Advanced-multi-step moving horizon estimation for large-scale nonlinear systems

Nonlinear Model Predictive Control (NMPC) is an optimization-based control strategy that directly incorporates nonlinear dynamic models and has desirable stability and robustness properties. State estimation is an essential counterpart to NMPC and Moving Horizon Estimation (MHE) is also an optimization-based strategy that directly incorporates the nonlinear dynamics and constraints. However, NMPC and MHE are challenged by the computational expense of solving NLPs at each time step. For NMPC, this is avoided by advanced-step and advanced-multi-step approaches, which solve the detailed optimization off-line (possibly over multiple sampling times) and perform sensitivity-based corrections to the optimal solution on-line, with over two orders of magnitude less computation. This work complements advanced-multi-step NMPC with an advanced-multi-step MHE approach. The development solves rigorous optimization problems in background along with detailed updates to the arrival cost. On-line corrections are enabled by fast sensitivity-based NLP. The amsMHE approach is demonstrated on two large-scale distillation case studies with hundreds of state variables, and shows that nonlinear state estimation for large-scale systems can be implemented with negligible on-line computation. (c) 2022 The Author(s). Published by Elsevier Ltd. This is an open access article under the CC BY license (http://creativecommons.org/licenses/by/4.0/).