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September 1989 - present

## Publications

Publications (504)

An important requirement of wastewater treatment plants (WWTPs) is compliance with the local regulations on effluent discharge, which are going to become more stringent in the future. The operation of WWTPs exhibits a trade-off between operational cost and effluent quality, which provides a scope for optimization. Process optimization is usually do...

In real-time optimization, the solution quality depends on the model ability to predict the plant Karush-Kuhn-Tucker (KKT) conditions. In the case of non-parametric plant-model mismatch, one can add input-affine modifiers to the model cost and constraints as is done in modifier adaptation (MA). These modifiers require estimating the plant cost and...

A batch process is characterized by the repetition of time-varying operations of finite duration. Due to this repetition, there are two independent “time” variables, namely, the run time within a batch and the batch index. Accordingly, the optimization objective can be defined for a given batch or over several batches. This chapter formulates the d...

The paper proposes a tracking-error passivity-based control scheme for the asymptotic stabilization of homogeneous reaction systems. The approach uses the concept of vessel extents in the Port-Hamiltonian (PH) framework. Concretely, the extent-based representation that is obtained by linear time-invariant transformation of the reaction model is exp...

Various offset-free economic model predictive control schemes that include a disturbance model and the modifier-adaptation principle have been proposed in recent years. These schemes are able to reach plant optimality asymptotically even in the presence of plant–model mismatch. All schemes are affected by a major issue that is common to all modifie...

In many machine learning applications, one wants to learn the unknown objective and constraint functions of an optimization problem from available data and then apply some technique to attain a local optimizer of the learned model. This work considers Gaussian processes as global surrogate models and utilizes them in conjunction with derivative-fre...

This paper investigates the problem of load-sharing optimization of gas compressors in the presence of uncertainty. The objective is to operate a set of compressor units in an energy-efficient way, while at the same time meeting a varying load demand. The main challenge is the fact that the available models, and in particular the compressor efficie...

This note investigates the computation of extents of reaction from a limited number of state measurements. It is shown that this computation differs depending on whether the transformation to vessel extents is based on the heat or the enthalpy balance. Accordingly, two different ways of implementing these computations are described and compared, wh...

As a real-time optimization technique, modifier adaptation (MA) has gained much significance in recent years. This is mainly due to the fact that MA can deal explicitly with structural plant-model mismatch and unknown disturbances. MA is an iterative technique that is ideally suited to real-life applications. Its two main features are the way measu...

Economic model predictive control formulations that combine online optimizing control with offset-free methodologies such as modifier adaptation have been proposed recently. These new algorithms are able to achieve asymptotic optimal performance despite the presence of plant-model mismatch. However, there is a major requirement stemming from the mo...

For the investigation of complex reaction systems, it has been proposed to decouple the various rate processes using a linear time-invariant transformation that is constructed from knowledge of stoichiometry, reaction enthalpies, inlet compositions and temperatures, and initial conditions, that is, without any kinetic information. The resulting tra...

This paper presents an input parameterization for dynamic optimization that allows reducing the number of decision variables compared to traditional direct methods. A small number of decision variables is likely to be beneficial for various applications such as global optimization and real‐time optimization in the presence of plant‐model mismatch....

This paper addresses the steady-state optimization of continuous processes in the presence of uncertainty in the form of unknown or time-varying model parameters, structural plant-model mismatch, and disturbances. To address these issues, we assume that certain measurements are available in real time, and the question is how the plant inputs can be...

In the presence of plant-model mismatch, the estimation of plant gradients is key to the performance of measurement-based iterative optimization schemes. However, gradient estimation requires time-consuming experiments, wherein the plant is sequentially perturbed in all input directions. To ease this gradient estimation task, it has been proposed t...

This paper describes an optimization strategy for operating solid-oxide fuel-cell systems at optimal efficiency. Specifically, we present the experimental validation of a real-time optimization (RTO) strategy applied to a commercial solid-oxide fuel-cell system. The proposed RTO scheme effectively pushes the system to higher levels of efficiency an...

This position paper is an outcome of discussions that took place at the third FIPSE Symposium in Rhodes, Greece, on June 20−22, 2016 (http://fi-in-pse.org). The FIPSE objective is to discuss open research challenges in topics in Process Systems Engineering (PSE). Here, we discuss the societal and industrial context in which systems thinking and pro...

