Observability and Observers for Nonlinear Systems
SIAM Journal on Control and Optimization
Brief paper: High gain observers with updated gain and homogeneous correction terms
Automatica (Journal of IFAC)
High-gain observers in the presence of measurement noise: A switched-gain approach
Automatica (Journal of IFAC)
Consensus Optimization on Manifolds
SIAM Journal on Control and Optimization
Brief paper: An adaptive high-gain observer for nonlinear systems
Automatica (Journal of IFAC)
Paper: Instability analysis and improvement of robustness of adaptive control
Automatica (Journal of IFAC)
Time-varying increasing-gain observers for nonlinear systems
Automatica (Journal of IFAC)
| Hi-index | 22.15 |
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-gain observer 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 gain adaptation 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 gain adaptation 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.