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.

非线性模型预测控制 (NMPC) 是一种基于优化的控制策略，它直接结合非线性动态模型，并具有理想的稳定性和鲁棒性。状态估计是 NMPC 的重要对应物，移动地平线估计 (MHE) 也是一种基于优化的策略，直接结合了非线性动力学和约束。然而，NMPC 和 MHE 受到在每个时间步求解 NLP 的计算成本的挑战。对于 NMPC，这可以通过高级步骤和高级多步骤方法来避免，它们离线解决详细的优化（可能在多个采样时间上）并在线对最优解进行基于灵敏度的校正，超过两个数量级更少的计算。这项工作通过先进的多步 MHE 方法补充了先进的多步 NMPC。该开发解决了后台严格的优化问题以及对到达成本的详细更新。在线校正由基于快速灵敏度的 NLP 实现。amsMHE 方法在两个具有数百个状态变量的大型蒸馏案例研究中得到了证明，并表明大型系统的非线性状态估计可以通过可忽略的在线计算来实现。