Stability for Receding-horizon Stochastic Model Predictive Control

A stochastic model predictive control (SMPC) approach is presented for discrete-time linear systems with arbitrary time-invariant probabilistic uncertainties and additive Gaussian process noise. Closed-loop stability of the SMPC approach is established by appropriate selection of the cost function. Polynomial chaos is used for uncertainty propagation through system dynamics. The performance of the SMPC approach is demonstrated using the Van de Vusse reactions.Comment: American Control Conference (ACC) 201

No-Regret Constrained Bayesian Optimization of Noisy and Expensive Hybrid Models using Differentiable Quantile Function Approximations

This paper investigates the problem of efficient constrained global optimization of hybrid models that are a composition of a known white-box function and an expensive multi-output black-box function subject to noisy observations, which often arises in real-world science and engineering applications. We propose a novel method, Constrained Upper Quantile Bound (CUQB), to solve such problems that directly exploits the composite structure of the objective and constraint functions that we show leads substantially improved sampling efficiency. CUQB is a conceptually simple, deterministic approach that avoid constraint approximations used by previous methods. Although the CUQB acquisition function is not available in closed form, we propose a novel differentiable sample average approximation that enables it to be efficiently maximized. We further derive bounds on the cumulative regret and constraint violation under a non-parametric Bayesian representation of the black-box function. Since these bounds depend sublinearly on the number of iterations under some regularity assumptions, we establis bounds on the convergence rate to the optimal solution of the original constrained problem. In contrast to most existing methods, CUQB further incorporates a simple infeasibility detection scheme, which we prove triggers in a finite number of iterations when the original problem is infeasible (with high probability given the Bayesian model). Numerical experiments on several test problems, including environmental model calibration and real-time optimization of a reactor system, show that CUQB significantly outperforms traditional Bayesian optimization in both constrained and unconstrained cases. Furthermore, compared to other state-of-the-art methods that exploit composite structure, CUQB achieves competitive empirical performance while also providing substantially improved theoretical guarantees

Stochastic Physics-Informed Neural Ordinary Differential Equations

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

Model Predictive Control of an Integrated Continuous Pharmaceutical Manufacturing Pilot Plant

This paper considers the model predictive control (MPC) of critical quality attributes (CQAs) of products in an end-to-end continuous pharmaceutical manufacturing pilot plant, which was designed and constructed at the Novartis-MIT Center for Continuous Manufacturing. Feedback control is crucial for achieving the stringent regulatory requirements on CQAs of pharmaceutical products in the presence of process uncertainties and disturbances. To this end, a key challenge arises from complex plant-wide dynamics of the integrated process units in a continuous pharmaceutical process, that is, dynamical interactions between several process units. This paper presents two plant-wide MPC designs for the end-to-end continuous pharmaceutical manufacturing pilot plant using the quadratic dynamic matrix control algorithm. The plant-wide MPC designs are based on different modeling approaches - subspace identification and linearization of nonlinear differential-algebraic equations that yield, respectively, linear low-dimensional and high-dimensional state-space models for the plant-wide dynamics. The closed-loop performance of the plant-wide MPC designs is evaluated using a nonlinear plant simulator equipped with a stabilizing control layer. The closed-loop simulation results demonstrate that the plant-wide MPC systems can facilitate effective regulation of CQAs and flexible process operation in the presence of uncertainties in reaction kinetics, persistent drifts in efficiency of filtration units, temporary disturbances in purity of intermediate compounds, and set point changes. The plant-wide MPC allows for incorporating quality-by-design considerations into the control problem through input and output constraints to ensure regulatory compliant process operation

Sorption and Photodegradation Processes Govern Distribution and Fate of Sulfamethazine in Freshwater−Sediment Microcosms

The antibiotic sulfamethazine can be transported from manured fields to surface water bodies. We investigated the degradation and fate of sulfamethazine in pond water using 14C-phenyl-sulfamethazine in small pond water microcosms containing intact sediment and pond water. We found a 2.7-day half-life in pond water and 4.2-day half-life when sulfamethazine was added to the water (5 mg L–1 initial concentration) with swine manure diluted to simulate runoff. Sulfamethazine dissipated exponentially from the water column, with the majority of loss occurring via movement into the sediment phase. Extractable sulfamethazine in sediment accounted for 1.9–6.1% of the applied antibiotic within 14 days and then declined thereafter. Sulfamethazine was transformed mainly into nonextractable sediment-bound residue (40–60% of applied radioactivity) and smaller amounts of photoproducts. Biodegradation, as indicated by metabolite formation and 14CO2 evolution, was less significant than photodegradation. Two photoproducts accounted for 15–30% of radioactivity in the water column at the end of the 63-day study; the photoproducts were the major degradates in the aqueous and sediment phases. Other unidentified metabolites individually accounted for \u3c7% of radioactivity in the water or sediment. Less than 3% of applied radioactivity was mineralized to 14CO2. Manure input significantly increased sorption and binding of sulfamethazine residues to the sediment. These results show concurrent processes of photodegradation and sorption to sediment control aqueous concentrations and establish that sediment is a sink for sulfamethazine and sulfamethazine-related residues. Accumulation of the photoproducts and sulfamethazine in sediment may have important implications for benthic organisms

