Redesign of adaptive observers for improved parameter identification in nonlinear systems

• Published in: Automatica (Oxford) Vol. 47; no. 2; pp. 403 - 410
• Main Authors: Stamnes, Øyvind Nistad, Aamo, Ole Morten, Kaasa, Glenn-Ole
• Format: Journal Article
• Language: English
• Published: Kidlington Elsevier Ltd 01.02.2011; Elsevier
• Subjects: Adaptative systems; Adaptive systems; Applied sciences; Computer science; control theory; systems; Control system analysis; Control theory. Systems; Dynamical systems; Dynamics; Exact sciences and technology; Mathematical models; Modelling and identification; Nonlinear dynamics; Nonlinear systems; Observers; Parameter estimation; Parameter identification; Observers; Adaptive systems; Parameter identification; Nonlinear systems; Parameter estimation; Error estimation; Machining; Non linear control; Exponential stability; Modeling; Asymptotic stability; Uncertain system; Robustness; System identification; Adaptive observer; State estimation; Numerical convergence; Drilling; Lower bound; Estimation error; Non linear estimation; Non linear system; Upper bound; Friction; Global stabilization; Non linear observer
• ISSN: 0005-1098; 1873-2836
• DOI: 10.1016/j.automatica.2010.11.005

We propose a method for redesigning adaptive observers for nonlinear systems. The redesign uses an adaptive law that is based on delayed observers. This increases the computational burden, but gives significantly better parameter identification and robustness properties. In particular, given that a special persistency of excitation condition is satisfied, we prove uniform global asymptotic stability and semi-global exponential stability of the origin of the state and parameter estimation error, and give explicit lower bounds on the convergence rate of both the state and parameter estimation error dynamics. For initial conditions with a known upper bound, we prove tunable exponential convergence rate. To illustrate the use of the proposed method, we apply it to estimate the unmeasured flow rate and the uncertain friction parameters in a model of a managed pressure drilling system. The simulation results clearly show the improved performance of the redesigned adaptive observer compared to a traditional design.