Joint state and parameter estimation for discrete-time polytopic linear parameter-varying systems

Linear parameter-varying systems are very suitable for modelling nonlinear systems, since well-established methods from the linear-systems domain can be applied. Knowledge about the scheduling parameter is an important condition in this modelling framework. In case this parameter is not known, joint state and parameter-estimation methods can be employed, e.g., using interacting multiple-model estimation methods, or using an extended Kalman filter. However, these methods cannot be directly used in case the parameters lie in a polytopic set. Furthermore, these existing methods require tuning in order to have convergence and stability. In this paper, we propose to solve the joint-estimation problem in a two-step, Dual Estimation approach, where we first solve the parameter-estimation problem by solving a constrained optimisation problem in a recursive manner and secondly, employ a robust polytopic observer design for state estimation. Simulations show that our novel method outperforms the existing joint-estimation methods and is a promising first step for further research.