Adaptive high gain observers for a class of MIMO nonlinear systems

This paper deals with adaptive observers designs for some class of uniformly observable systems. Indeed, an adaptive observer is proposed for the on-line estimation of the state and the unknown parameters involved in the system dynamics as well as in the output expression. It is shown that the equations of the proposed observer can be derived using two approaches, namely the adaptive approach and extended-high gain observer-based approach. The observer design is detailed under both approaches and the equivalence between the underlying observer equations is established.

I. Introduction

The design of adaptive observers has attracted considerable attention in the last decades. Roughly speaking, one can classify the methods to derive adaptive observers into two approaches: the adaptive approach from which are derived most existing algorithms and the extended-observer based-approach. The design of most observers derived according to the adaptive approach (heavily) borrows from the state observer design and the structure of the adaptive observers is similar to that of the state observers with the difference that the unknown parameters are replaced by some estimates that are updated through appropriately chosen adaptation laws. In the extended observer based approach, the observer design is based on an extended system obtained by accounting for the dynamics of the unknown parameters. By doing so, one can take advantage of state observer designs that are available for the class of systems including the so obtained augmented system. In [1], the authors have shown the equivalence between two adaptive observers each one of which has been designed by adopting one of the above two approaches.