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Observer design using a partial nonlinear observer canonical form

Klaus Röbenack, Alan Lynch (2006)

International Journal of Applied Mathematics and Computer Science

This paper proposes two methods for nonlinear observer design which are based on a partial nonlinear observer canonical form (POCF). Observability and integrability existence conditions for the new POCF are weaker than the well-established nonlinear observer canonical form (OCF), which achieves exact error linearization. The proposed observers provide the global asymptotic stability of error dynamics assuming that a global Lipschitz and detectability-like condition holds. Examples illustrate the...

Observers for Canonic Models of Neural Oscillators

D. Fairhurst, I. Tyukin, H. Nijmeijer, C. van Leeuwen (2010)

Mathematical Modelling of Natural Phenomena

We consider the problem of state and parameter estimation for a class of nonlinear oscillators defined as a system of coupled nonlinear ordinary differential equations. Observable variables are limited to a few components of state vector and an input signal. This class of systems describes a set of canonic models governing the dynamics of evoked potential in neural membranes, including Hodgkin-Huxley, Hindmarsh-Rose, FitzHugh-Nagumo, and Morris-Lecar...

On determining unknown functions in differential systems, with an application to biological reactors

Éric Busvelle, Jean-Paul Gauthier (2003)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we consider general nonlinear systems with observations, containing a (single) unknown function ϕ . We study the possibility to learn about this unknown function via the observations: if it is possible to determine the [values of the] unknown function from any experiment [on the set of states visited during the experiment], and for any arbitrary input function, on any time interval, we say that the system is “identifiable”. For systems without controls, we give a more or less complete...

On determining unknown functions in differential systems, with an application to biological reactors.

Éric Busvelle, Jean-Paul Gauthier (2010)

ESAIM: Control, Optimisation and Calculus of Variations

In this paper, we consider general nonlinear systems with observations, containing a (single) unknown function φ. We study the possibility to learn about this unknown function via the observations: if it is possible to determine the [values of the] unknown function from any experiment [on the set of states visited during the experiment], and for any arbitrary input function, on any time interval, we say that the system is “identifiable”. For systems without controls, we give a more or less complete...

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