153 results found
Mutran VM, Ribeiro CO, Nascimento CO, et al., 2020, Risk-conscious optimization model to support bioenergy investment in the Brazilian sugarcane industry, Applied Energy, Vol: 258, Pages: 1-15, ISSN: 0306-2619
The past decades have seen a diversification of the sugarcane industry with the emergence of new technology to produce bioenergy from by-product and waste process streams. Given Brazil’s ambitious goal of reducing green-house gas emissions by over 40% below 2005 levels by 2030, it is of paramount importance to develop reliable decision-making systems in order to stimulate investment in these low-carbon technologies. This paper seeks to develop a more accurate optimization model to inform risk-conscious investment decisions for bioenergy generation capacity in sugarcane mills. The main objective is for the model to enable a better understanding of how Brazilian government policies, such as the electricity price in the regulated market, may impact these investments, by taking into account the uncertainty in sugar, ethanol and spot electricity markets and the interdependency between production and investment decisions in terms of saleable product mix. The proposed methodology combines portfolio optimization theory with superstructure process modeling and it relies on simple surrogates derived from a detailed sugarcane plant simulator to retain computational tractability and enable scenario analysis. The case study of an existing sugarcane plant is used to demonstrate the methodology and illustrate how the model can assist decision-makers. In all of the scenarios assessed, the model recommends investment in extra bioelectricity capacity via the anaerobic digestion of vinasse but advises against investment in second-generation ethanol production via the hydrolysis of surplus bagasse. Furthermore, the decision to upgrade the cogeneration system with a condensation turbine is highly sensitive to the electricity price practiced in the regulated market, capacity constraints on the sugar-ethanol mix, and the accepted level of risk. Another key insight drawn from the case study is that recent market conditions have favored a production focused on the sugar business, maki
Kusumo KP, Gomoescu L, Paulen R, et al., 2019, Bayesian approach to probabilistic design space characterization: a nested sampling strategy, Industrial & Engineering Chemistry Research, ISSN: 0888-5885
Quality by design in pharmaceutical manufacturing hinges on computational methods and tools that are capable of accurate quantitative prediction of the design space. This paper investigates Bayesian approaches to design space characterization, which determine a feasibility probability that can be used as a measure of reliability and risk by the practitioner. An adaptation of nested sampling—a Monte Carlo technique introduced to compute Bayesian evidence—is presented. The nested sampling algorithm maintains a given set of live points through regions with increasing probability feasibility until reaching a desired reliability level. It furthermore leverages efficient strategies from Bayesian statistics for generating replacement proposals during the search. Features and advantages of this algorithm are demonstrated by means of a simple numerical example and two industrial case studies. It is shown that nested sampling can outperform conventional Monte Carlo sampling and be competitive with flexibility-based optimization techniques in low-dimensional design space problems. Practical aspects of exploiting the sampled design space to reconstruct a feasibility probability map using machine learning techniques are also discussed and illustrated. Finally, the effectiveness of nested sampling is demonstrated on a higher-dimensional problem, in the presence of a complex dynamic model and significant model uncertainty.
González-Garay A, Pozo C, Galán-Martín Á, et al., 2019, Assessing the performance of UK universities in the field of chemical engineering using data envelopment analysis, Education for Chemical Engineers, Vol: 29, Pages: 29-41, ISSN: 1749-7728
University rankings have become an important tool to compare academic institutions within and across countries. Yet, they rely on aggregated scores based on subjective weights which render them sensitive to experts’ preferences and not fully transparent to final users. To overcome this limitation, we apply Data Envelopment Analysis (DEA) to evaluate UK universities in the field of chemical engineering as a case study, using data retrieved from two national rankings. DEA is a non-parametric approach developed for the multi-criteria assessment of entities that avoids the use of subjective weightings and aggregated scores; this is accomplished by calculating an efficiency index, on the basis of which universities can be classified as either ‘efficient’ or ‘inefficient’. Our analysis shows that the Higher Education Institutions (HEI) occupying the highest positions in the chemical engineering rankings might not be the most efficient ones, and vice versa, which highlights the need to complement the use of rankings with other analytical tools. Overall, DEA provides further insight into the assessment of HEIs, allowing institutions to better understand their weaknesses and strengths, while pinpointing sources of inefficiencies where improvement efforts must be directed.
