Adaptive observer design for a class of nonlinear systems with coupled structures

In this paper, we propose a global exponential adaptive observer for a class of uniformly observable nonlinear systems in order to jointly estimate miss- ing states and unknown constant parameters. This class consists of cascade sub- systems where every sub-system is associated with a subset of outputs. Moreover, a full triangular structure is not assumed since the dynamics of some particular states of each subsystem may depend on the whole state vector. Of fundamen- tal importance, the global exponential convergence of the proposed observers was shown to be guaranteed under the well known persistent excitation condition. The gain of this observer involves a design function that has to satisfy some mild con- ditions which are given. Different expressions of such a function are proposed. Of particular interest, it is shown that adaptive high gain like observers and adaptive sliding mode like observers can be derived by considering particular expressions of the design function.