arXiv subjects

Richard D. Braatz

Publications and source records attributed to Richard D. Braatz.

At least 19 recordsLinked to original sources

arXiv2026

Physics-Informed Neural Network Surrogates with Polynomial Chaos-Based Uncertainty Propagation for Stochastic Model Predictive Control

Stochastic partial differential equations (PDEs) govern critical engineering and geophysical systems but are challenging to use for real-time control under parametric uncertainty. We present a unified framework that couples Physics-Informed Neural Networks (PINNs) with Polynomial Chaos Expansion (PCE) to construct a fast and differentiable surrogate. The PCE representation enables analytical propagation of parametric uncertainty and computation of the corresponding moments without requiring Monte Carlo sampling. We provide an error decomposition for the PINN-PCE surrogate that separates PCE truncation, stochastic quadrature, and PINN approximation errors. Embedding this surrogate into a stochastic model predictive control (SMPC) scheme enables finite-horizon control updates based on analytic mean and covariance predictions. We further show how the surrogate approximation error can be incorporated into tightened probabilistic constraints. The approach is validated on three benchmarks: the Korteweg-de Vries equation, Burgers' equation, and the two-dimensional incompressible Navier-Stokes equations, representing dispersive, convective, and convective-diffusive dynamics. Across all cases, the surrogate enables real-time control updates while maintaining prescribed risk levels and closely matching the corresponding high-fidelity solvers at substantially lower computational cost.

eess.SY↗

arXiv2026

Integrated Population Balance and Multiphysics Modeling for Predicting Undesired Agglomeration in Small Molecule Manufacturing

Agitated filter dryers (AFDs) are a crucial unit operation in small molecule manufacturing that enables simultaneous filtration, washing, and drying of active pharmaceutical ingredients. One of the key challenges in AFDs is associated with undesired agglomeration, where the presence of hard agglomerates results in off-spec products, equipment damage, and additional downstream processing. This article presents a novel mechanistic model that describes the formation of soft and hard agglomerates during agitated filter drying. By integrating population balance and multiphysics modeling, the model can accurately predict the evolution of the product temperature, moisture content, and particle size distribution, and hence quantify the extend and impact of undesired agglomeration across various operating conditions. Our proposed model-based framework enables the rational design and operation of AFDs for improving the product quality and process reliability.

cs.CE↗

arXiv2026

Nonadaptive Learning in Robust Nonlinear Output Regulation

This paper considers robust nonadaptive regulation for general nonlinear systems in an output-feedback setting with arbitrarily high relative degree. We develop a nonadaptive design that combines an input-driven filter and a generic internal model with a recursive backstepping law, thereby recasting the regulation problem as the robust input-to-state stabilization of an augmented error system. Unlike adaptive schemes, the proposed method does not rely on linearly parameterized regressors and does not require the construction of Lyapunov functions having merely nonpositive derivatives. Under standard assumptions on the exosystem, including purely imaginary and simple eigenvalues, together with a minimum-phase input-to-state stability condition on the internal dynamics, we establish global asymptotic regulation and derive explicit, verifiable inequalities for selecting the design gains. The resulting nonadaptive framework guarantees convergence of the estimation and tracking errors even when the controlled-system dynamics are complex or only partially known. The effectiveness of the theoretical results is demonstrated using a benchmark controlled Duffing system.

eess.SY↗

arXiv2026

Nonparametric Steady-State Learning for Nonlinear Output Feedback Regulation

This article addresses the nonparametric and robust output regulation problem of the general nonlinear output feedback system with error output. The global robust output regulation problem for a class of general output feedback nonlinear systems with an uncertain exosystem and high relative degree can be tackled by constructing a linear generic internal model, provided that a continuous nonlinear mapping exists. Leveraging the proposed nonadaptive framework facilitates the conversion of the nonlinear robust output regulation problem into a robust nonadaptive stabilization formulation for the augmented system endowed with Input-to-State Stable dynamics. This approach removes the need for constructing a specific Lyapunov function with positive semidefinite derivatives and avoids the common assumption of linear parameterization of the nonlinear system. The nonadaptive approach is extended by incorporating the nonparametric learning framework to ensure the feasibility of the nonlinear mapping, which can be tackled using a data-driven method. Moreover, the introduced nonparametric learning framework allows the controlled system to learn the dynamics of the steady-state input behavior from the signal generated from the internal model with the output error as the feedback. As a result, the nonparametric approach can be advantageous to guarantee the convergence of the estimation and tracking error even when the underlying controlled system dynamics are complex or poorly understood. The effectiveness of the theoretical results is illustrated for three practical examples: regulation of a magnetic levitation system, regulation of a virtual synchronous generator, and heading control of a surface vessel.

