Optimistic vs pessimistic moving-horizon estimation for quasi-LPV discrete-time systems

In this paper we focus on estimation for nonlinear plants that can be rewritten under the form of quasi-linea parameter-varying systems with bounded unknown parameters. Moving-horizon estimators are proposed to estimate the state of such systems according to two different formulations, i.e., "optimistic" and "pessimistic". In the former case, we perform estimation by minimizing the least-squares moving-horizon cost w.r.t. both state variables and parameters simultaneously. In the latter, we minimize such a cost w.r.t. the state variables after picking up the maximum w.r.t. the parameters. Under suitable assumptions, the stability analysis of the estimation is proved in both cases. A simple numerical example is provided to compare the proposed approaches.