State estimation and output feedback control of nonlinear systems using homogeneous observers

This thesis considers the state estimation and output feedback control of two classes of nonlinear systems: upper-triangular and lower-triangular systems with unmeasurable states. Due to the presence of the high-order nonlinearities, most of the existing state estimation methods can only yield local results. In this thesis, we will show that the newly developed homogeneous observers can be used to estimate the states of some nonlinear systems in larger regions than a small neighborhood of the origin. More specifically, in the case of lower-triangular system, we show that the low-order homogeneous observer will asymptotically converge to the real system when the initial error is small. Under the same condition, we also design an asymptotically convergent high-order observer for the upper-triangular system. The observer is also combined with the output feedback controller to stabilize the upper-triangular systems.

To satisfy the requirements of small initial error for the homogeneous observers, we propose a method of estimating the initial values based on the least square estimation method which provides us initial estimation for the homogeneous observer. In addition, we will combine the unscented Kalman filter and the homogeneous observers and thus this combined system will have the ability of filtering noise and estimating the unmeasurable states. Computer simulations are conducted to demonstrate the effectiveness of the proposed method.