Stochastic nonlinear minimax filtering in continuous-time

Abstract

This paper discusses nonlinear stochastic minimax games in which the minimizing player is the state estimate while the maximizing players are square-integrable stochastic disturbances. A pathwise optimization method is considered, and an information state is introduced as in [1], which is governed by a second-order Hamilton-Jacobi-Bellman (HJB) equation. The HJB equation is subsequently employed to characterize the dissipation properties of the estimator error with respect to the stochastic disturbances, and to introduce a certainty equivalence estimator.