There still exists a large gap between simulation work and industrial applications in the context of control and optimization of solid-oxide fuel-cell (SOFC) systems. In an effort to bridge this gap, this study describes the experimental implementation of steady-state real-time optimization (RTO) to an SOFC system that consists of both hardware and...

This paper discusses the use of parsimonious input parameterization for the dynamic optimization of reaction systems. This parameterization is able to represent the optimal inputs with only a few parameters. In the context of batch, semi-batch and continuous reactors, the method takes advantage of the concept of extents to allow the analytical comp...

Modeling chemical reaction systems is an important but complex task. The identified kinetic model mustbe able to explain all the underlying rateprocesses such as chemical reactions andheat and mass transfers. Traditionally, the modeling task is carried out using a simultaneous approach, which, for modelprediction,requireshaving model candidatesfora...

The experimental implementation of real-time optimization (RTO) to a commercial solid-oxide fuel-cell (SOFC) system is reported in this paper. The goal of RTO is to maximize the system efficiency at steady state subject to several operating constraints. The proposed RTO strategy is a constraint-adaptation approach, which consists in adding bias cor...

In the context of real-time optimization, modifier-adaptation schemes update the model-based optimization problem by adding first-order correction terms to the cost and constraint functions of the optimization problem. This guarantees meeting the plant first-order optimality conditions upon convergence, despite the presence of parametric and struct...

The steady-state performance of a parametrically or structurally uncertain system can be optimized using iterative real-time optimization methods such as modifier adaptation. Here, we extend a recently proposed second-order modifier-adaptation scheme in two important directions. First, we accelerate its convergence, that is, we reduce the number of...

Modifier adaptation is a real-time optimization (RTO) methodology that uses plant gradient estimates to correct model gradients, thereby driving the plant to optimality. However, obtaining accurate gradient estimates requires costly plant experiments at each RTO iteration. In directional modifier adaptation (DMA), the model gradients are corrected...

Iterative real-time optimization schemes that employ modifier adaptation add bias and gradient correction terms to the model that is used for optimization. These affine corrections lead to meeting the first-order necessary conditions of optimality of the plant despite plant-model mismatch. However, since the added terms do not include curvature inf...

Dynamic optimization plays an important role toward improving the operation of chemical systems, such as batch and semi-batch processes. The preferred strategy to solve constrained nonlinear dynamic optimization problems is to use a so-called direct approach. Nevertheless, based on the problem at hand and the solution algorithm used, direct approac...

Recently, a feasible-side globally convergent modifier-adaptation scheme has been proposed for the real-time optimization of uncertain systems. We show that this scheme is related to proximal-gradient algorithms in numerical optimization and we exploit this relationship to analyze its convergence in the case of inexact gradient information. We also...

For lumped homogeneous reaction systems, this paper presents a kinetic model identification scheme that provides maximum-likelihood parameter estimates and guarantees convergence to global optimality. The use of the extent-based incremental approach allows one to (i) identify each reaction individually, and (ii) reduce the number of parameters to b...

The trend towards high-quality, low-volume chemical production has put more emphasis on batch and semi-batch processing due to its increased operational flexibility. The transient behavior of these processes makes their real-time optimization very challenging. In particular, the large prediction horizons required in shrinking-horizon NMPC increase...

Current and future challenges of optimization in the process industry are discussed. The gap between academic research and industrial workflow is analyzed. Moreover, issues arising from the shift from conventional fossil fuels as both feedstock and energy source to nonconventional feedstocks (shale gas, tar sands, CO2 and biomass) and penetration o...

Experimental assessment or prediction of plant steady state is important for many applications in the area of modeling and operation of continuous processes. For example, the iterative implementation of static real-time optimization requires reaching steady state for each successive operating point, which may be quite time consuming. This paper pre...

This contribution presents an input parameterization for dynamic optimization problems, which allows reducing the number of decision variables compared to traditional direct methods. Firstly, a finite set of plausible arc sequences is postulated. Then, each arc sequence is described by a small number of parameters that include switching times and i...

