Zero-order moving horizon estimation for large-scale nonlinear processes

Abstract

Moving Horizon Estimation (MHE) is an optimization-based approach to nonlinear state estimation where the state estimate is obtained as the solution of a nonlinear optimization problem. Especially for large-scale nonlinear systems, the computational burden associated with the numerical solution of nonlinear optimization problems poses a major challenge when applying MHE in practice. To alleviate the computational effort, we propose an inexact, but computationally less expensive variant of the Gauss–Newton algorithm tailored to the nonlinear least-squares problem arising from the MHE formulation. The proposed algorithm combines two ideas: On the one hand, it uses the fact that the arrival cost matrix appears naturally within the Gauss–Newton Hessian approximation in order to avoid any explicit arrival cost update. On the other hand, the method follows a zero-order optimization approach, where fixed sensitivity approximations are used in order to reduce the number of sensitivity evaluations, while accepting some loss of optimality. The combination of these two ideas allows one to reuse the factorizations of the Hessian blocks associated with each stage, when moving from one MHE problem to the next, therefore significantly reducing the computational complexity. Additionally, a tailored integration method for large-scale stiff systems is proposed that can efficiently propagate approximate forward sensitivities, which are used within the inexact MHE algorithm. Both estimation accuracy and computational efficiency of the proposed method are evaluated by applying it to two case studies: a small-scale batch reactor model and the large-scale dynamic process of acrylic acid production.