151 results found
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, 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.
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.
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.
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.
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.
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
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.
Marchetti A, Chachuat B, Bonvin D, 2009, Real-time optimization with estimation of experimental gradients, IFAC Proceedings Volumes (IFAC-PapersOnline), Vol: 7, Pages: 524-529, ISSN: 1474-6670
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 uses experimental gradient information and does not require the model parameters to be estimated on-line. 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 lies in 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 in simulation via the real-time optimization of a continuous reactor.
Chachuat B, Srinivasan B, Bonvin D, 2009, Adaptation strategies for real-time optimization, COMPUTERS & CHEMICAL ENGINEERING, Vol: 33, Pages: 1557-1567, ISSN: 0098-1354
Mitsos A, Chachuat B, Barton PI, 2009, Towards global bilevel dynamic optimization, JOURNAL OF GLOBAL OPTIMIZATION, Vol: 45, Pages: 63-93, ISSN: 0925-5001
Marchetti A, Chachuat B, Bonvin D, 2009, Modifier-Adaptation Methodology for Real-Time Optimization, INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH, Vol: 48, Pages: 6022-6033, ISSN: 0888-5885
Michalik C, Chachuat B, Marquardt W, 2009, Incremental Global Parameter Estimation in Dynamical Systems, INDUSTRIAL & ENGINEERING CHEMISTRY RESEARCH, Vol: 48, Pages: 5489-5497, ISSN: 0888-5885
Chachuat B, 2009, Optimal Design and Steady-State Operation, Pages: 199-222
Gros S, Srinivasan B, Chachuat B, et al., 2009, Neighbouring-extremal control for singular dynamic optimisation problems. Part I: single-input systems, INTERNATIONAL JOURNAL OF CONTROL, Vol: 82, Pages: 1099-1112, ISSN: 0020-7179
Gros S, Chachuat B, Bonvin D, 2009, Neighbouring-extremal control for singular dynamic optimisation problems. Part II: multiple-input systems, INTERNATIONAL JOURNAL OF CONTROL, Vol: 82, Pages: 1193-1211, ISSN: 0020-7179
Deshpande S, Chachuat B, Bonvin D, 2009, Parametric Sensitivity of Path-Constrained Optimal Control: Towards Selective Input Adaptation, American Control Conference 2009, Publisher: IEEE, Pages: 349-+, ISSN: 0743-1619
Mitsos A, Chachuat B, Barton PI, 2009, McCormick-Based Relaxations of Algorithms, SIAM Journal on Optimization, Vol: 20, Pages: 573-601, ISSN: 1052-6234
Theory and implementation for the global optimization of a wide class of algorithms is presented via convex/affine relaxations. The basis for the proposed relaxations is the systematic construction of subgradients for the convex relaxations of factorable functions by McCormick [Math. Prog., 10 (1976), pp. 147-175]. Similar to the convex relaxation, the subgradient propagation relies on the recursive application of a few rules, namely, the calculation of subgradients for addition, multiplication, and composition operations. Subgradients at interior points can be calculated for any factorable function for which a McCormick relaxation exists, provided that subgradients are known for the relaxations of the univariate intrinsic functions. For boundary points, additional assumptions are necessary. An automated implementation based on operator overloading is presented, and the calculation of bounds based on a. ne relaxation is demonstrated for illustrative examples. Two numerical examples for the global optimization of algorithms are presented. In both examples a parameter estimation problem with embedded differential equations is considered. The solution of the differential equations is approximated by algorithms with a fixed number of iterations.
Gros S, Chachuat B, Bonvin D, 2008, NCO tracking for singular control problems using neighboring extremals, IFAC Proceedings Volumes (IFAC-PapersOnline), Vol: 17, ISSN: 1474-6670
A powerful approach for dynamic optimization in the presence of uncertainty is to incorporate measurements into the optimization framework so as to track the necessary conditions of optimality (NCO), the so-called NCO-tracking approach. For nonsingular control problems, this can be done by tracking active constraints along boundary arcs, and using neighboring-extremal (NE) control along interior arcs to force the first-order variation of the NCO to zero. In this paper, an extension of NE control to singular control problems is proposed. The idea is to design NE controllers from successive time differentiations of the first-order variation of the NCO. Based on these results, a NCO-tracking controller that is easily tractable from a real-time optimization perspective is proposed, whose application guarantees that the first-order variation of the NCO converges to zero exponentially. The performance of this NCO-tracking controller is illustrated via the case study of a steered car, a 5th-order two-input dynamical system. Copyright © 2007 International Federation of Automatic Control All Rights Reserved.
Marchetti A, Chachuat B, Bonvin D, 2008, Estimation of experimental gradients for real-time optimization
Mitsos A, Lemonidis P, Bollas GM, et al., 2008, A bilevel framework for process design & operation
Mitsos A, Chachuat B, Barton PI, 2008, Global optimization of algorithms
Radivojevic A, Chachuat B, Bonvin D, et al., 2008, Study of tricyclic cascade networks using dynamic optimization
Yunt M, Chachuat B, Mitsos A, et al., 2008, Designing man-portable power generation systems for varying power demand, AICHE JOURNAL, Vol: 54, Pages: 1254-1269, ISSN: 0001-1541
Chachuat B, Marchetti A, Bonvin D, 2008, Process optimization via constraints adaptation, JOURNAL OF PROCESS CONTROL, Vol: 18, Pages: 244-257, ISSN: 0959-1524
Marchetti A, Chachuat B, Bonvin D, 2008, Real-Time Optimization via Adaptation and Control of the Constraints, 18th European Symposium on Computer Aided Process Engineering (ESCAPE-18), Publisher: ELSEVIER SCIENCE BV, Pages: 393-398, ISSN: 1570-7946
Chachuat B, Barton PI, 2008, Numerical simulation of a class of PDAEs with a separation of time scales, 14th European Conference for Mathematics in Industry, Publisher: SPRINGER-VERLAG BERLIN, Pages: 512-+, ISSN: 1612-3956
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