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Many chemical engineering applications, such as safety verification and parameter estimation, require global optimization of dynamic models. Global optimization algorithms typically require obtaining global bounding information of the dynamic system, to aid in locating and verifying the global optimum. The typical approach for providing these bounds is to generate convex relaxations of the dynamic system and minimize them using a local optimization solver. Tighter convex relaxations typically lead to tighter lower bounds, so that the number of iterations in global optimization algorithms can be reduced. To carry out this local optimization efficiently, subgradient-based solvers require gradients or subgradients to be furnished. Smooth convex relaxations would aid local optimization even more. To address these issues and improve the computational performance of global dynamic optimization, this thesis proposes several novel formulations for constructing tight convex relaxations of dynamic systems. In some cases, these relaxations are smooth. Firstly, a new strategy is developed to generate convex relaxations of implicit functions, under minimal assumptions. These convex relaxations are described by parametric programs whose constraints are convex relaxations of the residual function. Compared with established methods for relaxing implicit functions, this new approach does not assume uniqueness of the implicit function and does not require the original residual function to be factorable. This new strategy was demonstrated to construct tighter convex relaxations in multiple numerical examples. Moreover, this new convex relaxation strategy extends to inverse functions, feasible-set mappings in constraint satisfaction problems, as well as parametric ordinary differential equations (ODEs). Using a proof-of-concept implementation in Julia, numerical examples are presented to illustrate the convex relaxations produced for various implicit functions and optimal-value functions. In certain cases, these convex relaxations are tighter than those generated with existing methods. Secondly, a novel optimization-based framework is introduced for computing time-varying interval bounds for ODEs. Such interval bounds are useful for constructing convex relaxations of ODEs, and tighter interval bounds typically translate into tighter convex relaxations. This framework includes several established bounding approaches, but also includes many new approaches. Some of these new methods can generate tighter interval bounds than established methods, which are potentially helpful for constructing tighter convex relaxations of ODEs. Several of these approaches have been implemented in Julia. Thirdly, a new approach is developed to improve a state-of-the-art ODE relaxation method and generate tighter and smooth convex relaxations. Unlike state-of-the-art methods, the auxiliary ODEs used in these new methods for computing convex relaxations have continuous right-hand side functions. Such continuity not only makes the new methods easier to implement, but also permits the evaluation of the subgradients of convex relaxations. Under some additional assumptions, differentiable convex relaxations can be constructed. Besides that, it is demonstrated that the new convex relaxations are at least as tight as state-of-the-art methods, which benefits global dynamic optimization. This approach has been implemented in Julia, and numerical examples are presented. Lastly, a new approach is proposed for generating a guaranteed lower bound for the optimal solution value of a nonconvex optimal control problem (OCP). This lower bound is obtained by constructing a relaxed convex OCP that satisfies the sufficient optimality conditions of Pontryagin's Minimum Principle. Such lower bounding information is useful for optimizing the original nonconvex OCP to a global minimum using deterministic global optimization algorithms. Compared with established methods for underestimating nonconvex OCPs, this new approach constructs tighter lower bounds. Moreover, since it does not involve any numerical approximation of the control and state trajectories, it provides lower bounds that are reliable and consistent. This approach has been implemented for control-affine systems, and numerical examples are presented. Thesis Doctor of Philosophy (PhD)

As the pharmaceutical industry seeks more efficient methods for the production of higher value therapeutics, the associated data analysis, data visualization, and predictive modeling require dependable data origination, management, transfer, and integration. As a result, the management and integration of data in a consistent, organized, reliable manner is a big challenge for the pharmaceutical industry. The S88 recipe model, an international standard for describing standard batch processes, has been adapted in this study to deliver a well-defined data structure that will improve the data communication inside the system architecture for continuous processing. This work has been divided into two parts due to differing requirements between laboratory-based analytical measurements and the pilot-plant continuous pharmaceutical process. In the laboratory platform, recipes have been developed for a sub-set of material property tests that for instance, could be performed on the analytical instrument (e.g. FT4 for flow). Drupal, an open source content management system, is implemented on an Amazon web service for data transfer between the analytical devices eventually a data management platform. A recipe module for Drupal is developed for recipe management, in which users could create, import, and modify recipes. Scientists can access recipes through Drupal’s web page interface and perform experiments following standard recipe steps. Research data can be recorded by manual input or automatically parsing data files on the backend of the server. This system works like a recipe based electronic laboratory notebook. In the continuous manufacturing pilot plant, process data is generated by unit operation equipment and integrated process analytical technology (PAT) instruments 1. A process control system (e.g. DeltaV (Emerson)) collects the data from equipment and a PAT data management tool (e.g. synTQ (Optimal Industrial Automation)). The PAT data management collects data from an inline/online measurement system 2. The recipe for the whole continuous process is implemented in DeltaV. Data in DeltaV is collected according to the recipe and is transferred to a data storage hub (PI system (OSI Soft)) in the same structure. The Event Frame feature from PI system allows the possibility to create an individual recipe based on continuous data feeding. From PI system, the data is sent to online data storage box and cloud system. From the box/cloud, the data can be access at different physical company sites, can be analyzed and applied for various applications. This study is the first attempt to apply ISA-88, a batch control standard, to continuous pharmaceutical manufacturing. All the detailed information of the lab-based experiment and process manufacturing, including equipment, samples and parameters are documented in the recipe. Recipes containing data can be exported from this system to be shared and transferred. After detaching the data from recipes, a reliable and consistent data source is provided for data visualization and process modeling. Another feature is the two-dimensional barcode labels that are used in this strategy. Every ingredient and equipment of the analytical experiment or manufacturing process will have a unique barcode, which can be used to identify the item and trace all the information related. This enforces material traceability, which is an essential requirement in the overall Quality by Design (QbD) initiative.