Wang Y, Markides CN, Chachuat B, 2019, Optimization-based investigations of a two-phase thermofluidic oscillator for low-grade heat conversion, BMC Chemical Engineering, Vol: 1, ISSN: 2524-4175
BackgroundThe non-inertive-feedback thermofluidic engine (NIFTE) is a two-phase thermofluidic oscillator capable of utilizing heat supplied at a steady temperature to induce persistent thermal-fluid oscillations. The NIFTE is appealing in its simplicity and ability to operate across small temperature differences, reported as low as 30 ∘C in early prototypes. But it is also expected that the NIFTE will exhibit low efficiencies relative to conventional heat recovery technologies that target higher-grade heat conversion. Mathematical modeling can help assess the full potential of the NIFTE technology.ResultsOur analysis is based on a nonlinear model of the NIFTE, which we extend to encompass irreversible thermal losses. Both models predict that a NIFTE may exhibit multiple cyclic steady states (CSS) for certain design configurations, either stable or unstable, a behavior that had never been hypothesized. A parametric analysis of the main design parameters of the NIFTE is then performed for both models. The results confirm that failure to include the irreversible thermal losses in the NIFTE model can grossly overpredict its performance, especially over extended parameter domains. Lastly, we use the NIFTE model with irreversible thermal losses to assess the optimization potential of this technology by conducting a multi-objective optimization. Our results reveal that most of the optimization potential is achievable via targeted modifications of three design parameters only. The Pareto frontier between exergetic efficiency and power output is also found to be highly sensitive to these optimized parameters.ConclusionsThe NIFTE is of practical relevance to a range of applications, including the development of solar-driven pumps to support small-holder irrigation in the developing world. Given its low capital cost, potential improvements greater than 50% in efficiency or power output are significant for the uptake of this technology. Conventional heat recovery technologies a
Ogunnaike BA, Chachuat B, 2019, Preface to the Dominique Bonvin Festschrift, INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH, Vol: 58, Pages: 13421-13422, ISSN: 0888-5885
Bernardi A, Gomoescu L, Wang J, et al., 2019, Kinetic Model Discrimination for Methanol and DME Synthesis using Bayesian Estimation, 12th International-Federation-of-Automatic-Control (IFAC) Symposium on Dynamics and Control of Process Systems including Biosystems (DYCOPS), Publisher: ELSEVIER SCIENCE BV, Pages: 335-340, ISSN: 2405-8963
Chanona EADR, Alves Graciano JE, Bradford E, et al., 2019, Modifier-Adaptation Schemes Employing Gaussian Processes and Trust Regions for Real-Time Optimization, 12th International-Federation-of-Automatic-Control (IFAC) Symposium on Dynamics and Control of Process Systems including Biosystems (DYCOPS), Publisher: ELSEVIER, Pages: 52-57, ISSN: 2405-8963
Chachuat B, Bernard O, Normey-Rico JE, 2019, 12th IFAC Symposium on Dynamics and Control of Process Systems, including Biosystems DYCOPS 2019 Florianopolis, Brazil, 23-26 April 2019 FOREWORD, 12th International-Federation-of-Automatic-Control (IFAC) Symposium on Dynamics and Control of Process Systems including Biosystems (DYCOPS), Publisher: ELSEVIER, Pages: VI-VI, ISSN: 2405-8963
Villanueva ME, Feng X, Paulen R, et al., 2019, Convex Enclosures for Constrained Reachability Tubes, 12th International-Federation-of-Automatic-Control (IFAC) Symposium on Dynamics and Control of Process Systems including Biosystems (DYCOPS), Publisher: ELSEVIER, Pages: 118-123, ISSN: 2405-8963
Rodriguez-Vallejo DF, Galan-Martin A, Guillen-Gosalbez G, et al., 2019, Targeting of sustainable chemical processes using data envelopment analysis: application to liquid fuels for transportation, Editors: Kiss, Zondervan, Lakerveld, Ozkan, Publisher: ELSEVIER SCIENCE BV, Pages: 331-336, ISBN: 978-0-12-819939-8
Mutran VM, Ribeiro CO, Nascimento COA, et al., 2019, Risk-conscious approach to optimizing bioenergy investments in the Brazilian sugarcane industry, Editors: Kiss, Zondervan, Lakerveld, Ozkan, Publisher: ELSEVIER SCIENCE BV, Pages: 361-366, ISBN: 978-0-12-819939-8
Sun M, Villanueva M, Pistikopoulos EN, et al., 2019, Methodology for robust multi-parametric control in linear continuous-time systems, Journal of Process Control, Vol: 73, Pages: 58-74, ISSN: 0959-1524
This paper presents an extension of the recent multi-parametric (mp-)NCO-tracking methodology by Sun et al. [Comput. Chem.Eng. 92:64-77, 2016] for the design of robust multi-parametric controllers for constrained continuous-time linear systems in thepresence of uncertainty. We propose a robust-counterpart formulation and solution of multi-parametric dynamic optimization (mp-DO), whereby the constraints are backed-offbased on a worst-case propagation of the uncertainty using either interval analysis orellipsoidal calculus and an ancillary linear state feedback. We address the case of additive uncertainty, and we discuss approachesto dealing with multiplicative uncertainty that retain tractability of the mp-NCO-tracking design problem, subject to extra conser-vativeness. In order to assist with the implementation of these controllers, we also investigate the use of data classifiers based ondeep learning for approximating the critical regions in continuous-time mp-DO problems, and subsequently searching for a criticalregion during on-line execution. We illustrate these developments with the case studies of a fluid catalytic cracking (FCC) unit anda chemical reactor cascade.
