State and parameter estimation for canonic models of neural oscillators

Abstract

We consider the problem of how to recover the state and parameter values of typical model neurons, such as Hindmarsh-Rose, FitzHugh-Nagumo, Morris-Lecar, from in-vitro measurements of membrane potentials. In control theory, in terms of observer design, model neurons qualify as locally observable. However, unlike most models traditionally addressed in control theory, no parameter-independent diffeomorphism exists, such that the original model equations can be transformed into adaptive canonic observer form. For a large class of model neurons, however, state and parameter reconstruction is possible nevertheless. We propose a method which, subject to mild conditions on the richness of the measured signal, allows model parameters and state variables to be reconstructed up to an equivalence class.