eess.SY↗

arXiv2026

Polynomial Chaos-based Stochastic Model Predictive Control: An Overview and Future Research Directions

This article is devoted to providing a review of mathematical formulations in which Polynomial Chaos Theory (PCT) has been incorporated into stochastic model predictive control (SMPC). In the past decade, PCT has been shown to provide a computationally tractable way to perform complete and accurate uncertainty propagation through (smooth) nonlinear dynamic systems. As such, it represents a very useful computational tool for accelerating the computations needed in SMPC with time invariant uncertainties. It turns out that it can also be used to reduce complexity of chance constraints, which are an important component of SMPC. In this paper, we provide an overview of PCT and discuss how it can be applied in such time invariant settings.

eess.SY↗

arXiv2026

GlycoPy: A CasADi-based Python Framework for Hierarchical Modeling, Optimization, and Control of Bioprocesses

Efficient implementation of nonlinear model predictive control (NMPC) for bioprocesses remains challenging because large nonlinear models are difficult to organize, simulate, and embed within optimization and control workflows. This difficulty is particularly pronounced for large-scale and multiscale systems that require hierarchical model construction and customized simulation strategies. To address this issue, we present GlycoPy, a CasADi-based Python framework for hierarchical modeling, optimization, and control of bioprocesses. GlycoPy combines an equation-oriented, object-oriented modeling architecture with CasADi's symbolic and differentiable computational capabilities, enabling hierarchical model composition, numerical and symbolic simulation, parameter estimation, dynamic optimization, and NMPC within a unified workflow. A key feature of the framework is its support for customized differentiable simulation algorithms that can be embedded directly in gradient-based optimization and control. GlycoPy is demonstrated on a multiscale monoclonal antibody glycosylation process in Chinese hamster ovary cell culture, where it is used for hierarchical model construction, quasi-steady-state simulation, and adaptive NMPC. The results show that GlycoPy provides a practical and reusable framework for applying advanced optimization and control methods to computationally demanding bioprocesses.

cs.SE↗

arXiv2026

Improving Performance in Classification Tasks with LCEN and the Weighted Focal Differentiable MCC Loss

The LASSO-Clip-EN (LCEN) algorithm was previously introduced for nonlinear, interpretable feature selection and machine learning. However, its design and use was limited to regression tasks. In this work, we create a modified version of the LCEN algorithm that is suitable for classification tasks and maintains its desirable properties, such as interpretability. This modified LCEN algorithm is evaluated on four widely used binary and multiclass classification datasets. In these experiments, LCEN is compared against 10 other model types and consistently reaches high test-set macro F$_1$ score and Matthews correlation coefficient (MCC) metrics, higher than that of the majority of investigated models. LCEN models for classification remain sparse, eliminating an average of 56% of all input features in the experiments performed. Furthermore, LCEN-selected features are used to retrain all models using the same data, leading to statistically significant performance improvements in three of the experiments and insignificant differences in the fourth when compared to using all features or other feature selection methods. Simultaneously, the weighted focal differentiable MCC (diffMCC) loss function is evaluated on the same datasets. Models trained with the diffMCC loss function are always the best-performing methods in these experiments, and reach test-set macro F$_1$ scores that are, on average, 4.9% higher and MCCs that are 8.5% higher than those obtained by models trained with the weighted cross-entropy loss. These results highlight the performance of LCEN as a feature selection and machine learning algorithm also for classification tasks, and how the diffMCC loss function can train very accurate models, surpassing the weighted cross-entropy loss in the tasks investigated.

