Adaptive Robust Observer Design For A Class Of Uncertain Nonlinear Systems

In this paper the problem of state estimation for nonlinear uncertain systems in the presence of both parameter uncertainties and system disturbances will be discussed. An adaptive robust observer is proposed for a class of nonlinear uncertain systems, where two different categories of uncertainties are considered: the first category is the structured system uncertainty, which can be separated and expressed as the product of known functions of states and a set of unknown constants. The second category is the unstructured (interval) uncertainty, which is not separable but is bounded by a partially known function. It is further assumed that this partially known bounding function is convex to the set of unknown parameters, namely, the bounding function is no longer linear in parameters. The adaptive method is adopted to deal with the structured uncertainties, and the adaptive robust method is applied to deal with the unstructured uncertainty. Convergence analysis study shows that the state estimation errors can converge to zero asymptotically. This paper includes simulation studies to demonstrate the performance of the proposed observer.