Data-driven moving horizon state estimation of nonlinear processes using Koopman operator

Abstract

In this paper, a data-driven constrained state estimation method is proposed for nonlinear processes. Within the Koopman operator framework, we propose a data-driven model identification procedure for state estimation based on the algorithm of extended dynamic mode decomposition, which seeks an optimal approximation of the Koopman operator for a nonlinear process in a higher-dimensional space that correlates with the original process state-space via a prescribed nonlinear coordinate transformation. By implementing the proposed procedure, a linear state-space model can be established based on historic process data to describe the dynamics of a nonlinear process and the nonlinear dependence of the sensor measurements on process states. Based on the identified Koopman operator, a linear moving horizon estimation (MHE) algorithm that explicitly addresses constraints on the original process states is formulated to efficiently estimate the states in the higher-dimensional space. The states of the treated nonlinear process are recovered based on the state estimates provided by the MHE estimator designed in the higher-dimensional space. Two process examples are utilized to demonstrate the effectiveness and superiority of the proposed framework.