As the complexity and scale of chemical processes has increased, engineers have desired a process control strategy that can successfully and safely regulate modern processes. These processes are often subject to random noise and uncertainties in parameters or model structure which make regulation and control difficult. Stochastic model predictive control (SMPC) is an advanced process control strategy that can systematically seek tradeoffs between multiple (possibly competing) control objectives in the presence of constraints for multi-input multi-output systems. Furthermore, SMPC explicitly considers the stochasticity of system states and parameters, allowing for the systematic trade off of robustness and performance. Another key advantage of SMPC is the ability to implement chance constraints, which can be violated with a specified probability, instead of hard constraints which must be satisfied in all conditions. Because SMPC employs a probabilistic description of states and parameters, uncertainty propagation techniques are needed to determine the time evolution of these probability distributions. Monte Carlo methods are a widely used uncertainty propagation technique, but are too computationally expensive for real time optimization and control. Three approaches to efficient SMPC implementations are investigated in this dissertation. A SMPC algorithm with hard input constraints and joint chance constraints in the presence of (possibly) unbounded noise is presented. By recasting the nonlinear SMPC optimal control problem as a convex iterative deterministic program, the computational cost of determining the optimal control policy is significantly decreased. Two uncertainty propagation methods, the Fokker-Planck equation and adaptive polynomial chaos, are presented in the context of optimal control. The Fokker-Planck equation is a partial differential equation that can propagate the full probability distribution of uncertainties. This allows for shaping of the probability distribution function of states to desired distributions in an open loop sense as well as eliminating the need for conservative approximations when evaluating chance constraint violation. Closed-loop simulations of a SMPC controller regulating a bioreactor demonstrate the ability to shape the product probability distribution function when using the Fokker-Planck equation as an uncertainty propagation technique. Adaptive polynomial chaos (aPC) is an efficient technique that propagates the moments of (possibly) cross-correlated distributions. Unlike similar techniques, aPC only requires knowledge of the statistical moments of uncertain states and parameters, which can be readily estimated from experimental data. The error convergence properties of aPC are investigated in a continuous stirred tank reactor (CSTR) with correlated reaction kinetic parameters. All three approaches to uncertainty propagation and constraint handling in the context of SMPC discussed in this dissertation demonstrate promise for decreasing computational cost and reducing reliance on conservative approximations.

Low temperature plasma (LTP) assisted processes are receiving increasing attention for nitrogen fixation due to its more sustainable nature, as well as its lower theoretical energy cost compared to the predominant Haber-Bosch (H-B) process. The H-B process operates under high temperature and pressure, and generates a significant amount of greenhouse gases. However, a major barrier to practical implementation of LTP-assisted nitrogen fixation is the limited understanding of the underlying physics of plasma interactions with complex interfaces such as catalyst, which results in actual energy costs that are still far from its favorable theoretical limit. The complexity exacerbates further when catalysts are involved, as they are shown to reduce energy costs but also add another layer of complexity due to LTP-catalyst interactions. This dissertation aims to develop and apply data-driven techniques to deepen the understanding of LTP processes and LTP-catalyst interactions towards sustainable nitrogen fixation. The research presented in this dissertation can be summarized into three main contributions as follows.

The first contribution revolves around employing data-driven optimization methods to efficiently navigate the operating parameter space of a direct-current pin-to-pin plasma nitrogen fixation process towards minimizing the energy cost of NO$_\text{x}$ production. We observed that Bayesian optimization (BO) methods can significantly outperform random search of high-dimensional process parameter spaces, especially under the existence of process constraints. The resulting optimal process parameters were corroborated experimentally and via global sensitivity analyses, underscoring the effectiveness of data-driven optimization methods for LTP processes.

