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Optimal control problems are prevalent in model-based control, state and parameter estimation, and experimental design for complex dynamical systems. An approach for obtaining solutions to these problems is based on the notion of parsimonious input parameterization and comprises two tasks: the enumeration of arc sequences followed by the computation of optimal values of a small number of decision variables for each sequence. This paper proposes an efficient global solution method for single-input optimal control problems for nonlinear dynamical systems with a potentially large number of states or complex dynamics via sum-of-squares polynomials and parallel computing. The method approximates the problem for a given arc sequence as a polynomial optimization problem that can be efficiently solved to global optimality via semidefinite programming. It is established that the difference between the cost obtained by the proposed method and the globally optimal cost of the original problem is bounded and depends on the polynomial approximation error. The method is illustrated by simulation examples of a reaction system and a rocket.

Software engineering (SE) research has traditionally revolved around engineering the source code. However, novel approaches that analyze software through computer vision have been increasingly adopted in SE. These approaches allow analyzing the software from a different complementary perspective other than the source code, and they are used to either complement existing source code-based methods, or to overcome their limitations. The goal of this manuscript is to survey the use of computer vision techniques in SE with the aim of assessing their potential in advancing the field of SE research. We examined an extensive body of literature from top-tier SE venues, as well as venues from closely related fields (machine learning, computer vision, and human-computer interaction). Our inclusion criteria targeted papers applying computer vision techniques that address problems related to any area of SE. We collected an initial pool of 2,716 papers, from which we obtained 66 final relevant papers covering a variety of SE areas. We analyzed what computer vision techniques have been adopted or designed, for what reasons, how they are used, what benefits they provide, and how they are evaluated. Our findings highlight that visual approaches have been adopted in a wide variety of SE tasks, predominantly for effectively tackling software analysis and testing challenges in the web and mobile domains. The results also show a rapid growth trend of the use of computer vision techniques in SE research.

Cold atmospheric plasmas (CAPs) are increasingly used for applications requiring the processing of heat- and pressure-sensitive (bio)materials. A key challenge in model-based control of CAPs arises from the high computational requirements of theoretical plasma models as well as lack of mechanistic understanding of plasma-surface interactions. Thus, control strategies that rely on simple, physics-based models that can be adapted to mitigate plant-model mismatch will be particularly advantageous for CAP applications. This paper presents an optimal control approach for controlling the nonlinear and cumulative effects of CAPs delivered to a target surface using a simple system model. Through parsimonious input parameterization, the solution to the optimal control problem (OCP) is given by an arc sequence that does not include any singular arcs. A data-driven adaptive algorithm based on modifier adaptation is proposed to deal with the structural plant-model mismatch by estimating the mismatch in the cost and constraints of the OCP. The adaptive approach is shown to converge to a Karush-Kuhn-Tucker (KKT) point of the OCP for the true system. Moreover, a control strategy based on feedback linearization and derivative estimation is proposed for online tracking of path constraints in the presence of disturbances and model uncertainty. The proposed approach is demonstrated by simulations and real-time control experiments on a kHz-excited atmospheric pressure plasma jet in Helium, in which the plasma treatment time is minimized while delivering a desired amount of nonlinear thermal effects to the target surface.

Systematic design and verification of advanced control strategies for complex systems under uncertainty largely remains an open problem. Despite the promise of black-box optimization methods for automated controller tuning, they generally lack formal guarantees on the solution quality, which is especially important in the control of safety-critical systems. This letter focuses on obtaining closed-loop performance guarantees for automated controller tuning, which can be formulated as a black-box optimization problem under uncertainty. We use recent advances in non-convex scenario theory to provide a distribution-free bound on the probability of the closed-loop performance measures. To mitigate the computational complexity of the data-driven scenario optimization method, we restrict ourselves to a discrete set of candidate tuning parameters. We propose to generate these candidates using constrained Bayesian optimization run multiple times from different random seed points. We apply the proposed method for tuning an economic nonlinear model predictive controller for a semibatch reactor modeled by seven highly nonlinear differential equations.

The article investigates the problem of state observation for discrete-time Markov jump piecewise-affine (PWA) systems, which cover both Markov jump systems and traditional PWA systems as two special classes. A new method for determining the admissible region-switching paths between adjacent time instants is proposed for both the plant state and the estimator state, so that both the computation cost and the conservatism of the theoretical results are reduced. To analyze the mean-square stability of the observation error system, a novel piecewise Lyapunov function is constructed, which depends on the current mode and the region indices of both the system and observer states. As the partitions of the state space are different for different modes, the region indices are dependent on the system mode. Then, mode-dependent PWA observers are designed by means of $\mathcal {S}$ -procedure and ellipsoidal outer approximation such that the observation error system is mean-square stable. The proposed observation strategy is demonstrated via an illustrative example.

