State reconstruction for stochastic nonlinear systems with unknown local nonlinearities via output injection

Abstract

This paper addresses state estimation for dynamical systems involving localized unknown nonlinearities. Direct application of linear state estimation techniques, e.g., the Kalman filter, would yield erroneous state estimates. Existing approaches in the literature either assume or estimate the nonlinearities. Alternatively, the present paper proposes to reject the unknown nonlinearities as if they were unknown disturbances. By applying an existing disturbance rejection technique, the need to know or to estimate the nonlinearities is avoided. The efficiency of the proposed method is demonstrated through numerical simulations on a nonlinear mechanical system.