The second contribution of this dissertation investigates the impact of electric field effect on LTP-catalyst interactions within a dielectric barrier discharge for ammonia synthesis. Generally, LTP-catalysis interactions are overlooked in microkinetic modeling of LTP-catalytic processes due to underdeveloped theory of LTP-catalyst interactions. This research introduced a novel computational framework by integrating density functional theory (DFT) into microkinetic modeling to account for the effects of electric field. Our findings revealed that variation in the electric field can significantly alter the reaction pathway to NH$_3$, highlighting the critical importance of including electric field effects in modeling LTP-catalytic processes. Additionally, we systematically quantified the contribution of LTP process parameters to NH$_3$ production. We observed that the proposed integrated DFT-microkinetic model aligns more closely with experimental observations by more accurately accounting for the electric field's contribution, and also correcting the disproportionately high N$_2$ inlet ratio found in models without LTP-catalyst interactions. Lastly, we applied multi-objective BO to establish the trade-off between reactions responsible for NH$_3$ production and energy dissipation, illustrating the power of data-driven optimization methods in addressing the complexities of LTP-catalytic processes, where minor adjustments in operating parameters can lead to significant variations in process outcomes.

The third and final contribution of this dissertation explores how insights from thermal catalysis can be applied to LTP catalysis, particularly focusing on the surface charge effects in an Al$_2$O$_3$-single metal atom-adsorbate system. This approach is crucial for developing a more detailed plasma-catalyst interaction model. We utilized advanced data-driven models, specifically attention-based graph neural networks, to facilitate this transfer of knowledge. By employing transfer learning, we demonstrated that the extensive database from thermal catalysis, which includes millions of DFT calculations across various metal catalysts and adsorbates, can greatly enhance the LTP catalysis model. This transferred model not only incorporates knowledge from thermal catalysis, but also retains the capability to extrapolate to metals not present in the LTP catalysis dataset yet covered in thermal catalysis data. This work highlighted the value of thermal catalysis insights in developing models for LTP catalysis. Additionally, the attention mechanism within the model revealed strong correlations between the learned attention scores and the surface charge distributions, identifying key atoms that are critical to the adsorbate in LTP catalysis. This capability presents potential opportunities for guiding LTP catalyst design and screening processes. Furthermore, the transfer learning approach allows for utilizing the abundant, low-fidelity data from single atom systems to construct better data-driven models for more complex Al$_2$O$_3$-metal cluster-adsorbate systems. This advance underscores the potential of leveraging existing knowledge and data to enhance the understanding and development of LTP catalysis.

In summary, this dissertation advances the application of data-driven methods in studying LTP processes for nitrogen fixation, tackling significant challenges associated with limited understanding of LTP-catalyst interactions, as well as data scarcity in LTP catalysis. There is ample potential for future research to expand upon this work by incorporating additional LTP-catalyst interactions and employing data-driven techniques to investigate the collective effects of these interactions. Moreover, the attention mechanism offers substantial prospects for further research. These opportunities include refining plasma-catalyst interaction models using LTP process data and investigating how the attention mechanism can enhance catalyst design and screening by focusing on critical atoms identified in LTP catalysis.

Atmospheric Pressure Plasma Jets (APPJs) are versatile tools for materials processing and medical applications. A key objective for APPJ treatment is the delivery of cumulative and spatially distributed treatment effects, i.e., a plasma dose. However, variability in APPJ operation and their sensitivity to exogenous disturbances can compromise reliable treatment. Particularly, for medical applications, it is necessary to ensure that APPJ effects are delivered safely and repeatably. Feedback control strategies can be crucial in ensuring the APPJ effects are regulated and maintained below critical limits instantaneously and cumulatively.

The APPJ dynamics are nonlinear, multivariable and coupled across multiple timescales. Moreover, the dose delivery problem is spatially distributed. This presents a significant challenge for regulation of APPJ characteristics with basic control strategies based on proportional-integral type controllers. Optimization-based advanced control strategies, such as model predictive control, can systematically account for the APPJ dynamics and the complexities of the dose delivery problem. This work experimentally demonstrates the use of advanced control strategies for regulation of APPJ effects and dose delivery in the presence of common disturbances, including variations in substrate characteristics and changes in jet-tip-to-substrate separation distance. In particular, the thermal effects of the APPJ on treated substrate and thermal dose delivery is investigated. An experimental setup of a kHz-excited APPJ in He is constructed to allow implementation of control algorithms. The key issues of modeling, problem formulation, and control synthesis are undertaken for the development of control strategies.

