Robust NMPC of Large-Scale Systems and Surrogate Embedding Strategies for NMPC
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Date
2024-06-20
Authors
Elorza Casas, Carlos Andrés
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Journal ISSN
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Publisher
University of Waterloo
Abstract
Non-linear model predictive control (NMPC) is a promising control algorithm due to its ability to deal with constrained multivariable problems. However, NMPC can be computationally expensive to solve due to its non-linear nature, multiple interacting process units and the presence of model uncertainty. Real-world NMPC applications also necessitate state estimation for feedback control. While robust NMPC and state estimators have been studied individually for large-scale problems, understanding their combined impact is crucial for wider NMPC adoption. Integrating tractable Machine Learning (ML) surrogates, particularly Neural Networks (NNs), into NMPC to reduce the computational load is an emerging strategy. However, embedding NN surrogates in NMPC, in a form amenable to simultaneous solution approaches, remains unresolved.
This thesis aims to address two major NMPC implementation issues. First, this work analyses the combined impact of uncertainty and state estimation on the performance of NMPC on large-scale systems. Two scenario-based robust approaches to NMPC, multi-scenario NMPC (MSc-NMPC) and multi-stage NMPC (MS-NMPC), are implemented on the benchmark Tennessee-Eastman (TE) process in closed-loop using two standard state estimation algorithms, Extended Kalman Filter (EKF) and Moving Horizon Estimation (MHE). Robust NMPC with MHE is shown to prevent constraint violation while closely tracking the set-points under process uncertainty where traditional NMPC failed. The additional computational time required to solve the robust NMPC and MHE does not cause significant delays for the sampling time considered, demonstrating their applicability to challenging large-scale industrial chemical and manufacturing processes.
This work also aims to benchmark various strategies for embedding NN surrogates in NMPC. One strategy embeds NN models as explicit algebraic constraints within the optimization framework, leveraging the auto differentiation (AD) of algebraic modelling languages (AMLs) to evaluate the derivatives. Alternatively, the surrogate can be evaluated externally from the optimization framework, using the efficient AD of ML environments. Physics-informed NNs (PINNs) and Physics-informed Convolutional NNs (PICNNs) are used as NN surrogates due to their ability to maintain fidelity to fundamental physics laws while reducing the need for historical/process data. The study reveals that replacing mechanistic models with NN surrogates may not always offer computational advantages, even with highly nonlinear systems. Smooth activation functions provide little to no advantage over the mechanistic equations when a local non-linear program (NLP) solver is used. Moreover, the external evaluation of the NN surrogates often outperforms the embedding as algebraic constraints, likely due, to the difficulty in initializing the auxiliary variables and constraints introduced with the explicit algebraic reformulations.
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Keywords
robust NMPC, plant-model mismatch, state estimation, physic-informed neural networks, partial differential equations, deep learning