Global age-sex-specific fertility, mortality, healthy life expectancy (HALE), and population estimates in 204 countries and territories, 1950-2019 : a comprehensive demographic analysis for the Global Burden of Disease Study 2019

Background: Accurate and up-to-date assessment of demographic metrics is crucial for understanding a wide range of social, economic, and public health issues that affect populations worldwide. The Global Burden of Diseases, Injuries, and Risk Factors Study (GBD) 2019 produced updated and comprehensive demographic assessments of the key indicators of fertility, mortality, migration, and population for 204 countries and territories and selected subnational locations from 1950 to 2019. Methods: 8078 country-years of vital registration and sample registration data, 938 surveys, 349 censuses, and 238 other sources were identified and used to estimate age-specific fertility. Spatiotemporal Gaussian process regression (ST-GPR) was used to generate age-specific fertility rates for 5-year age groups between ages 15 and 49 years. With extensions to age groups 10–14 and 50–54 years, the total fertility rate (TFR) was then aggregated using the estimated age-specific fertility between ages 10 and 54 years. 7417 sources were used for under-5 mortality estimation and 7355 for adult mortality. ST-GPR was used to synthesise data sources after correction for known biases. Adult mortality was measured as the probability of death between ages 15 and 60 years based on vital registration, sample registration, and sibling histories, and was also estimated using ST-GPR. HIV-free life tables were then estimated using estimates of under-5 and adult mortality rates using a relational model life table system created for GBD, which closely tracks observed age-specific mortality rates from complete vital registration when available. Independent estimates of HIV-specific mortality generated by an epidemiological analysis of HIV prevalence surveys and antenatal clinic serosurveillance and other sources were incorporated into the estimates in countries with large epidemics. Annual and single-year age estimates of net migration and population for each country and territory were generated using a Bayesian hierarchical cohort component model that analysed estimated age-specific fertility and mortality rates along with 1250 censuses and 747 population registry years. We classified location-years into seven categories on the basis of the natural rate of increase in population (calculated by subtracting the crude death rate from the crude birth rate) and the net migration rate. We computed healthy life expectancy (HALE) using years lived with disability (YLDs) per capita, life tables, and standard demographic methods. Uncertainty was propagated throughout the demographic estimation process, including fertility, mortality, and population, with 1000 draw-level estimates produced for each metric. Findings: The global TFR decreased from 2·72 (95% uncertainty interval [UI] 2·66–2·79) in 2000 to 2·31 (2·17–2·46) in 2019. Global annual livebirths increased from 134·5 million (131·5–137·8) in 2000 to a peak of 139·6 million (133·0–146·9) in 2016. Global livebirths then declined to 135·3 million (127·2–144·1) in 2019. Of the 204 countries and territories included in this study, in 2019, 102 had a TFR lower than 2·1, which is considered a good approximation of replacement-level fertility. All countries in sub-Saharan Africa had TFRs above replacement level in 2019 and accounted for 27·1% (95% UI 26·4–27·8) of global livebirths. Global life expectancy at birth increased from 67·2 years (95% UI 66·8–67·6) in 2000 to 73·5 years (72·8–74·3) in 2019. The total number of deaths increased from 50·7 million (49·5–51·9) in 2000 to 56·5 million (53·7–59·2) in 2019. Under-5 deaths declined from 9·6 million (9·1–10·3) in 2000 to 5·0 million (4·3–6·0) in 2019. Global population increased by 25·7%, from 6·2 billion (6·0–6·3) in 2000 to 7·7 billion (7·5–8·0) in 2019. In 2019, 34 countries had negative natural rates of increase; in 17 of these, the population declined because immigration was not sufficient to counteract the negative rate of decline. Globally, HALE increased from 58·6 years (56·1–60·8) in 2000 to 63·5 years (60·8–66·1) in 2019. HALE increased in 202 of 204 countries and territories between 2000 and 2019