Leakage-type adaptive state and disturbance observers for uncertain nonlinear systems

This paper proposes a novel adaptive observer technique for estimating the state and disturbance of uncertain nonlinear systems. To remove the knowledge of the upper bounds of the disturbance and its derivative, a leakage-type (LT) algorithm is introduced to approximate the variations of their bounds. A state observer is first provided based on a conventional Walcott–Zak observer structure, and then, a disturbance observer is proposed by introducing an auxiliary dynamics. Due to the features of the LT adaptive law, the estimation error of the system state or the disturbance is bounded in a small neighborhood around zero in finite time. In addition, since the switching gain is automatically adapted to the disturbance change, the chattering in the estimation signal is effectively suppressed that is useful for the estimation precision in a practical system. Another important advantage of the proposed method lies in its simple structure compared to the existing finite-time observers. Lyapunov analysis demonstrates that for both types of observers, the estimation error is achieved to be globally uniformly ultimately bounded. To demonstrate the proposed method, simulation examples are separately carried out on a vehicle system and a linear motor system.