Publications
202 results found
Villanueva M, Paulen R, Houska B, et al., 2013, Enclosing the Reachable Set of Parametric ODEs using Taylor Models and Ellipsoidal Calculus, 23 EUROPEAN SYMPOSIUM ON COMPUTER AIDED PROCESS ENGINEERING, Vol: 32, Pages: 979-984, ISSN: 1570-7946
One of the main bottlenecks of state of the art algorithm for global dynamic optimizationis the computation of enclosures of parametric differential equations (ODEs). Afterreviewing existing techniques based on Taylor model propagation and ellipsoidal calculusfor nonlinear dynamic processes, we introduce a novel algorithm for computing suchstate enclosures. Here, the bounding strategy employs a Taylor series with an ellipsoidalremainder bound. We analyze the convergence properties of the new ODE enclosure forsmall parameter intervals and provide conditions under which higher order convergencecan be proven. Moreover, we discuss implementation details and practical advantages byapplying the method to a numerical test example.
Rajyaguru J, Chachuat B, 2013, Taylor models in deterministic global optimization for large-scale systems with few degrees of freedom, Vol: 32, Pages: 973-978, ISSN: 1570-7946
Many process systems applications comprise large sets of nonlinear model equations, whose participating variables can be split naturally into independent and dependent variable subsets. This structure can be exploited for deterministic global optimization based on a sequential approach, which performs the optimization in the reduced space of independent variables by considering the model as implicit equations. This paper presents a new method for constructing Taylor model estimators of the implicit equation solutions in order to generate tighter lower bounds on the reduced-space optimization problem. The convergence properties of these estimators are analyzed through numerical examples, and the global optimization approach is demonstrated on a numerical case study featuring a discretized PDE system. © 2013 Elsevier B.V.
Nikolaou A, Hartmann P, Bernard O, et al., 2013, A dynamic model coupling photoacclimation and photoinhibition in microalgae, Pages: 351-352
Bompadre A, Mitsos A, Chachuat B, 2012, Convergence analysis of Taylor models and McCormick-Taylor models, Journal of Global Optimization, Vol: 57, Pages: 75-114, ISSN: 1573-2916
This article presents an analysis of the convergence order of Taylor models and McCormick-Taylor models, namely Taylor models with McCormick relaxations as the remainder bounder, for factorable functions. Building upon the analysis of McCormick relaxations by Bompadre and Mitsos (J Glob Optim 52(1):1–28, 2012), convergence bounds are established for the addition, multiplication and composition operations. It is proved that the convergence orders of both qth-order Taylor models and qth-order McCormick-Taylor models are at least q + 1, under relatively mild assumptions. Moreover, it is verified through simple numerical examples that these bounds are sharp. A consequence of this analysis is that, unlike McCormick relaxations over natural interval extensions, McCormick-Taylor models do not result in increased order of convergence over Taylor models in general. As demonstrated by the numerical case studies however, McCormick-Taylor models can provide tighter bounds or even result in a higher convergence rate.
Radivojevic A, Chachuat B, Bonvin D, et al., 2012, Exploration of trade-offs between steady-state and dynamic properties in signaling cycles, PHYSICAL BIOLOGY, Vol: 9, ISSN: 1478-3967
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- Citations: 3
Deshpande SA, Bonvin D, Chachuat B, 2012, DIRECTIONAL INPUT ADAPTATION IN PARAMETRIC OPTIMAL CONTROL PROBLEMS, SIAM Journal on Control and Optimization, Vol: 50, Pages: 1995-2024, ISSN: 1095-7138
This paper deals with input adaptation in dynamic processes in order to guarantee feasible and optimal operation despite the presence of uncertainty. For those optimal control problems having terminal and mixed control-state path constraints, two orthogonal sets of adaptation directions can be distinguished in the input space: the sensitivity-seeking directions, along which a small variation from an optimal nominal solution will not affect the respective active constraints, and the complementary constraint-seeking directions, along which a variation will affect the respective constraints. It follows that selective input adaptation strategies can be defined, namely, adaptation in the sensitivity- and constraint-seeking directions. This paper proves the important result that, for small parametric perturbations, the cost variation resulting from adaptation in the sensitivity-seeking directions (over no input adaptation) is typically smaller than the cost variation due to adaptation in the constraint-seeking directions. It is also established that no selective input adaptation along a sensitivity-seeking direction can reduce the dominant, first-order term in the optimality gap; adaptation along a constraint-seeking direction is necessary to cancel it out. These results are illustrated with two numerical case studies.
