Nonlinear state estimation for uncertain systems with an integral constraint

This paper considers a problem of robust filtering for a class of uncertain nonlinear systems. The solution involves a set-valued state estimate that is obtained by solving a Hamilton-Jacobi-Bellman equation. In addition, a less computationally intensive approximate solution to the problem is obtained for filtering problems defined over a large time interval. The paper also presents an approximate solution to the robust filtering problem, which leads to a robust version of the extended Kalman filter.