Bernardi A, Graciano JEA, Chachuat B, 2019, Production of chemicals from syngas: an enviro-economic model-based investigation, Editors: Kiss, Zondervan, Lakerveld, Ozkan, Publisher: ELSEVIER SCIENCE BV, Pages: 367-372, ISBN: 978-0-12-819939-8
Houska B, Chachuat B, 2019, Global optimization in Hilbert space, Mathematical Programming, Vol: 173, Pages: 221-249, ISSN: 0025-5610
We propose a complete-search algorithm for solving a class of non-convex, possibly infinite-dimensional, optimization problems to global optimality. We assume that the optimization variables are in a bounded subset of a Hilbert space, and we determine worst-case run-time bounds for the algorithm under certain regularity conditions of the cost functional and the constraint set. Because these run-time bounds are independent of the number of optimization variables and, in particular, are valid for optimization problems with infinitely many optimization variables, we prove that the algorithm converges to an (Formula presented.)-suboptimal global solution within finite run-time for any given termination tolerance (Formula presented.). Finally, we illustrate these results for a problem of calculus of variations.
Rodríguez-Vallejo DF, Galán-Martín Á, Guillén-Gosálbez G, et al., 2018, Data envelopment analysis approach to targeting in sustainable chemical process design: Application to liquid fuels, AIChE Journal, ISSN: 0001-1541
© 2018 American Institute of Chemical Engineers This article presents a framework for combining data envelopment analysis with process systems engineering tools, aiming to improve the sustainability of chemical processes. Given a set of chemical processes, each characterized by performance indicators, the framework discriminates between efficient and inefficient processes in regard to these indicators. We develop an approach to quantifying the closest targets for an inefficient process to become efficient, while preventing unrealistic targets by accounting for thermodynamic limitations represented as mass and energy flow constraints. We demonstrate the capabilities of the framework by assessing a methanol production process with captured CO2 and fossil-based H2, in comparison to 10 alternatives. The methanol fuel is found to be suboptimal in comparison with other fuels. Making it competitive would require a significant (unrealistic in the short term) reduction in H2 price. Alternatively, the methanol fuel could become competitive upon combining fossil-based H2 with sustainably produced H2 via wind-powered electrolysis. © 2018 American Institute of Chemical Engineers AIChE J, 00: 000–000, 2018.
Graciano JEA, Chachuat B, Alves RMB, 2018, Enviro-economic assessment of thermochemical polygeneration from microalgal biomass, Journal of Cleaner Production, Vol: 203, Pages: 1132-1142, ISSN: 0959-6526
This paper presents a model-based assessment of the thermochemical conversion of microalgal biomass into Fischer-Tropsch liquids, hydrogen and electricity through polygeneration. Two novel conceptual plants are investigated, which are both comprised of the same operation units (gasification, water-gas shift, Fischer-Tropsch synthesis, upgrading, separation, Rankine cycle and gas turbines) and mainly differ in the location of the water-gas-shift unit. Both plants are found to present a carbon efficiency greater than conventional biomass-to-liquid processes. The most profitable plants in terms of the saleable products yields ca. 0.23 m3 (1.4 bbl) of liquid transportation fuels (gasoline, kerosene and diesel), ca. 16 kg of hydrogen (716.8 scm), and ca. 1.55 × 109 J (430 kW·h) of electricity per 1000 kg of dried microalgae. The corresponding displaced fossil fuels could offset the carbon emissions by 0.56 kg of carbon dioxide for every kg of processed dried microalgae. Nevertheless, predicted break-even prices are lower than 40 USD per ton of dried microalgae in the base case scenario, which is at least 10 times cheaper than the current best scenario for microalgal biomass production. These low prices are a major impediment to the viability of these thermochemical polygeneration plants, albeit presenting a good potential toward cleaner liquid fuel production.