Khor CS, Chachuat B, Shah N, 2012, A superstructure optimization approach for water network synthesis with membrane separation-based regenerators, European Symposium of Computer Aided Process Engineering - 21, Publisher: Elsevier, Pages: 48-63, ISSN: 0098-1354
This work addresses the problem of water network synthesis. We propose a superstructure with fixed topology for a water network that consists of three layers, similar to a pooling problem: sources for reuse/recycle; regenerators for contaminants removal; and sinks for acceptance of water for reuse/recycle. The superstructure encompasses multiple freshwater sources, membrane separation-based partitioning regenerators of the industrially favored ultrafiltration and reverse osmosis, and sinks for incineration and deep ocean discharge. A mixed-integer nonlinear program is formulated based on this superstructure to determine the optimal interconnections in terms of total flowrates and contaminant concentrations. The main decisions include determining the split fractions of the source flowrates, extents of regeneration, and mixing ratios of the sources and regenerated streams subject to compliance with the maximum allowable inlet contaminant concentration limits of the sinks and discharge regulations. We also develop linear models for the membrane regenerators that admit a more general expression for the retentate stream concentration based on liquid-phase recovery factors and removal ratios. Computational studies are performed using GAMS/BARON on an industrially significant case study of a petroleum refinery water system. We incorporate linear logical constraints using 0–1 variables that enforce certain design and structural specifications to tighten the model formulation and enhance solution convergence. A globally optimal water network topology is attained that promotes a 27% savings equivalent to about $218,000/year reduction in freshwater use.
Mairet F, Bernard O, Cameron E, et al., 2012, Three-reaction model for the anaerobic digestion of microalgae, Biotechnology and Bioengineering, Vol: 109, Pages: 415-425, ISSN: 1097-0290
Coupling an anaerobic digester to a microalgal culture has received increasing attention as an alternative process for combined bioenergy production and depollution. In this article, a dynamic model for anaerobic digestion of microalgae is developed with the aim of improving the management of such a coupled system. This model describes the dynamics of inorganic nitrogen and volatile fatty acids since both can lead to inhibition and therefore process instability. Three reactions are considered: Two hydrolysis–acidogenesis steps in parallel for sugars/lipids and for proteins, followed by a methanogenesis step. The proposed model accurately reproduces experimental data for anaerobic digestion of the freshwater microalgae Chlorella vulgaris with an organic loading rate of 1 gCOD L−1 d−1. In particular, the three-reaction pathway allows to adequately represent the observed decoupling between biogas production and nitrogen release. The reduced complexity of this model makes it suitable for developing advanced, model-based control and monitoring strategies.
Scott JK, Chachuat B, Barton PI, 2012, Nonlinear convex and concave relaxations for the solutions of parametric ODEs, Optimal Control Applications & Methods, Vol: 34, Pages: 145-163, ISSN: 1099-1514
Convex and concave relaxations for the parametric solutions of ordinary differential equations (ODEs) are central to deterministic global optimization methods for nonconvex dynamic optimization and open-loop optimal control problems with control parametrization. Given a general system of ODEs with parameter dependence in the initial conditions and right-hand sides, this work derives sufficient conditions under which an auxiliary system of ODEs describes convex and concave relaxations of the parametric solutions, pointwise in the independent variable. Convergence results for these relaxations are also established. A fully automatable procedure for constructing an appropriate auxiliary system has been developed previously by the authors. Thus, the developments here lead to an efficient, automatic method for computing convex and concave relaxations for the parametric solutions of a very general class of nonlinear ODEs. The proposed method is presented in detail for a simple example problem.