Binary colloidal superlattices (BSLs) have demonstrated enormous potential for the design of advanced multifunctional materials that can be synthesized via colloidal self-assembly. However, mechanistic understanding of the three-dimensional self-assembly of BSLs is largely limited due to a lack of tractable strategies for characterizing the many two-component structures that can appear during the self-assembly process. To address this gap, we present a framework for colloidal crystal structure characterization that uses branched graphlet decomposition with deep learning to systematically and quantitatively describe the self-assembly of BSLs at the single-particle level. Branched graphlet decomposition is used to evaluate local structure via high-dimensional neighborhood graphs that quantify both structural order (e.g., body-centered-cubic vs face-centered-cubic) and compositional order (e.g., substitutional defects) of each individual particle. Deep autoencoders are then used to efficiently translate these neighborhood graphs into low-dimensional manifolds from which relationships among neighborhood graphs can be more easily inferred. We demonstrate the framework on in silico systems of DNA-functionalized particles, in which two well-recognized design parameters, particle size ratio and interparticle potential well depth can be adjusted independently. The framework reveals that binary colloidal mixtures with small interparticle size disparities (i.e., A- and B-type particle radius ratios of

Optimal experiment design (OED) aims to optimize the information content of experimental observations by designing the experimental conditions. In Bayesian OED for parameter estimation, the design selection is based on an expected utility metric that accounts for the joint probability distribution of the uncertain parameters and the observations. This work presents solution methods for two approximate formulations of the Bayesian OED problem based on Kullback–Leibler divergence for the particular case of Gaussian prior and observation noise distributions and the general case of arbitrary prior distributions and arbitrary observation noise distributions when the observation noise corresponds to arbitrary functions of the states and random variables with an arbitrary multivariate distribution. The proposed methods also allow satisfying path constraints with a specified probability. The solution approach relies on the reformulation of the approximate Bayesian OED problem as an optimal control problem (OCP), for which a parsimonious input parameterization is adopted to reduce the number of decision variables. An efficient global solution method for OCPs via sum-of-squares polynomials and parallel computing is then applied, which is based on approximating the cost of the OCP by a polynomial function of the decision variables and solving the resulting polynomial optimization problem to global optimality in a tractable way via semidefinite programming. It is established that the difference between the cost obtained by solving the polynomial optimization problem and the globally optimal cost of the OCP is bounded and depends on the polynomial approximation error.

There has been an increasing interest in explicit and cheap-to-evaluate control policies that approximate (computationally expensive) control laws such as model predictive control (MPC). However, approximate control policies are subject to approximation errors, leading to asymptotic performance losses. The contribution of this paper is three-fold: (i) a closed-loop training scheme is presented for deep neural network approximation of economic MPC; (ii) an online adaptive correction scheme is presented to account for the performance losses induced by approximation errors; and (iii) an offline performance verification scheme is presented to ensure that the approximate control policy converges to an equilibrium point of the system. The proposed approach is illustrated using a Williams-Otto reactor problem.

The closed-loop performance of model predictive controllers (MPCs) is highly dependent on the choice of prediction models, controller formulation, and tuning parameters. However, prediction models are typically optimized for prediction accuracy, instead of performance, and MPC tuning is typically done manually to satisfy (probabilistic) constraints. In this work, we demonstrate a general approach for automating the tuning of MPC under uncertainty. In particular, we formulate the automated tuning problem as a constrained black-box optimization problem that can be tackled with derivative-free optimization. We rely on a constrained variant of Bayesian optimization to solve the MPC tuning problem that can directly handle noisy and expensive-to-evaluate functions. The benefits of the proposed automated tuning approach are demonstrated on a benchmark continuously stirred tank reactor case study.

Manual classification of particle defects on semiconductor wafers is labor-intensive, which leads to slow solutions and longer learning curves on product failures while being prone to human error. This work explores the promise of deep learning for the classification of the chemical composition of these defects to reduce analysis time and inconsistencies due to human error, which in turn can result in systematic root cause analysis for sources of semiconductor defects. We investigate a deep convolutional neural network (CNN) for defect classification based on a combination of scanning electron microscopy (SEM) images and energy-dispersive x-ray (EDX) spectroscopy data. SEM images of sections of semiconductor wafers that contain particle defects are fed into a CNN in which the defects’ EDX spectroscopy data is merged directly with the CNN’s fully connected layer. The proposed CNN classifies the chemical composition of semiconductor wafer particle defects with an industrially pragmatic accuracy. We also demonstrate that merging spectral data with the CNN’s fully connected layer significantly improves classification performance over CNNs that only take either SEM image data or EDX spectral data as an input. The impact of training data collection and augmentation on CNN performance is explored and the promise of transfer learning for improving training speed and testing accuracy is investigated.