cs.LG↗

arXiv2026

Fixed-time-stable ODE Representation of Lasso

Lasso problems arise in many areas, including signal processing, machine learning, and control, and are closely connected to sparse coding mechanisms observed in neuroscience. A continuous-time ordinary differential equation (ODE) representation of the Lasso problem not only enables its solution on analog computers but also provides a framework for interpreting neurophysiological phenomena. This article proposes a fixed-time-stable ODE representation of the Lasso problem by first transforming it into a smooth nonnegative quadratic program (QP) and then designing a projection-free Newton-based ODE representation of the Lasso problem by first transforming it into a smooth nonnegative quadratic program (QP) and then designing a projection-free Newton-based fixed-time-stable ODE system for solving the corresponding Karush-Kuhn-Tucker (KKT) conditions. Moreover, the settling time of the ODE is independent of the problem data and can be arbitrarily prescribed. Numerical experiments verify that the trajectory reaches the optimal solution within the prescribed time.

math.OC↗

arXiv2026

Polynomial Parametric Koopman Operators for Stochastic MPC

This paper develops a parametric Koopman operator framework for Stochastic Model Predictive Control (SMPC), where the Koopman operator is parametrized by Polynomial Chaos Expansions (PCEs). The model is learned from data using the Extended Dynamic Mode Decomposition -- Dictionary Learning (EDMD-DL) method, which preserves the convex least-squares structure for the PCE coefficients of the EDMD matrix. Unlike conventional stochastic Galerkin projection approaches, we derive a condensed deterministic reformulation of the SMPC problem whose dimension scales only with the control horizon and input dimension, and is independent of both the lifted state dimension and the number of retained PCE terms. Our framework, therefore, enables efficient nonlinear SMPC problems with expectation and second-order moment constraints with standard convex optimization solvers. Numerical examples demonstrate the efficacy of our framework for uncertainty-aware SMPC of nonlinear systems.

eess.SY↗

arXiv2026

LQR for Systems with Probabilistic Parametric Uncertainties: A Gradient Method

A gradient-based method is proposed for solving the linear quadratic regulator (LQR) problem for linear systems with nonlinear dependence on time-invariant probabilistic parametric uncertainties. The approach explicitly accounts for model uncertainty and ensures robust performance. By leveraging polynomial chaos theory (PCT) in conjunction with policy optimization techniques, the original stochastic system is lifted into a high-dimensional linear time-invariant (LTI) system with structured state-feedback control. A first-order gradient descent algorithm is then developed to directly optimize the structured feedback gain and iteratively minimize the LQR cost. We rigorously establish linear convergence of the gradient descent algorithm and show that the PCT-based approximation error decays algebraically at a rate $O(N^{-p})$ for any positive integer $p$, where $N$ denotes the order of the polynomials. Numerical examples demonstrate that the proposed method achieves significantly higher computational efficiency than conventional bilinear matrix inequality (BMI)-based approaches.

eess.SY↗

arXiv2026

A Lego Block Approach to Flow in Complex Microfluidic Networks

We present a new way to construct analytical solutions for flow in complex microfluidic channel networks, as well as planar disordered media. Using a combination of Schwarz-Christoffel maps and segmentation techniques inspired by integrated circuit analysis, we build a library of base building blocks which can be reassembled to model complex geometries, in the style of ``Lego Blocks''. Our approach requires minimal numerical computation, and can then generate analytical solutions for any combination of inlet and outlet flow rates. Moreover, our method can tackle multiply connected domains which are usually difficult to model using typical conformal transform approaches. The solutions are developed for microfluidic Hele-Shaw cell devices, but also apply to ideal flow and Darcy flow in complex geometries, or any other flow problem adequately modeled by Laplace's equation. We end by showing how the procedure can be used to model complex disordered media, fractal-like flow geometries, as well as problems of steady advection-diffusion in microfluidic mixers.