Villanueva ME, Chachuat B, Houska B, 2018, Robust optimal feedback control for periodic biochemical processes, 10th IFAC Symposium on Advanced Control of Chemical Processes ADCHEM 2018, Publisher: IFAC Secretariat, Pages: 756-761, ISSN: 2405-8963
This paper is concerned with optimal feedback control synthesis for periodic processes with economic control objectives. The focus is on tube-based methods which optimize over robust forward invariant tubes (RFITs) in order to determine the nonlinear feedback law. The main contribution is an approach to conservatively approximating this set-based periodic feedback control optimization problem by a tractable optimal control problem, which can be solved with existing optimal control solvers. The approach is applied to an uncertain periodic biochemical production process, where the objective is to maximize the profit subject to robust safety constraints.
Wang Y, Markides CN, Chachuat B, 2018, Optimization-based investigations of a thermofluidic engine for low-grade heat recovery, IFAC-PapersOnLine, Vol: 51, Pages: 690-695, ISSN: 2405-8963
This paper presents an analysis of the non-inertive-feedback thermofluidic engine (NIFTE) under cyclic steady-state conditions. The analysis is based on a nonlinear model of NIFTE that had previously been validated experimentally, and applies an optimization-based approach to detect the cyclic steady states (CSS). The stability of the CSS is furthermore determined by analyzing their monodromy matrix. It is found that NIFTE can exhibit multiple CSS for certain values of the design parameters, which may be either stable or unstable, a result that had not been reported before. Subsequently, a parametric study is conducted by varying key design parameters, revealing that higher efficiencies could be achieved by controlling the engine at different CSS, including unstable ones. Lastly, the paper investigates the trade-offs between efficiency and work output in NIFTE.
Peric N, Paulen R, Villanueva ME, et al., 2018, Set-membership nonlinear regression approach to parameter estimation, Journal of Process Control, Vol: 70, Pages: 80-95, ISSN: 0959-1524
This paper introducesset-membership nonlinear regression(SMR), a new approach to nonlinearregression under uncertainty. The problem is to determine the subregion in parameter spaceenclosing all (global) solutions to a nonlinear regression problem in the presence of boundeduncertainty on the observed variables. Our focus is on nonlinear algebraic models. We investigatethe connections of SMR with (i) the classical statistical inference methods, and (ii) the usual set-membership estimation approach where the model predictions are constrained within boundedmeasurement errors. We also develop a computational framework to describe tight enclosures ofthe SMR regions using semi-infinite programming and complete-search methods, in the form oflikelihood contour and polyhedral enclosures. The case study of a parameter estimation problemin microbial growth is presented to illustrate various theoretical and computational aspects of theSMR approach.
Pitt JA, Gomoescu L, Pantelides CC, et al., 2018, Critical assessment of parameter estimation methods in models of biological oscillators, IFAC-PapersOnLine, Vol: 51, Pages: 72-75, ISSN: 2405-8963
Many biological systems exhibit oscillations in relation to key physiological or cellular functions, such as circadian rhythms, mitosis and DNA synthesis. Mathematical modelling provides a powerful approach to analysing these biosystems. Applying parameter estimation methods to calibrate these models can prove a very challenging task in practice, due to the presence of local solutions, lack of identifiability, and risk of overfitting. This paper presents a comparison of three state-of-the-art methods: frequentist, Bayesian and set-membership estimation. We use the Fitzhugh-Nagumo model with synthetic data as a case study. The computational performance and robustness of these methods is discussed, with a particular focus on their predictive capability using cross-validation.
