Sampled-data based state and parameter estimation for state-affine systems with uncertain output equation

The problem of sampled-data observer design is addressed for a class of state- and parameter-affine nonlinear systems. The main novelty in this class lies in the fact that the unknown parameters enter the output equation and the associated regressor is nonlinear in the output. Wiener systems belong to this class. The difficulty with this class of systems comes from the fact that output measurements are only available at sampling times causing the loss of the parameter-affine nature of the model (except at the sampling instants). This makes existing adaptive observers inapplicable to this class of systems. In this paper, a new sampled-data adaptive observer is designed for these systems and shown to be exponentially convergent under specific persistent excitation (PE) conditions that ensure system observability and identifiability. The new observer involves an inter-sample output predictor that is different from those in existing observers and features continuous trajectories of the state and parameter estimates.