State and parameter estimation for nonlinear systems

State and parameter estimators are obtained for systems described by nonlinear evolution equations. Linear infinite dimensional observability theory together with a variety of fixed point theorems can be employed to obtain a finite time observer. Moreover, a nonlinear asymptotic observer is produced using stability results. The problem of joint state and parameter estimation is converted to the state estimation case, via an augmented state, so that these observer results can be utilised. Examples and remarks on the generality of the results are given.