Seong Khor C, Chachuat B, Shah N, 2012, Optimal water network synthesis with membrane separation-based regenerators, Vol: 30, Pages: 36-40, ISSN: 1570-7946
This article is concerned with the water network synthesis problem. We propose a superstructure that consists of three layers similar to a pooling problem: sources for reuse/recycle; regenerators for contaminants removal; and sinks for acceptance of water for direct or regeneration-reuse/recycle. The superstructure accounts for membrane separation-based regenerators such as ultrafiltration and reverse osmosis. Linear models are developed for the membrane regenerators. A MINLP is then formulated based on the superstructure to determine the optimal interconnections in terms of total flowrates and contaminant concentrations. Computational experiments are performed using GAMS/BARON on an industrial case study of a petroleum refinery water system. We include model-tightening linear logical constraints to enhance solution convergence, resulting in a globally optimal water network that promotes 27% savings in freshwater use. © 2012 Elsevier B.V.
Gros S, Chachuat B, 2012, Methodology for Emergency Shut-Down of Multi-Megawatt Wind Turbine Generators, 11th International Symposium on Process Systems Engineering (PSE), Publisher: ELSEVIER SCIENCE BV, Pages: 1251-1255, ISSN: 1570-7946
Chachuat B, Villanueva M, 2012, Bounding the Solutions of Parametric ODEs: When Taylor Models Meet Differential Inequalities, 22nd European Symposium on Computer Aided Process Engineering (ESCAPE), Publisher: ELSEVIER SCIENCE BV, Pages: 1307-1311, ISSN: 1570-7946
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- Citations: 14
Khor CS, Chachuat B, Shah N, 2012, Optimal water network synthesis with detailed membrane-based regenerator models, 11th International Symposium on Process Systems Engineering (PSE), Publisher: ELSEVIER SCIENCE BV, Pages: 1457-1461, ISSN: 1570-7946
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- Citations: 1
Khor CS, Chachuat B, Shah N, 2012, Optimal water network synthesis with membrane separation-based regenerators, 22nd European Symposium on Computer Aided Process Engineering (ESCAPE), Publisher: ELSEVIER SCIENCE BV, Pages: 36-40, ISSN: 1570-7946
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- Citations: 1
Marchetti A, Gopalakrishnan A, Chachuat B, et al., 2011, Robust Real-Time Optimization of a Solid Oxide Fuel Cell Stack, JOURNAL OF FUEL CELL SCIENCE AND TECHNOLOGY, Vol: 8, ISSN: 1550-624X
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- Citations: 15
Sahlodin AM, Chachuat B, 2011, Discretize-then-relax approach for convex/concave relaxations of the solutions of parametric ODEs, APPLIED NUMERICAL MATHEMATICS, Vol: 61, Pages: 803-820, ISSN: 0168-9274
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- Citations: 29
Sahlodin AM, Chachuat B, 2011, Convex/concave relaxations of parametric ODEs using Taylor models, COMPUTERS & CHEMICAL ENGINEERING, Vol: 35, Pages: 844-857, ISSN: 0098-1354
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- Citations: 48
Podmajerský M, Chachuat B, Fikar M, 2011, Integrated two-time-scale scheme for real-time optimisation of batch processes, IFAC Proceedings Volumes (IFAC-PapersOnline), Vol: 44, Pages: 11405-11410, ISSN: 1474-6670
This paper studies a problem of uncertainties in optimal process control of batch processes. We assume that several batches are processed and that run-to-run optimisation can be performed. We propose an integrated two-time scale that optimises between batches to meet terminal constraints and within batches to improve calculated optimal trajectory for model-mismatch. The results obtained from a batch reactor control indicate that the resulting scheme has better convergence properties than individual schemes dealing either with terminal constraints adaptation or with in-batch neighbouring-extremal (NE) control. © 2011 IFAC.
