Optimal online parameter estimation for a class of infinite dimensional systems using Kalman filters

We consider the problem of online parameter estimation for a class of structurally perturbed infinite dimensional systems. By viewing the system as an augmented system with the unknown constant parameters being the additional states, a time varying infinite dimensional system results whose evolution operator depends on the available output signal. An optimal filter for the resulting time varying system is proposed which optimally reconstructs both the state and unknown parameters. Well-posedness results for the optimal observer are summarized along with an example that illustrate the applicability of this approach to a parabolic partial differential equation.