Development of control-oriented models of APPJs, which describe the dynamic response of controlled outputs to manipulated variables, are required for model-based control strategies. A lumped-parameter physics-based model is developed to describe dynamics of power dissipation in the APPJ and the consequent thermal effects on treated substrates. A fluid model of the transport phenomena in the APPJ in COMSOL informs the structure of the lumped-parameter model, which take the form of a set of differential-algebraic equations. The lumped-parameter model is found to adequately describe the experimentally observed APPJ dynamics despite its simplicity. Moreover, a linear data-driven modeling strategy is shown to be a viable alternative in describing the aspects of APPJ operation that are difficult to model based on physics, albeit for a limited range of operating conditions.

Experimental investigation reveals that basic proportional-integral (PI) strategies tuned using internal model control rules allow rejection of a range of disturbances in a single-input-single-output setting. However, basic control strategies are found to be ineffective in simultaneous control of multiple APPJ effects and for dose delivery. In contrast, MPC strategies are shown to be capable of systematically addressing the multi-variable APPJ dynamics as well as the cumulative nature of the dose delivery problem. With MPC strategies simultaneous regulation of multiple APPJ effects as well as the delivery of a point-wise multi-component dose is made possible in the presence of disturbances. For spatially uniform dose delivery, a hierarchical control strategy is developed. Lower-level basic controllers are found to allow disturbance rejection in fast timescales. On the other hand, the MPC framework allows systematically addressing the different aspects of the dose delivery problem, including the total treatment time, spatially distributed APPJ effects, the multivariable system dynamics, and the translation trajectory of the APPJ over the treated substrate.

Results presented in this work indicate that advanced feedback control strategies are crucial in enabling reliable and reproducible operation of APPJs, particularly in medical applications where safety considerations are stringent and high performance operation is required. The effective regulation of APPJ characteristics can create opportunities for new APPJ applications and the study of APPJ effects by creating controlled environments. Emerging areas for future work include the application of data analytics and machine learning methods for real-time diagnostics, modeling, and control of the complex time-varying APPJ phenomena.

Computational models have emerged as a key tool to study and characterize the behavior of biological systems. In order to accurately describe biological systems, computational models need to capture inherently complex features of biological behavior, such as nonlinear and probabilistic dynamics. Probabilistic models of biological systems can account for our lack of knowledge in model structure or parameters (uncertainty), as well as the physical sources of probabilistic behavior leading to heterogeneity.

Uncertainty quantification and optimal experiment design frameworks play a key role in the development of probabilistic models for biological systems, as they can enable system learning from informative experimental data by improving the accuracy of model structures and parameter estimates. Despite the extensive implementation of uncertainty quantification and experimental design frameworks in complex engineering systems, their application in biological systems has been lagging. This is because of their high computational cost, which can be further exacerbated when accounting for the large number of parameters and cellular constituents that characterize biological models. There is a need for computationally efficient tools that can capture complex biological properties to enable learning of biological systems in a systematic manner.

In this thesis, we present novel uncertainty quantification and optimal experiment design tools that can capture complex traits of biological behavior, namely uncertainty, heterogeneity, nonlinearities, and large numbers of parameters and cellular constituents. More specifically, we introduce novel surrogate modeling methods for fast propagation of sources of uncertainty and heterogeneity, which enable the application of uncertainty quantification and optimal experiment design tools in biological systems. Subsequently, we introduce novel Bayesian methods for the estimation of genome-scale model parameters from noisy, sparse, and incomplete biological datasets. Additionally, we introduce computationally efficient methods to design experiments that yield informative data to refine parameter estimates and model structures in an offline and online manner (i.e., in the course of an experiment). The contributions of this thesis will create new opportunities for seamless implementation of uncertainty quantification and optimal experiment design for systematic and hypothesis-based modeling in biological systems.