$$\mathcal {H}_\infty $$ Observer Design for LPV Systems with Uncertain Measurements on Scheduling Variables: Application to an Electric Ground Vehicle

In this chapter, we aim to study the observer design problem for polytopic linear-parameter-varying (LPV) systems with uncertain measurements on scheduling variables. Due to the uncertain measurements, the uncertainties are considered in the weighting factors. It is assumed that the vertices of polytope are the same when the measurements on scheduling variables are uncertain and perfect. Then, an LPV system with the uncertain weighting factors can be transferred to an LPV system with uncertainties. To deal with the uncertainties and unknown disturbance in the observer design problem, we propose a gain-scheduled sliding mode observer. Defining the estimation error as the state vector minus the estimated state vector, the estimation error dynamics is established. The sliding mode observer design method is developed based on analysis results of the established estimation error system. The proposed observer design method is then applied to an electric ground vehicle (EGV) in which the measurement of longitudinal velocity is assumed to be uncertain. Experimental tests and comparisons are given to show the advantages of the proposed design method and the designed observer.