Khor CS, Giarola S, Chachuat B, et al., 2011, An optimization-based framework for process planning under uncertainty with risk management, Pages: 449-450
Cameron E, Mairet F, Bernard O, et al., 2011, Anaerobic digestion of microalgae: Identification for optimization and control, IFAC Proceedings Volumes (IFAC-PapersOnline), Vol: 44, Pages: 5052-5057, ISSN: 1474-6670
Coupling an anaerobic digester to a microalgal culture is currently considered one of the most promising avenues towards the production of renewable bioenergy, either in the form of biodiesel or biogas. Accurate mathematical models are crucial tools to assess the potential of such coupled biotechnological processes and help optimize their design, operation and control. This paper focuses on the compartment of anaerobic digestion of microalgae. Using experimental data for the anaerobic digestion of Chlorella vulgaris, a grey-box model is developed that allows good prediction capabilities and retains low complexity. The proposed methodology proceeds in two steps, namely a structural and a parametric identification steps. The fitted model is then used to conduct preliminary optimization for the production of biogas from Chlorella vulgaris. The results provide some insight into the potential for bioenergy production from the digestion of microalgae and, more generally, the coupled process. © 2011 IFAC.
Rodger EA, Chachuat B, 2011, Design methodology of modifier adaptation for on-line optimization of uncertain processes, IFAC Proceedings Volumes (IFAC-PapersOnline), Vol: 44, Pages: 4113-4118, ISSN: 1474-6670
This paper is concerned with the on-line optimization of uncertain processes using the modifier-adaptation technology. In this approach, an optimization model is solved repeatedly and the available measurements are used to correct the values and gradients of the predicted outputs in that model. Following the paradigm of dual control, a successful modifier-adaptation scheme must reconcile two conflicting objectives, namely optimizing the process and obtaining accurate gradient information. During the on-line execution phase, a certain quality of the gradient estimates is enforced through additional constraints in the optimization problem. Then, a systematic off-line procedure is developed for the design of these constraints. © 2011 IFAC.
Sahlodin AM, Chachuat B, 2011, Tight Convex and Concave Relaxations via Taylor Models for Global Dynamic Optimization, Computer Aided Chemical Engineering, Vol: 29, Pages: 537-541, ISSN: 1570-7946
This article presents a discretize-then-relax method to construct convex/concave bounds for the solutions of parametric nonlinear ODEs. It builds upon Taylor model methods for verified ODE solution. To enable the propagation of convex/concave state bounds, a new type of Taylor model is introduced, whereby the remainder term consists of convex/concave bounds in lieu of the usual interval bounds. At each time step, a two-phase procedure is applied for the verified integration. A priori convex/concave bounds that are valid over the entire time step are calculated in the first phase, then pointwise-in-time convex/concave bounds at the end of the time step are obtained in the second phase. The algorithm is demonstrated by the case study of a Lotka-Volterra system. © 2011 Elsevier B.V.
Chachuat B, 2011, Tight LP relaxations for optimization problems with nonlinear parametric ODEs, Pages: 53-54
Sahlodin AM, Chachuat B, 2011, Tight Convex and Concave Relaxations via Taylor Models for Global Dynamic Optimization, 21st European Symposium on Computer Aided Process Engineering (ESCAPE-21), Publisher: ELSEVIER SCIENCE BV, Pages: 537-541, ISSN: 1570-7946
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- Citations: 1
Marchetti AG, Chachuat B, Bonvin D, 2010, A Dual Modifier Adaptation Approach for Real-Time Optimization, Journal of Process Control, Vol: 20, Pages: 1027-1037
For good performance in practice, real-time optimization schemes need to be able to deal with the inevitable plant-model mismatch problem. Unlike the two-step schemes combining parameter estimation and optimization, the modifier-adaptation approach does not estimate the model parameters on-line. Instead, it uses information regarding the constrained variables and selected gradients to improve plant operation. The dual modifier-adaptation approach presented in this paper drives the process towards optimality, while paying attention to the accuracy of the estimated gradients. The gradients are estimated from successive operating points generated by the optimization algorithm. The novelty regards the development of an upper bound on the norm of the gradient errors, which is used as a constraint when determining the next operating point. The proposed approach is demonstrated via the numerical simulation of both an unconstrained and a constrained problem.