Graciano JEA, Chachuat B, Alves RMB, 2018, Conversion of CO2-Rich Natural Gas to Liquid Transportation Fuels via Trireforming and Fischer-Tropsch Synthesis: Model-Based Assessment, INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH, Vol: 57, Pages: 9964-9976, ISSN: 0888-5885
This paper presents a model-based analysis of a process coupling trireforming and Fischer–Tropsch technologies for the production of liquid fuels from CO2-rich natural gas. The process also includes an upgrading section based on hydrocracking, a separation section, a water gas shift unit, and a Rankine cycle unit for recovering the excess thermal energy produced by the Fischer–Tropsch reactor. Simulations are carried out in the process simulator Aspen Plus using standard unit operation models where applicable, while modeling the nonconventional units, such as the Fischer–Tropsch and hydrocracking reactors, using Aspen Custom Modeler. The proposed process could achieve a carbon conversion efficiency upward of 50% in the analyzed scenario, despite a natural gas feedstock with 30 mol % CO2. The analysis also reveals that the plant-wide electricity consumption could be covered nearly entirely by the Rankine cycle unit, enabling significant cost savings alongside a reduction of the overall global warming potential by about 10% in this specific case study. Finally, the results of a detailed economic assessment indicate that cheap natural gas is a prerequisite to the economic viability of the process, which would remain attractive in the current US scenario, yet presents a major impediment for its deployment in Brazil.
Quek V, Shah N, Chachuat B, 2018, Modeling for design and operation of high-pressure membrane contactors in natural gas sweetening, Chemical Engineering Research and Design, Vol: 132, Pages: 1005-1019, ISSN: 1744-3598
Over the past decade, membrane contactors (MBC) for CO2 absorption have been widely recognized for their large intensification potential compared to conventional absorption towers. MBC technology uses microporous hollow-fiber membranes to enable effective gas and liquid mass transfer, without the two phases dispersing into each other. The main contribution of this paper is the development and verification of a predictive mathematical model of high-pressure MBC for natural gas sweetening applications, based on which model-based parametric analysis and optimization can be conducted. The model builds upon insight from previous modeling studies by combining 1-d and 2-d mass-balance equations to predict the CO2 absorption flux, whereby the degree of membrane wetting itself is calculated from the knowledge of the membrane pore-size distribution. The predictive capability of the model is tested for both lab-scale and pilot-scale MBC modules, showing a close agreement of the predictions with measured CO2 absorption fluxes at various gas and liquid flowrates, subject to a temperature correction to account for the heat of reaction in the liquid phase. The results of a model-based analysis confirm the advantages of pressurized MBC operation in terms of CO2 removal efficiency. Finally, a comparison between vertical and horizontal modes of operation shows that the CO2 removal efficiency in the latter can be vastly superior as it is not subject to the liquid static head and remediation strategies are discussed.
Chachuat B, Sager S, 2018, Introduction to the Special Issue on Global and Robust Optimization of Dynamic Systems, Optimal Control Applications and Methods, Vol: 39, Pages: 425-426, ISSN: 0143-2087
Graciano JEA, Giudici R, Alves RMB, et al., 2018, A simple PLS-based approach for the construction of compact surrogate models, Computer Aided Chemical Engineering, Pages: 421-426
© 2018 Elsevier B.V. This work describes a simple algorithm based on partial least square (PLS) to enable the construction of surrogate models using a single tuning parameter. The proposed algorithm is illustrated with the case study of a membrane module for natural gas sweetening, where a mechanistic model is used as data generator. The effect of the tuning parameter is analysed, and it is shown that this parameter captures the trade-off between the surrogates’ accuracy and their complexity (number of terms). The algorithm performance is also compared with four different approaches from the literature, showing a similar performance.
Graciano JEA, Alves RMB, Chachuat B, 2018, Surrogate-based Optimization Approach to Membrane Network Synthesis in Gas Separation, Editors: Friedl, Klemes, Radl, Varbanov, Wallek, Publisher: ELSEVIER SCIENCE BV, Pages: 597-602
Peric ND, Villanueva ME, Chachuat B, 2017, Sensitivity analysis of uncertain dynamic systems using set-valued integration, SIAM Journal on Scientific Computing, Vol: 39, Pages: A3014-A3039, ISSN: 1064-8275
We present an extension of set-valued integration to enable efficient sensitivity analysis of parameter-dependent ordinary differential equation (ODE) systems, using both the forward and adjoint methods. The focus is on continuous-time set-valued integration, whereby auxiliary ODE systems are derived whose solutions describe high-order inclusions of the parametric trajectories in the form of polynomial models. The forward and adjoint auxiliary ODE systems treat the parameterization error of the original differential variables as a time-varying uncertainty, and propagate the sensitivity bounds forward and backward in time, respectively. This construction enables building on the sensitivity analysis capabilities of state-of-the-art solvers, such as CVODES in the SUNDIALS suite. Several numerical case studies are presented to assess the performance and accuracy of these set-valued sensitivity integrators.
