On the performance of high-gain observers with sign-indefinite gain adaptation under measurement noise

Ricardo Sanfelice (1) , Laurent Praly (2)

1 Department of Aerospace and Mechanical Engineering
2 CAS - Centre Automatique et Systèmes

We address the problem of state observation for a system whose dynamics may involve poorly known, perhaps even nonlocally Lipschitz functions and whose output measurement may be corrupted by noise. It is known that one way to cope with all these uncertainties and noise is to use a high-gainobserver with a gain adapted on-line. The proposed method, while presented for a particular case, relies on a "generic" analysis tool based on the study of differential inequalities involving quadratic functions of the error system in two coordinate frames plus the gainadaptation law. We establish that, for bounded system solutions, the estimated state and the gain are bounded. Moreover, we provide an upper bound for the mean value of the error signals as a function of the observer parameters. Since due to perturbations the gainadaptation law may drive the observer/plant interconnection to nearby boundary of its stability region, oscillatory behavior may emerge. To overcome this issue, we suggest an adaptive procedure based on a space averaging technique involving several copies of the observer.

Domaines: Automatique / Robotique

Ricardo Sanfelice, Laurent Praly. On the performance of high-gain observers with sign-indefinite gain adaptation under measurement noise. Automatica, 2011, 47 (10), pp.2165-2176. ⟨10.1016/j.automatica.2011.08.002⟩. ⟨hal-00643452⟩