Design of an Adaptive Observer with Finite-Time Convergence

Abstract

This paper presents a finite-time adaptive observer for a class of linear systems to achieve state observation and parameter estimation simultaneously. Different from classical adaptive observers based on the state observation error, the adaptive law in the developed observer is designed based on the parameter estimation error and the sliding mode term, where the parameter estimation error is extracted by auxiliary variables and algebraic operations. As a result, the coupling effect between parameter estimation and state observation is highly reduced such that the finite-time convergence of the parameter estimation error can be explicitly given. Besides, the persistent excitation condition of the system can be online verified by calculating minimal eigenvalue of the designed auxiliary variable. For the observer design, a time delay is introduced in order to achieve the state observation error converging to zero in finite time. Finally, comparative simulation results for a robotic arm is given to show the effectiveness of the proposed finite-time adaptive observer.