A Pseudospectral Observer for Nonlinear Systems

In this paper, we present an observer design method for nonlinear systems based on pseudospectral discretizations and a moving horizon strategy. The observer has a low computational burden, a fast convergence rate and the ability to handle measurement noise. In addition to ordinary differential equations, our observer is applicable to nonlinear systems governed by deferential-algebraic equations (DAE), which are considered very difficult to deal with by other designs such as Kalman filters. The performance of the proposed observer is demonstrated by several numerical experiments on a time-varying chaotic nonlinear system with unknown parameters and a nonlinear circuit with a singularity-induced bifurcation.