Individual chance constraints can be used to systematically seek trade-offs between control performance and constraint violation for a given disturbance description. This paper presents a Stochastic Model Predictive Control (SMPC) approach with adaptive individual chance constraints that relies on online adaptation of the disturbance description using the empirical cumulative distribution (ECDF). Individual chance constraints are ensured by using a suitable worst-case confidence interval derived from the ECDF. The confidence interval may, however, be excessively conservative due to the empirical nature of the ECDF. To reduce this conservatism, the proposed approach accounts for the updated disturbance information, which is sampled online from the one-step ahead prediction error. Hence, the initial ECDF can be obtained from a reduced number of samples since the conservative handling of the chance constraint is continuously mitigated. This will also allow for using simpler models of the stochastic system disturbances. Convergence and recursive feasibility of the proposed adaptive approach are established. A DC-DC converter benchmark problem is used to illustrate the usefulness of the proposed approach.

Atmospheric pressure plasma jets (APPJs) are increasingly used for biomedical applications. Reproducible and effective operation of APPJs hinges on controlling the nonlinear effects of plasma on a target substrate in the face of intrinsic variabilities of the plasma as well as exogenous disturbances. This paper presents a low-memory fast approximate nonlinear model predictive control (NMPC) strategy for an APPJ with prototypical applications in plasma medicine. The NMPC objective is to regulate the delivery of the cumulative thermal effects of plasma to a substrate, while adhering to constraints pertaining to a patient’s safety and comfort. Deep neural networks are used to approximate the implicit NMPC law with a cheap-to-evaluate explicit control law that has low memory requirements. Robust constraint satisfaction is guaranteed by projecting the output of the neural network onto a set that ensures the state stays within an appropriately defined invariant set. Closed-loop simulations and real-time control experiments indicate that the proposed approximate NMPC strategy is effective in handling nonlinear control costs at fast sampling times, while guaranteeing satisfaction of safety-critical system constraints. This work takes a crucial step toward fast NMPC of safety-critical plasma applications using resource-limited embedded control hardware.

Mars life support system models consist of numerous mission-critical, interrelated, and scenario-specific parameters. The large size and involved nature of these models make them computationally expensive, with parameters that are subject to several sources of uncertainty. Accurately characterizing these uncertainties and their impact on overall model predictions is crucial for decision-support and mission optimization. This paper focuses on uncertainty quantification of a model of a space crop cultivation system, which is one of several systems that are required on a long-duration manned Mars mission. The model performs constrained optimization of the equivalent system mass (ESM) metric, which augments shipped mass costs with those of pressurized volume, demanded power, thermal control, and needed crew time. This paper uses surrogate modeling for fast quantification of the effect of probabilistic uncertainty in mission-critical parameters of semi-empirical equations that describe crop growth and equipment operation. This work shows sparse polynomial chaos-Kriging (PCK) yields a computationally cheap-to-evaluate surrogate for the minimum ESM that accounts for probabilistic uncertainty in 86 model parameters. This surrogate model accelerates a global sensitivity analysis that elucidates which crop growth and equipment operation parameters are critical to mission outcome variability. The PCK surrogate model realizes a 100-fold computational speed gain in the estimation of the probability distribution of the minimum ESM.

Computational models are increasingly used to investigate and predict the complex dynamics of biological and biochemical systems. Nevertheless, governing equations of a biochemical system may not be (fully) known, which would necessitate learning the system dynamics directly from, often limited and noisy, observed data. On the other hand, when expensive models are available, systematic and efficient quantification of the effects of model uncertainties on quantities of interest can be an arduous task. This paper leverages the notion of flow-map (de)compositions to present a framework that can address both of these challenges via learning data-driven models useful for capturing the dynamical behavior of biochemical systems. Data-driven flow-map models seek to directly learn the integration operators of the governing differential equations in a black-box manner, irrespective of structure of the underlying equations. As such, they can serve as a flexible approach for deriving fast-toevaluate surrogates for expensive computational models of system dynamics, or, alternatively, for reconstructing the long-term system dynamics via experimental observations. We present a data-efficient approach to data-driven flow-map modeling based on polynomial chaos Kriging. The approach is demonstrated for discovery of the dynamics of various benchmark systems and a co-culture bioreactor subject to external forcing, as well as for uncertainty quantification of a microbial electrosynthesis reactor. Such data-driven models and analyses of dynamical systems can be paramount in the design and optimization of bioprocesses and integrated biomanufacturing systems.

The performance of advanced controllers depends on the selection of several tuning parameters that can affect the closed-loop control performance and constraint satisfaction in highly nonlinear and nonconvex ways. There has been a significant interest in auto-tuning of complex control structures using Bayesian optimization (BO). However, an open challenge is how to deal with uncertainties in the closed-loop system that cannot be attributed to a lumped, small-scale noise term. This paper develops an adversarially robust BO (ARBO) method that is suited to auto-tuning problems with significant time-invariant uncertainties in a plant simulator. ARBO uses a Gaussian process model that jointly describes the effect of the tuning parameters and uncertainties on the closed-loop performance. ARBO uses an alternating confidence-bound procedure to simultaneously select the next candidate tuning and uncertainty realizations, implying only one expensive closed-loop simulation is needed at each iteration. The advantages of ARBO are demonstrated on two case studies.