physics.flu-dyn↗

arXiv2026

Koopman-BoxQP: Solving Large-Scale NMPC at kHz Rates

Solving large-scale nonlinear model predictive control (NMPC) problems at kilohertz (kHz) rates on standard processors remains a formidable challenge. This paper proposes a Koopman-BoxQP framework that i) learns a linear Koopman high-dimensional model, ii) eliminates the high-dimensional observables to construct a multi-step prediction model of the states and control inputs, iii) penalizes the multi-step prediction model into the objective, which results in a structured box-constrained quadratic program (BoxQP) whose decision variables include both the system states and control inputs, iv) develops a structure-exploited and warm-starting-supported variant of the feasible Mehrotra's interior-point algorithm for BoxQP. Numerical results demonstrate that Koopman-BoxQP can solve a large-scale NMPC problem with $1040$ variables and $2080$ inequalities at a kHz rate.

eess.SY↗

arXiv2026

Least-Squares Multi-Step Koopman Operator Learning for Model Predictive Control

MPC is widely used in real-time applications, but practical implementations are typically restricted to convex QP formulations to ensure fast and certified execution. Koopman-based MPC enables QP-based control of nonlinear systems by lifting the dynamics to a higher-dimensional linear representation. However, existing approaches rely on single-step EDMD. Consequently, prediction errors may accumulate over long horizons when the EDMD operator is applied recursively. Moreover, the multi-step prediction loss is nonconvex with respect to the single-step EDMD operator, making long-horizon model identification particularly challenging. This paper proposes a multi-step EDMD framework that directly learns the condensed multi-step state-control mapping required for Koopman-MPC, thereby bypassing explicit identification of the lifted system matrices and subsequent model condensation. The resulting identification problem admits a convex least-squares formulation. We further show that the problem decomposes across prediction horizons and state coordinates, enabling parallel computation and row-wise $\ell_1$-regularization for automatic dictionary pruning. A non-asymptotic finite-sample analysis demonstrates that, unlike one-step EDMD, the proposed method avoids error compounding and yields error bounds that depend only on the target multi-step mapping. Numerical examples validate improved long-horizon prediction accuracy and closed-loop performance.

eess.SY↗

arXiv2025

Mechanistic Modeling of Continuous Lyophilization for Biopharmaceutical Manufacturing

Lyophilization (aka freeze drying) is a typical process in pharmaceutical manufacturing used for improving the stability of various drug products, including its recent applications to mRNA vaccines. While extensive efforts have been dedicated to shifting the pharmaceutical industry toward continuous manufacturing, the majority of industrial-scale lyophilization is still being operated in a batch mode. This article presents the first mechanistic model for a complete continuous lyophilization process, which comprehensively incorporates and describes key transport phenomena in all three steps of lyophilization, namely freezing, primary drying, and secondary drying. The proposed model considers the state-of-the-art lyophilization technology, in which vials are suspended and move continuously through the process. The validated model can accurately predict the evolution of critical process parameters, including the product temperature, ice/water fraction, sublimation front position, and concentration of bound water, for the entire process. Several applications related to model-based process design and optimization of continuous lyophilization are also demonstrated. The final model is made available in MATLAB and Julia as an open-source software package called ContLyo, which can ultimately be leveraged for guiding the design and development of future continuous lyophilization processes.

cs.CE↗

arXiv2025

LCEN: A Nonlinear, Interpretable Feature Selection and Machine Learning Algorithm

Interpretable models can have advantages over black-box models, and interpretability is essential for the application of machine learning in critical settings, such as aviation or medicine. This article introduces the LASSO-Clip-EN (LCEN) algorithm for nonlinear, interpretable feature selection and machine learning modeling. In a wide variety of artificial and empirical datasets, LCEN constructed sparse and frequently more accurate models than other methods, including sparse, nonlinear methods, on tested datasets. LCEN was empirically observed to be robust against many issues typically present in datasets and modeling, including noise, multicollinearity, and data scarcity. As a feature selection algorithm, LCEN matched or surpassed the thresholded elastic net but was, on average, 10.3-fold faster based on our experiments. LCEN for feature selection can also rediscover multiple physical laws from empirical data. As a machine learning algorithm, when tested on processes with no known physical laws, LCEN achieved better results than many other dense and sparse methods -- including being comparable to or better than ANNs on multiple datasets.

