On robust pi adaptive observers for nonlinear uncertain systems with bounded disturbances

Robust adaptive observers for uncertain systems corrupted by bounded disturbances have to overcome two main problems. They have to guarantee a bounded parameter estimation, because it is well known that an arbitrarily small disturbance might drift to infinity the parameter estimation error even if the state estimate error remains bounded, and they have to ensure a robust state and parameter estimation independently of the uncertainty of the system. The contribution of this paper is a solution of both issues. We present a robust adaptive observer based on a normalized dead zone which guarantees a bounded estimate dealing with noise corrupted systems and on an adaptive gain which increases the robustness against uncertain systems. Tuning parameters are computed minimizing the effect of disturbances on the estimation error. The performance and the stability of the proposed adaptive observer is analyzed and demonstrated through simulation examples.