Plasma, the fourth and most pervasive state of matter in the visible universe, is a fascinating medium that is connected to the beginning of our universe itself. Man-made plasmas are at the core of many technological advances that include the fabrication of semiconductor devices, which enabled the modern computer and communication revolutions. The introduction of low temperature, atmospheric pressure plasmas to the biomedical field has ushered a new revolution in the healthcare arena that promises to introduce plasma-based therapies to combat some thorny and long-standing medical challenges. This article presents an overview of where research is at today and discusses innovative concepts and approaches to overcome present challenges and take the field to the next level. It is written by a team of experts who took an in-depth look at the various applications of plasma in hygiene, decontamination, and medicine, made critical analysis, and proposed ideas and concepts that should help the research community focus their efforts on clear and practical steps necessary to keep the field advancing for decades to come.

Reinvigorated public interest in human space exploration has led to the need to address the science and engineering challenges described by NASA's Space Technology Grand Challenges (STGCs) for expanding the human presence in space. Here we define Space Bioprocess Engineering (SBE) as a multi-disciplinary approach to design, realize, and manage a biologically-driven space mission as it relates to addressing the STGCs for advancing technologies to support the nutritional, medical, and incidental material requirements that will sustain astronauts against the harsh conditions of interplanetary transit and habitation offworld. SBE combines synthetic biology and bioprocess engineering under extreme constraints to enable and sustain a biological presence in space. Here we argue that SBE is a critical strategic area enabling long-term human space exploration; specify the metrics and methods that guide SBE technology life-cycle and development; map an approach by which SBE technologies are matured on offworld testing platforms; and suggest a means to train the next generation spacefaring workforce on the SBE advantages and capabilities. In doing so, we outline aspects of the upcoming technical and policy hurdles to support space biomanufacturing and biotechnology. We outline a perspective marriage between space-based performance metrics and the synthetic biology Design-Build-Test-Learn cycle as they relate to advancing the readiness of SBE technologies. We call for a concerted effort to ensure the timely development of SBE to support long-term crewed missions using mission plans that are currently on the horizon.

Stochastic differential equations (SDEs) are used to describe a wide variety of complex stochastic dynamical systems. Learning the hidden physics within SDEs is crucial for unraveling fundamental understanding of these systems' stochastic and nonlinear behavior. We propose a flexible and scalable framework for training artificial neural networks to learn constitutive equations that represent hidden physics within SDEs. The proposed stochastic physics-informed neural ordinary differential equation framework (SPINODE) propagates stochasticity through the known structure of the SDE (i.e., the known physics) to yield a set of deterministic ODEs that describe the time evolution of statistical moments of the stochastic states. SPINODE then uses ODE solvers to predict moment trajectories. SPINODE learns neural network representations of the hidden physics by matching the predicted moments to those estimated from data. Recent advances in automatic differentiation and mini-batch gradient descent with adjoint sensitivity are leveraged to establish the unknown parameters of the neural networks. We demonstrate SPINODE on three benchmark in-silico case studies and analyze the framework's numerical robustness and stability. SPINODE provides a promising new direction for systematically unraveling the hidden physics of multivariate stochastic dynamical systems with multiplicative noise.

This paper presents a stochastic-tube model predictive control (MPC) strategy that systematically handles plant-model mismatch, guarantees stability in the presence of changing operating conditions, and ensures offset-free tracking for all reachable operating conditions. The key notion of this work is to separate the system uncertainty into two distinct sources of additive bounded state error. The first source is a non-random uncertainty that represents mismatch between the linear model of the controller and the true plant (as well as other types of persistent disturbances). The second source represents random fluctuations due to either the intrinsic stochastic variability of the system, or exogenous disturbances. Recursive feasibility and stability of the stochastic-tube MPC strategy is guaranteed by defining the terminal invariant set to include the effect of changes in the steady-state operating conditions. Offset-free tracking is achieved with a disturbance estimator that can be tuned independently of the controller. To reduce the conservatism inherent to robust control performance, a new filter model for deterministic disturbances is proposed that predicts uncertainty in the future evolution of the disturbances based on a bound on how quickly the plant-model mismatch can vary. The stochastic-tube MPC strategy is demonstrated on two simulation case studies—a benchmark DC-DC converter and an industrially-motivated fluidized-bed catalytic cracking unit.