Chachuat B, Mitsos A, Barton PI, 2010, Optimal Start-up of Microfabricated Power Generation Processes Employing Fuel Cells, Optimal Control Applications and Methods, Vol: 31, Pages: 471-495
Microfabricated fuel cell systems have the potential to outperform batteries for man-portable power generation. Because many electronic devices operate at various loads, with frequent start-ups and shut-downs, transient aspects are highly important and must be considered thoroughly. In this paper, the focus is on the optimal start-up of microfabricated fuel cell systems using numerical open-loop optimal control. For start-up purposes, a small rechargeable battery is used to provide the energy needed to heat up the fuel cell stack and meet the power demand when the fuel cell is unavailable or can only satisfy part of the demand. The objective of the start-up problem is to bring the system to a desired operating point with a minimal total mass of the system (battery and fuels), while meeting the nominal power demand at any time and satisfying the operational restrictions. The model for the fuel cell stack consists of partial differential-algebraic equations with multiple time scales and numerical techniques that exploit a separation of these time scales are used for efficient and reliable integration of the state and sensitivity equations. A case study of a microfabricated power generation system employing a high-temperature solid-oxide fuel cell and using ammonia and butane as fuels is presented.
Chachuat B, 2010, Introduction to the special issue on optimal process control, Optimal Control Applications and Methods, Vol: 31, Pages: 391-392
Deshpande S, Bonvin D, Chachuat B, 2010, Selective input adaptation in parametric optimal control problems with path constraints, IFAC Proceedings Volumes (IFAC-PapersOnline), Vol: 43, Pages: 1320-1325, ISSN: 1474-6670
This paper is concerned with input adaptation in dynamic processes in order to guarantee feasible and optimal operation despite the presence of uncertainty. For optimal control problems having mixed control-state constraints, two sets of directions can be distinguished in the input function space: the so-called sensitivity-seeking directions, along which a small input variation does not affect the active constraints, and the complementary constraint-seeking directions, along which an input variation does affect the respective constraints. Two selective input adaptation scenarios can be defined, namely, adaptation along each set of input directions. This paper proves the important result that the cost variation due to the adaptation along the sensitivity-seeking directions is typically smaller than that due to the adaptation along the constraint-seeking directions. © 2010 IFAC.
Sahlodin AM, Chachuat B, 2010, Discretize-Then-Relax Approach For State Relaxations In Global Dynamic Optimization, 20th European Symposium on Computer Aided Process Engineering (ESCAPE), Publisher: ELSEVIER SCIENCE BV, Pages: 427-432, ISSN: 1570-7946
This paper presents a discretize-then-relax approach to construct convex/concave bounds for the solutions of a wide class of parametric nonlinear ODEs. The procedure builds upon interval-based techniques implemented in state-of-the-art validated ODE solvers and uses McCormick's relaxation technique to propagate the convex/concave bounds. At each time step, a two-phase procedure is applied: a priori convex/concave bounds that are valid over the entire time step are calculated in the first phase; then, pointwise-in-time convex/concave bounds at the end of the time step are obtained in the second phase. This approach is implemented in an object-oriented manner using templates and operator overloading. It is demonstrated by a case study of a Lotka-Volterra system.
Deshpande S, Bonvin D, Chachuat B, 2010, Selective Input Adaptation in Parametric Optimal Control Problems involving Terminal Constraints, American Control Conference, Publisher: IEEE, Pages: 4782-4787, ISSN: 0743-1619
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