Adaptive observers for a class of uniformly observable systems with nonlinear parametrization and sampled outputs

International audienceIn this paper, we propose an adaptive observer for a class of uniformly observable nonlinear systems withnonlinear parametrization and sampled outputs. A high gain adaptive observer is first designed under theassumption that the output is continuously measured and its exponential convergence is investigated,thanks to a well defined persistent excitation condition. Then, we address the case where the outputis available only at (non uniformly spaced) sampling instants. To this end, the continuous-time outputobserver is redesigned leading to an impulsive observer with a corrective term involving instantaneousstate impulses corresponding to the measured samples and their estimates. Moreover, it is shown that theproposed impulsive observer can be put under the form of a hybrid system composed of a continuous-timeobserver coupled with an inter-sample output predictor. Two design features are worth to be emphasized.Firstly, the observer calibration is achieved through the tuning of a scalar design parameter. Secondly, theexponential convergence to zero of the observation and parameter estimation errors is established undera well defined condition on the maximum value of the sampling partition diameter. More specifically,the observer design is firstly carried out in the case of linear parametrization before being extended tothe nonlinear one. The theoretical results are corroborated through simulation results involving a typicalbioreactor