Structural model uncertainty is prevalent in control design and arises from incomplete knowledge of the system or the existence of different modes of dynamic behavior, such as those arising from system faults and malfunctions. This paper addresses control of stochastic nonlinear systems using model predictive control, or mpc , under structural model uncertainty. Inspired by dual control, the mpc strategy with active learning presented here can probe the uncertain system to select, among a set of candidates, the model that best describes the observed closed-loop system data. The proposed controller involves online model selection based on estimation of the model-hypothesis probabilities and minimization of a computationally tractable measure of the predicted Bayes risk of selection error. The performance of the proposed approach is compared to that of nominal mpc with no learning, mpc with passive learning, and a robust mpc approach that systematically accounts for structural model uncertainty but has no learning mechanism. Simulation results on a nonlinear bioreactor demonstrate that active learning can have significant advantages in maintaining adequate control performance in the presence of structural uncertainty. Active learning can be particularly beneficial for improving online model discrimination and active fault diagnosis under closed-loop control.

Real-time diagnostics of cold atmospheric plasma (CAP) sources can be challenging due to the requirement for expensive equipment and complicated analysis. Data analytics that rely on machine learning (ML) methods can help address this challenge. In this paper, we demonstrate the application of several ML methods for real-time diagnosis of CAPs using information-rich optical emission spectra and electro-acoustic emission. We show that data analytics based on ML can provide a simple and effective means for estimation of operation-relevant parameters such as rotational and vibrational temperature and substrate characteristic in real-time. Our findings indicate a great potential promise for ML for real-time diagnostics of CAPs.

The optimal design of experiments is crucial for maximizing the information content of data across a wide-range of experimental goals. This paper presents a Bayesian approach to optimal experiment design (OED) for parameter inference in constrained, dynamic, and nonlinear systems under noisy, incomplete, and indirect measurements. Bayesian OED maximizes an expected utility objective, which accounts for prior and posterior uncertainty in the model parameters from an information-theoretic standpoint. Due to the complicated form of the expected utility, it must be estimated using sample-based methods and, in particular, a nested Monte Carlo estimator that is expensive to evaluate using the full dynamic model. We propose a novel surrogate model based on arbitrary polynomial chaos (aPC), which readily applies to any type of prior distribution. The aPC expansions are constructed locally at each design visited during the iterative optimization procedure. The main cost in aPC, which is the determination of the expansion coefficients, is minimized by estimating these coefficients from only a minimal set of dynamic model evaluations. Although sample-based estimators can also be applied to the chance constraints, this leads to a potentially large number of binary variables, such that a smooth moment-based approximation is preferred in this work. Numerical simulations indicate that the proposed surrogate can significantly lower the computational cost of the Bayesian OED, while guaranteeing the original chance constraints are satisfied without noticeably increasing the average time to find a solution. As such, this methodology appears to have the potential to pave the way for real-time or sequential dynamic experiment design in a fully Bayesian setting.

Reliably diagnosing faults and malfunctions has become increasingly challenging in modern technical systems because of their growing complexity as well as increasingly stringent requirements on safety, availability, and high-performance operation. Traditional methods for fault detection and diagnosis rely on nominal input–output data, which can contain insufficient information to support reliable conclusions. Recent years have witnessed a growing interest in active fault diagnosis, which addresses this issue by injecting input signals specifically designed to reveal the fault status of the system. This paper provides an overview of state-of-the-art methods for input design for active fault diagnosis and discusses the primary considerations in the formulation and solution of the input-design problem. We also discuss the primary challenges and suggest avenues for future research in this rapidly evolving field.

This paper presents a comparative study between two constraint-tightening approaches for tube-based stochastic nonlinear model predictive control (SNMPC) with and without terminal constraints. A simple constraint-tightening method based on the exponential decay rate of a δ-Lyapunov function is extended to the stochastic setting. This method uses the notion of incremental stabilizability to alleviate the need for offline, but involved computation of terminal constraints. The proposed method is compared to a SNMPC formulation that employs terminal constraints and Lipschitz constant-based constraint tightening. A comparative analysis is presented on a benchmark continuous stirred-tank reactor problem. Practical approximations for computing terminal sets are discussed in the context of this comparison.

Automated model-based test generation presents a viable alternative to the costly manual test creation currently employed for regression testing of web apps. However, existing model inference techniques rely on threshold-based whole-page comparison to establish state equivalence, which cannot reliably identify near-duplicate web pages in modern web apps. Consequently, existing techniques produce inadequate models for dynamic web apps, and fragile test oracles, rendering the generated regression test suites ineffective. We propose a model-based test generation technique, FRAGGEN, that eliminates the need for thresholds, by employing a novel state abstraction based on page fragmentation to establish state equivalence. FRAGGEN also uses fine-grained page fragment analysis to diversify state exploration and generate reliable test oracles. Our evaluation shows that FRAGGEN outperforms existing whole-page techniques by detecting more near-duplicates, inferring better web app models and generating test suites that are better suited for regression testing. On a dataset of 86,165 state-pairs, FRAGGEN detected 123% more near-duplicates on average compared to whole-page techniques. The crawl models inferred by FRAGGEN have 62% more precision and 70% more recall on average. FRAGGEN also generates reliable regression test suites with test actions that have nearly 100% success rate on the same version of the web app even if the execution environment is varied. The test oracles generated by FRAGGEN can detect 98.7% of the visible changes in web pages while being highly robust, making them suitable for regression testing., Comment: 16 pages with 13 figures and 9 tables. Accepted at IEEE Transactions on Software Engineering (IEEE TSE)

