic convergence is developed for Arcak's two-DOF nonlinear observer for time-invariant nonlinear systems. In addition to ensuring asymptotic convergence, extension of this observer design technique to optimization of a L₂ performance criterion is presented, which improves disturbance rejection performance of the observer. Next, augmentation of this technique to parameter varying nonlinear (PVNL) systems is developed. Different from methods suggested in the LPV literature, a simple but non-conservative finite dimensional relaxation method for quadratic parameter dependent LMIs is presented. These results constitute perhaps the first systematic observer design methodology in literature for PVNL systems. Finally, the performance of the developed observers is evaluated for estimation of slip angle using the commercial vehicle dynamics software CARSIM. Unlike previous results which use a LTI or a time invariant nonlinear model for observer design, this technical note presents a PVNL observer guaranteed to work with continuously varying velocity of the vehicle.