Fault estimation based adaptive observer for a class of Lipschitz nonlinear systems

Aiming at the problem of fault estimation for a class of nonlinear systems with Lipschitz nonlinear term, a new adaptive observer is proposed in this paper. The system is subject to sensor fault, actuator fault and unknown disturbance simultaneously. The sensor fault vector is transformed into an augmented state vector, the original system is transformed into an augmented nonsingular system which includes unknown disturbance and actuator fault of unknown upper bound. A new adaptive observer is designed to estimate the states and actuator fault simultaneously, and it can also eliminate (or attenuate) the influence of the unknown disturbance. The solution of the adaptive observer gain matrix is transformed into a multi-objective optimization problem, and the solution method of the observer is given in the form of a theorem by means of linear matrix inequality (LMI). It is proved that the states of the error system are uniformly ultimately bounded. Finally, an example is given to verify the effectiveness of the proposed observer for nonlinear systems fault estimation.