We introduce PoCET: a free and open-scource Polynomial Chaos Expansion Toolbox for Matlab, featuring the automatic generation of polynomial chaos expansion (PCE) for linear and nonlinear dynamic systems with time-invariant stochastic parameters or initial conditions, as well as several simulation tools. It offers a built-in handling of Gaussian, uniform, and beta probability density functions, projection and collocation-based calculation of PCE coefficients, and the calculation of stochastic moments from a PCE. Efficient algorithms for the calculation of the involved integrals have been designed in order to increase its applicability. PoCET comes with a variety of introductory and instructive examples. Throughout the paper we show how to perform a polynomial chaos expansion on a simple ordinary differential equation using PoCET, as well as how it can be used to solve the more complex task of optimal experimental design., 6 pages, 4 figures, Accepted for the 21st IFAC WC 2020

This article considers the stochastic optimal control of discrete-time linear systems subject to (possibly) unbounded stochastic disturbances, hard constraints on the manipulated variables, and joint chance constraints on the states. A tractable convex second-order cone program (SOCP) is derived for calculating the receding-horizon control law at each time step. Feedback is incorporated during prediction by parametrizing the control law as an affine function of the disturbances. Hard input constraints are guaranteed by saturating the disturbances that appear in the control law parametrization. The joint state chance constraints are conservatively approximated as a collection of individual chance constraints that are subsequently relaxed via the Cantelli-Chebyshev inequality. Feasibility of the SOCP is guaranteed by softening the approximated chance constraints using the exact penalty function method. Closed-loop stability in a stochastic sense is established by establishing that the states satisfy a geometric drift condition outside of a compact set such that their variance is bounded at all times. The SMPC approach is demonstrated using a continuous acetone-butanol-ethanol fermentation process, which is used for production of high-value-added drop-in biofuels.

Optimal experiment design (OED) aims to optimize the information content of experimental observations for various types of applications by designing the experimental conditions. In Bayesian OED for parameter estimation, the design selection is based on an expected utility metric that accounts for the joint probability distribution of the uncertain parameters and the observations. This work presents an approximation of the Bayesian OED problem based on Kullback–Leibler divergence that is amenable to global optimization. The experiment design adopts a parsimonious input parametrization that reduces the number of design variables. This leads to a tractable polynomial optimization problem that can be solved to global optimality via the concept of sum-of-squares polynomials.

Stochastic model predictive control (SMPC) provides a probabilistic framework for MPC of systems with stochastic uncertainty. A key feature of SMPC is the inclusion of chance constraints, which enables a systematic trade-off between attainable control performance and probability of state constraint violations in a stochastic setting. This paper presents an overview of core concepts in SMPC in relation to MPC and stochastic optimal control, with numerical illustrations on a typical chemical process. Estimation of stochastic disturbances as well as the impact of estimation quality of stochastic disturbances on the SMPC performance are discussed. Some avenues for future research in SMPC are suggested.

Atmospheric pressure plasma jets (APPJs) have widespread use in materials processing and biomedical applications. Safe and effective operation of hand-held APPJs is, however, highly sensitive to the intrinsic variability of plasma characteristics as well as exogenous disturbances such as variations in the separation distance between the device tip and target surface. This paper investigates feedback control of the thermal effect and intensity of a kHz-excited APPJ in helium using a proportional-integral control strategy and a model predictive control (MPC) strategy. A data-driven model of the APPJ, developed for a linear operating range using the subspace identification method, is utilized in the design of both control strategies. Real-time control experiments reveal that feedback control is crucial for effective operation of the APPJ in the presence of step disturbances in the device tip-to-surface separation distance. It is observed that the MPC strategy can more effectively regulate the multivariable dynamics of the APPJ for effective setpoint tracking and constraint handling in the face of disturbances.

We present a numerical method for solving a class of systems of partial differential equations (PDEs) that arises in modeling environmental processes undergoing advection and biogeochemical reactions. The salient feature of these PDEs is that all partial derivatives appear in linear expressions. As a result, the system can be viewed as a set of ordinary differential equations (ODEs), albeit each one along a different characteristic. The method then consists of alternating between equations and integrating each one step-wise along its own characteristic, thus creating a customized grid on which solutions are computed. Since the solutions of such PDEs are generally smoother along their characteristics, the method offers the potential of using larger time steps while maintaining accuracy and reducing numerical dispersion. The advantages in efficiency and accuracy of the proposed method are demonstrated in two illustrative examples that simulate depth-resolved reactive transport and soil carbon cycling.