cs.LG↗

arXiv2025

Arbitrarily Small Execution-Time Certificate: What was Missed in Analog Optimization

Numerical optimization (solving optimization problems using digital computers) currently dominates but has three major drawbacks: high energy consumption, poor scalability, and lack of an execution time certificate. To address these challenges, this article explores the recent resurgence of analog computers, proposing a novel paradigm of arbitrarily small execution-time-certified analog optimization (solving optimization problems via analog computers). To achieve ultra-low energy consumption, this paradigm transforms optimization problems into ordinary differential equations (ODEs) and leverages the ability of analog computers to naturally solve ODEs (no need for time discretization) in physically real time. However, this transformation can fail if the optimization problem, such as the general convex nonlinear programs (NLPs) considered in this article, has no feasible solution. To avoid transformation failure and enable infeasibility detection, we introduce the homogeneous monotone complementarity problem formulation for convex NLPs. To achieve scalability and an execution time certificate, this paper introduces the Newton-based fixed-time-stable scheme for the transformed ODE, whose settling time $T_p$ can be prescribed by choosing the ODE's time coefficient as $k=\fracπ{2T_p}$. This equation certifies that the settling time (execution time) is independent of the dimension of the optimization problems and can be arbitrarily small if the analog computer allows.

math.OC↗

arXiv2025

Adaptive Nonlinear Model Predictive Control of Monoclonal Antibody Glycosylation in CHO Cell Culture

N-glycosylation is a critical quality attribute of monoclonal antibodies (mAbs), the dominant class of biopharmaceuticals. Controlling glycosylation remains difficult due to intrinsic pathway complexity, limited online measurements, and a lack of tailored control strategies. This work applies an adaptive nonlinear model predictive control (ANMPC) framework to a fed-batch mAb production process, using a multiscale model that links extracellular conditions to intracellular Golgi reactions to predict glycan profiles. Model parameters are updated online as new measurements arrive, after which a shrinking-horizon optimization computes the control inputs; only the first control move is implemented each cycle. Case studies show that, with a minimal day-1 galactose excitation, ANMPC mitigates model-plant mismatch and achieves up to 130% and 96% higher performance than open-loop optimization and state NMPC, respectively. Under more realistic conditions (partial measurement availability and longer preparation time), ANMPC maintains comparable performance, indicating robustness to practical limitations. Overall, the results demonstrate that ANMPC can actively shape glycan distributions in silico and offers a viable path toward closed-loop control of mAb glycosylation.

math.OC↗

arXiv2025

Advanced Characterization Methods for Crystals of an Extraordinary Material

Physicochemical characterization of materials is central to the field of science and engineering and is essential to design new/engineered materials with specific properties. Assays available for small-molecules, e.g., XRD, NMR, LC-MS, can't be applied to macromolecules easily. Thus, it is extremely challenging to characterize complex materials such as adeno-associated virus capsids (MW 5.8MDa). Capsid crystals produced in hanging-drop are characterized in-situ using cross-polarized light and ex-situ using scanning electron microscopy, energy dispersive X-ray, and transmission electron microscopy. Cross-polarized light can be used to identify capsid crystals within a heterogenous-system of kosmotropic/chaotropic-salt crystals, fibers, dense solid-phase, opaques crystals. Despite highly-conserved structures, crystal birefringence suggests that capsids possess serotype-specific structural differences. SEM demonstrated that crystal-growth occurs by random 2D-nucleation followed by kink-site attachment and/or spread by more 2D-nuclei and proteinaceous assemblies tend to form semi-crystalline solids appearing as dense/opaque materials. EDX shows that C, O, and N are present in ratio of 2.33+-0.222:1:0.583+-0.019 for serotypes 5, 8, and 9 and can be an alternative to protein sequencing-based virus identification. Biological macromolecular assemblies are found to facilitate plural-scattering responsible for Kikuchi-diffraction pattern even for thin-crystals (~300nm). For an optimal spot-diffraction, crystals must possess at least one dimension consisting of at most 8 layers of capsids.

physics.chem-ph↗