This work provides a comprehensive review of techniques for solving the discrete algebraic Riccati equation and guidance for selecting an appropriate method for various user-specified DAREs. Motivated by process control, chemical engineering practitioners are driven by safety, profit optimization, and reduced process variability. The solution to the DARE offers a way to regulate and accurately track process behavior through the linear quadratic regulator and the linear quadratic estimator. This study offers a comparison between the iterative Riccati equation (IRE), generalized real-Schur vector methods (GSV), and Newton's method as algorithms for computing the solution to the DARE. Through numerical studies, we find Newton's method struggles as a stand-alone method as it requires information on the solution a priori. For large system sizes (more than 1000 states), the IRE seems to suffer from numerical instability and the GSV severely scales with system size. We offer two switch method alternatives by utilizing Newton's method as a refinement technique on IRE iterations. The A+BK stability switch (ABKSS) prioritizes Newton's method's reliability close to the solution and switches once a stable closed-loops state transfer matrix is found via the IRE. We also pose the IRE proximity switch (IREPS), which computes the iterations to the discrete Riccati equation until iterates are sufficiently close to the stabilizing solution and refined through iterations of Newton's method. For randomly generated systems of 1000 or more states, both switch methods offer a high-accuracy alternative that surpasses the GSV in computation time and circumvents the numerical instability experienced by the IRE. Furthermore, we find that the GSV and IRE are highly susceptible to systems that are close to being unstabilizable (nearly unstable directions of state matrix or nearly zero influence in the control matrix). IREPS and ABKSS offer significant improvements for computing the solution to barely stabilizable systems. Lastly, we initiate an investigation into utilizing Newton's method for DAREs with singular R. While not as general as positive semidefinite R, we prove that Newton's method can compute the solution to DAREs with R equal to zero as a special case. The purpose of this study is to revisit methods for the DARE with modernized computation tools. We find that as we pose more challenging problems, standard algorithms for computing the solution to the DARE become unviable and require a new approach with these old tools.

The recent advances in the field of machine learning, the availability of powerful computing resources, and growing data collection capabilities across industries present new opportunities to upgrade the existing feedback control and automation methods implemented in applications. This thesis presents novel approaches and methods to use machine learning algorithms to develop feedback controllers and process models for dynamical systems. In the first half of this thesis, we develop approaches to use reinforcement learning and neural networks to design feedback controllers for multivariable systems. We develop a novel model-free Q-learning approach suitable to estimate linear, unconstrained feedback controllers from noisy process data. We present a neural network (NN) design approach to approximate the model predictive control (MPC) feedback law for large-scale applications that may be out of reach with available QP solvers. The proposed NN design approach is applied to a large industrial crude distillation unit model, and we demonstrate that NNs can be used to execute MPC orders of magnitude faster compared to an available QP solver.

The next half of this thesis focuses on developing hybrid model identification approaches that utilize both the advantages of neural networks and some first principles process knowledge usually available in applications. We consider building systems affected by large occupancy induced heat disturbances. For these systems, we develop a novel two step grey-box dynamic and NN disturbance model identification framework. We use a NN to model the heat disturbance so that it can be used to provide feedforward predictions of the disturbance in an MPC controller for improved energy cost optimization. We also present a hybrid modeling approach for nonlinear chemical engineering processes. For this class of systems, we use NNs to approximate some functions in the overall dynamic model, e.g, reaction kinetics, which may be challenging to parameterize using the available domain knowledge. The estimated hybrid models are used for steady-state economic optimization at the real time optimization layer. Throughout this thesis, we present examples with heating, ventilation, and air-conditioning and chemical engineering systems to demonstrate the effectiveness of the proposed controller design and process modeling methods. We compare the proposed methods with existing approaches and illustrate their potential to design high-performance control systems.

Uncertainty is inherent to all science and engineering models. Any algorithm proposed to design, schedule, or control an industrial process must therefore be robust, i.e., the algorithm must be able to withstand and overcome this uncertainty. In this dissertation, we focus specifically on model predictive control (MPC), the advanced control algorithm of choice for chemical process control with a growing list of applications in several other engineering disciplines as well. For deterministic descriptions of this uncertainty, MPC is known to be robust to sufficiently small disturbances. This robustness is afforded by feedback and does not require any characterization of this uncertainty within the control algorithm.

Stochastic descriptions of uncertainty, however, are often better suited to model the behavior of physical systems and have proven highly useful in a variety of science and engineering applications. To that end, we expand the theory of robustness for MPC to address these stochastic descriptions of uncertainty and establish that MPC is robust in this stochastic context. We then apply this theory to the emerging field of stochastic MPC (SMPC), in which a stochastic model of this uncertainty is used directly in the control algorithm. Through the concept of distributional robustness, we further establish that SMPC is robust to uncertainty within even the stochastic model used in the control algorithm. This result in fact unifies the analysis of both MPC and SMPC, thereby allowing a novel comparison of the theoretical properties afforded by these two algorithms. We also demonstrate via suitable examples that including stochastic information in a control algorithm is not always beneficial to the controller's performance. In the second part of this dissertation, we consider the stochastic robustness of MPC to a new class of large and infrequent disturbances, motivated by recent applications of MPC to production planning and scheduling problems. Using these results and the MPC framework, we then design a closed-loop scheduling algorithm that is robust to the large and infrequent disturbances pertinent to production scheduling problems. This algorithm is further modified to address computational and practical limitations and is therefore suitable for large-scale production scheduling applications.

An out-of-the-box model predictive control (MPC) algorithm, or a “turnkey” model predictive controller has long been a dream of both academics and practitioners. MPC practice currently includes time-consuming and ad hoc tuning steps to achieve adequate performance in the face of persistent disturbances and plant-model mismatch. In this dissertation, we present progress towards developing a turnkey model predictive controller by developing identification methods suitable for out-of-the-box MPC implementations, applying those identification methods to the offset-free control of real-world systems, and developing the theory of the stability of MPC under plant-model mismatch.

In the first part of this dissertation, we propose algorithms for identifying plant and disturbance models. Maximum likelihood (ML) estimation methods are applied directly and in a nested fashion to identify complete plant and disturbance models. For the direct methods, high-level design constraints are imposed on the resulting offset-free controller through eigenvalue constraints on the modeled system matrices. For the nested methods, we present simple algorithms with closed-form solutions that can easily be implemented by practitioners.

In the second part of this dissertation, we apply identification methods to the offset- free control of two real-world systems: a benchmark temperature controller (TCLab), and an industrial-scale chemical reactor. Both case studies showcase the ability of the identification algorithms to produce models adequate for out-of-the-box MPC designs with guaranteed offset-free performance. The industrial application also demonstrates an outsize real-world benefit for adopting a turnkey approach, where we report a 38% improvement in setpoint tracking performance compared to an existing hand-tuned controller.

In the third and final part of this dissertation, we investigate the theoretical properties of offset-free MPC subject to plant-model mismatch. We first investigate the offset-free performance of linear offset-free MPC for control of nonlinear plants. We then investigate stability of standard MPC under mismatch when the plant and model steady states are fixed and aligned. Finally, we investigate the offset-free performance of nonlinear offset-free MPC, with and without plant-model mismatch.