Optimization based non-linear observers revisited

Optimization based non-linear observers are those where the integrated output prediction error is used to define the dynamic of the observer's state. Their main advantage is genericity and the natural assumptions that are needed for the related convergence results to hold. Here, we present some new theoretical results concerning these observers. Despite the title we use, our observer is not based on the search for a global minimum of a cost function. It is based on a descent-like approach without the use of the Hessian matrix. A nice feature is that the resulting observer takes a classical form of in the sense that it is defined by a set of ordinary differential equations. Besides the theoretical results, some implementation issues are discussed. In particular, we propose to use the post stabilization approach, well known when dealing with differential systems with invariant submanifolds. This enables to increase the sampling period while keeping very good precision. Two illustrative examples are presented to show the efficiency of the proposed method.