Reliable and timely diagnosis of system faults under uncertainties is imperative for safe, reliable, and profitable operation of technical systems. This paper presents an input design method for active fault diagnosis for nonlinear systems that are subject to probabilistic model uncertainty and stochastic disturbances, and are under operational constraints. A computationally efficient sample-based method is presented for joint propagation of model uncertainty and stochastic disturbances using non-intrusive generalized polynomial chaos and unscented transformation. A tractable sample-based distance measure, inspired by the k-nearest neighbors algorithm, is used for fault diagnosis, which seeks to discriminate between probabilistic predictions of the model hypotheses for normal and faulty operation. Simulation results on a benchmark bioreactor case study demonstrate the effectiveness of the proposed input design method for reliable fault diagnosis under uncertainty through online model discrimination.

The majority of work on chance constrained model predictive control (MPC) for stochastic systems adopts the concept of implicit constraint backoffs for handling state chance constraints. However, implicit backoffs cannot be computed analytically in nonlinear MPC (NMPC), so that they must be approximated and, as a result, chance constraints are not guaranteed by the closed-loop system. This paper proposes a strategy for explicit computation of constraint backoffs that allows tightly guaranteeing chance constraints in NMPC for stochastic systems with arbitrary uncertainty distributions. The proposed method relies on uncertainty propagation through closed-loop system dynamics. Thus, this paper also investigates the use of stochastic surrogate models for constructing the distribution of closed-loop quantities of interest such as state constraint functions or any general performance objectives. To this end, an extension of polynomial chaos that can handle arbitrary probability measures is proposed for a class of disturbance models representing plant-model mismatch. The proposed methods are illustrated on a benchmark continuously-stirred tank reactor problem.

This paper addresses the problem of model predictive control with multiple models for nonlinear systems subject to stochastic disturbances. The multiple models can represent various operating conditions such as system faults or failures, or arise from model structure uncertainty. The paper presents a stochastic nonlinear model predictive control (SNMPC) approach with endogenous learning for active discrimination between the competing models based on closed-loop system observations. The system learning is endogenized through explicit inclusion of a model discrimination measure into the stochastic optimal control problem, which facilitates probabilistic discrimination between the predictions of multiple models. The control approach uses a Bayesian estimation algorithm for recursive estimation of the probabilities that represent the degree to which each model predicts the online system observations. The performance of the proposed SNMPC approach with active model discrimination is demonstrated for closed-loop fault diagnosis.

Dynamic simulation of stochastic systems requires uncertainty propagation. Traditional sample-based uncertainty propagation methods are often computationally intractable for online optimization-based estimation and control applications. Generalized polynomial chaos (gPC) is an efficient uncertainty propagation method that has been used for solving various nonlinear estimation and optimal control problems. However, gPC requires knowledge of the exact probability distribution of the random variables, and does not explicitly account for correlations between these random variables. This paper demonstrates the use of arbitrary polynomial chaos (aPC) for propagation of correlated multivariate random variables. aPC constructs orthogonal polynomial basis functions from only the raw moments of the random variables. Thus, aPC can be used for propagation of uncertainties with arbitrary probability distributions, even if their functional forms are unknown. The main contributions of this paper consist of presenting an algorithm for generating a set of orthogonal polynomial basis functions for correlated multivariate random variables and applying the Galerkin projection to compute closed-form expressions for the dynamics of the aPC expansion coefficients. An algorithm is also presented for efficient calculation of inner products between polynomial basis functions needed in the Galerkin projection. The error convergence properties of aPC are investigated and compared to that of gPC and Monte Carlo using a dynamic simulation case study.

This paper presents a robust model predictive control (MPC) approach for offset-free tracking of piece-wise constant references in the presence of bounded deterministic and stochastic disturbances. The system is considered to be linear with two sources of additive bounded uncertainties on the states. The first uncertainty source accounts for unknown, deterministic structural/parametric plant-model mismatch. The second uncertainty source represents stochastic exogenous system disturbances. The proposed deterministic-stochastic robust MPC approach uses estimates of the deterministic model uncertainties to modify the nominal state and input targets. This allows for achieving offset-free tracking of the mean of the controlled variables. A non-conservative constraint tightening procedure is used to handle probabilistic state constraints and hard input constraints in the presence of stochastic uncertainties. The computational complexity of the proposed robust MPC approach is comparable to that of nominal MPC. The closed-loop performance of the proposed robust MPC approach is compared to that of robust tube-based MPC and stochastic MPC in a simulation study.