Feng X, Villanueva ME, Chachuat B, et al., 2017, Branch-and-Lift algorithm for obstacle avoidance control, IEEE 56th Annual Conference on Decision and Control (CDC), Publisher: IEEE, ISSN: 0743-1546
Obstacle avoidance problems are a class of non-convex optimal control problems for which derivative-based optimization algorithms often fail to locate global minima. The goal of this paper is to provide a tutorial on how to apply Branch & Lift algorithms, a novel class of global optimal control methods, for solving such obstacle avoidance problems to global optimality. The focus of the technical developments is on how Branch & Lift methods can exploit the particular structure of Dubin models, which can be used to model a variety of practical obstacle avoidance problems. The global convergence properties of Branch & Lift in the context of obstacle avoidance is discussed from a theoretical as well as a practical perspective by applying it to a tutorial example.
Bernardi A, Nikolaou A, Meneghesso A, et al., 2017, Semi-empirical modeling of microalgae photosynthesis in different acclimation states - Application to N. gaditana., Journal of Biotechnology, Vol: 259, Pages: 63-72, ISSN: 0168-1656
The development of mathematical models capable of accurate predictions of the photosynthetic productivity of microalgae under variable light conditions is paramount to the development of large-scale production systems. The process of photoacclimation is particularly important in outdoor cultivation systems, whereby seasonal variation of the light irradiance can greatly influence microalgae growth. This paper presents a dynamic model that captures the effect of photoacclimation on the photosynthetic production. It builds upon an existing semi-empirical model describing the processes of photoproduction, photoregulation and photoinhibition via the introduction of acclimation rules for key parameters. The model is calibrated against a dataset comprising pulsed amplitude modulation fluorescence, photosynthesis rate, and antenna size measurements for the microalga Nannochloropsis gaditana in several acclimation states. It is shown that the calibrated model is capable of accurate predictions of fluorescence and respirometry data, both in interpolation and in extrapolation.
Puchongkawarin C, Vaupel Y, Guo M, et al., 2017, Towards the synthesis of wastewater recovery facilities using enviroeconomic optimization, The Water-Food-Energy Nexus - Processes, Technologies, and Challenges, Editors: Mujtaba, Srinivasan, Elbashir, ISBN: 9781498760843
The wastewater treatment industry is undergoing a major shift towards a proactive interest in recovering materials and energy from wastewater streams, driven by both economic incentives and environmental sustainability. With the array of available treatment technologies and recovery options growing steadily, systematic approaches to determining the inherent trade-off between multiple economic and environmental objectives become necessary, namely enviroeconomic optimization.The main objective of this chapter is to present one such methodology based on superstructure modeling and multi-objective optimization, where the main environmental impacts are quantified using life cycle assessment (LCA). This methodology is illustrated with the case study of a municipal wastewater treatment facility. The results show that accounting for LCA considerations early on in the synthesis problem may lead to dramatic changes in the optimal process configuration, therebysupporting LCA integration into decision-making tools for wastewater treatment alongside economical selection criteria.
Sun M, Villanueva ME, Pistikopoulos EN, et al., 2017, Robust multi-parametric control of continuous-time linear dynamic systems, IFAC-PapersOnLine, Vol: 50, Pages: 4660-4665, ISSN: 2405-8963
We extend a recent methodology called multi-parametric NCO-tracking for the design of parametric controllers for continuous-time linear dynamic systems in the presence of uncertainty The approach involves backing-off the path and terminal state constraints based on a worst-case uncertainty propagation determined using either interval analysis or ellipsoidal calculus. We address the case of additive uncertainty and we discuss approaches to handling multiplicative uncertainty that retain tractability of the mp-NCO-tracking design problem, subject to extra conservatism. These developments are illustrated with the case study of a fluidized catalytic cracking (FCC) unit operated in partial combustion mode.
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