Client-side JavaScript is widely used in web applications to improve user-interactivity and minimize client-server communications. Unfortunately, JavaScript is known to be error-prone. While prior studies have demonstrated the prevalence of JavaScript faults, no attempts have been made to determine their causes and consequences. The goal of our study is to understand the root causes and impact of JavaScript faults and how the results can impact JavaScript programmers, testers and tool developers. We perform an empirical study of 502 bug reports from 19 bug repositories. The bug reports are thoroughly examined to classify and extract information about each bug' cause (the error ) and consequence (the failure and impact ). Our results show that the majority (68 percent) of JavaScript faults are DOM-related , meaning they are caused by faulty interactions of the JavaScript code with the Document Object Model (DOM) . Further, 80 percent of the highest impact JavaScript faults are DOM-related. Finally, most JavaScript faults originate from programmer mistakes committed in the JavaScript code itself, as opposed to other web application components. These results indicate that JavaScript programmers and testers need tools that can help them reason about the DOM. Additionally, developers can use the error patterns we found to design more powerful static analysis tools for JavaScript.

Programmers spend a substantial amount of time manually repair- ing code that does not compile. We observe that the repairs for any particular error class typically follow a pattern and are highly mechanical. We propose a novel approach that automatically learns these patterns with a deep neural network and suggests program repairs for the most costly classes of build-time compilation failures. We describe how we collect all build errors and the human-authored, in-progress code changes that cause those failing builds to transition to successful builds at Google. We generate an AST diff from the textual code changes and transform it into a domain-specific language called Delta that encodes the change that must be made to make the code compile. We then feed the compiler diagnostic information (as source) and the Delta changes that resolved the diagnostic (as target) into a Neural Machine Translation network for training. For the two most prevalent and costly classes of Java compilation errors, namely missing symbols and mismatched method signatures, our system called DeepDelta, generates the correct repair changes for 19,314 out of 38,788 (50%) of unseen compilation errors. The correct changes are in the top three suggested fixes 86% of the time on average.

E2E web test suites are prone to test dependencies due to the heterogeneous multi-tiered nature of modern web apps, which makes it difficult for developers to create isolated program states for each test case. In this paper, we present the first approach for detecting and validating test dependencies present in E2E web test suites. Our approach employs string analysis to extract an approximated set of dependencies from the test code. It then filters potential false dependencies through natural language processing of test names. Finally, it validates all dependencies, and uses a novel recovery algorithm to ensure no true dependencies are missed in the final test dependency graph. Our approach is implemented in a tool called TEDD and evaluated on the test suites of six open-source web apps. Our results show that TEDD can correctly detect and validate test dependencies up to 72% faster than the baseline with the original test ordering in which the graph contains all possible dependencies. The test dependency graphs produced by TEDD enable test execution parallelization, with a speed-up factor of up to 7x., 11 pages, published in the Proceedings of the 2019 27th ACM Joint Meeting on European Software Engineering Conference and Symposium on the Foundations of Software Engineering (ESEC/FSE 2019), pp. 154-164

We present a novel surrogate modeling method that can be used to accelerate the solution of uncertainty quantification (UQ) problems arising in nonlinear and non-smooth models of biological systems. In particular, we focus on dynamic flux balance analysis (DFBA) models that couple intracellular fluxes, found from the solution of a constrained metabolic network model of the cellular metabolism, to the time-varying nature of the extracellular substrate and product concentrations. DFBA models are generally computationally expensive and present unique challenges to UQ, as they entail dynamic simulations with discrete events that correspond to switches in the active set of the solution of the constrained intracellular model. The proposed non-smooth polynomial chaos expansion (nsPCE) method is an extension of traditional PCE that can effectively capture singularities in the DFBA model response due to the occurrence of these discrete events. The key idea in nsPCE is to use a model of the singularity time to partition the parameter space into two elements on which the model response behaves smoothly. Separate PCE models are then fit in both elements using a basis-adaptive sparse regression approach that is known to scale well with respect to the number of uncertain parameters. We demonstrate the effectiveness of nsPCE on a DFBA model of an E. coli monoculture that consists of 1075 reactions and 761 metabolites. We first illustrate how traditional PCE is unable to handle problems of this level of complexity. We demonstrate that over 800-fold savings in computational cost of uncertainty propagation and Bayesian estimation of parameters in the substrate uptake kinetics can be achieved by using the nsPCE surrogates in place of the full DFBA model simulations. We then investigate the scalability of the nsPCE method by utilizing it for global sensitivity analysis and maximum a posteriori estimation in a synthetic metabolic network problem with a larger number of parameters related to both intracellular and extracellular quantities., Author summary Construction and validation of mathematical models in biological systems involving genome-scale biomolecular networks is a challenging problem. This article presents a novel surrogate modeling method that can accelerate parameter inference from experimental data and the quantification of uncertainty in the predictions of complex dynamic biological models, with a particular emphasis on nonlinear models with non-smooth behavior. The method is applied to infer extracellular kinetic parameters in a batch fermentation reactor consisting of diauxic growth of E. coli on a glucose/xylose mixed media as well as a larger synthetic metabolic network problem. The proposed approach enables rigorous quantification of parameter uncertainty to determine whether or not available data is sufficient for estimation of all unknown model parameters.