Optimal operating conditions for a process plant are typically obtained via model-based optimization. However, due to modeling errors, the operating conditions found are often sub-optimal or, worse, they can violate critical process constraints. Hence, model corrections become a necessity and are done by exploiting measured process data. To this en...

Nonlinear model predictive control (NMPC) is an important tool to perform real-time optimization for batch and semi-batch processes. Direct methods are often the methods of choice to solve the corresponding optimal control problems, in particular for large-scale problems (Wächter and Biegler, 2006; Zavala and Biegler, 2009). However, the matrix fac...

Dynamic optimization is an important task in the batch chemical industry. Given a reliable process model, dynamic optimization can be considered as a promising tool for reducing production costs, improving product quality and meeting safety and environmental restrictions. Dynamic optimization methods available in the literature belong to the catego...

Models of chemical reaction systems can be complex as they need to include information regarding the reactions and the mass and heat transfers. The commonly used state variables, namely, concentrations and temperatures, express the interplay between many phenomena. As a consequence, each state variable is affected by several rate processes. On the...

This paper proposes a set of distributed real-time optimization schemes for the steady-state optimization of parametrically and structurally uncertain systems that are composed of multiple interconnected subsystems. These schemes are derived in the framework of modifier adaptation and use uncertain system models of varying complexity. Consequently,...

A batch process is characterized by the repetition of time-varying operations of finite duration. Due to the repetition, there are two independent "time" variables, namely, the run time during a batch and the batch index. Accordingly, the control and optimization objectives can be defined for a given batch or over several batches. This chapter desc...

Nonlinear model predictive control (NMPC) is an important tool for the real-time optimization of batch and semi-batch processes. Direct methods are often the methods of choice to solve the corresponding optimal control problems, in particular for large-scale problems. However, the matrix factorizations associated with large prediction horizons can...

Modifier adaptation enables the real-time optimization (RTO) of plant operation in
the presence of considerable plant-model mismatch. For this, modifier adaptation requires the
estimation of plant gradients, which is experimentally expensive as this might involves several
online experiments. Recently, a directional modifier-adaptation approach has...

We propose a distributed real-time optimization scheme for structurally uncertain systems consisting of multiple interconnected subsystems. In particular, we investigate a novel distributed variant of modifier adaptation that exploits a coordinator and knowledge of interconnection model. This way, each subsystem can compute its optimal inputs using...

The steady-state performance of a parametrically or structurally uncertain system can be optimized using iterative real-time optimization methods such as modifier adaptation (MA). Here, we extend a recently proposed MA scheme in two important and novel directions. First, we accelerate its convergence, i.e., we reduce the number of potentially time-...

Modifier adaptation enables the real-time optimization (RTO) of plant operation in the presence of considerable plant-model mismatch. For this, modifier adaptation requires the estimation of plant gradients, which is experimentally expensive as this might involves several online experiments. Recently, a directional modifier-adaptation approach has...

Modifier adaptation (MA) is an iterative real-time optimization (RTO) method characterized by its ability to enforce plant optimality upon convergence despite the presence of model uncertainty The approach is based on correcting the available model using gradient estimates computed at each iteration. MA uses steady-state measurements and solves a s...

The identification of kinetic models can be simplified via the computation of extents of reaction on the basis of invariants such as stoichiometric balances. In the extent space, one can identify the structure and the parameters of reaction rates individually, which significantly reduces the number of parameters that need to be estimated simultaneo...

Modifier adaptation is a real-time optimization method that has the ability to reach the plant optimum upon convergence despite the presence of uncertainty in the form of plant-model mismatch and disturbances. The approach is based on modifying the cost and constraint functions predicted by the model by means of appropriate first-order correction t...

In the context of static real-time optimization (RTO) of uncertain plants, the standard modifier-adaptation scheme consists in adding first-order correction terms to the cost and constraint functions of a model-based optimization problem. If the algorithm converges, the limit is guaranteed to be a KKT point of the plant. This paper presents a gener...

The one-dimensional tubular reactor model with advection and possibly axial diffusion is the classical model of distributed chemical reaction systems. This system is described by partial differential equations that depend on the time t and the spatial coordinate z. In this article, semi-analytical solutions to these partial differential equations a...

The development of a wide array of process technologies to enable the shift from conventional biological wastewater treatment processes to resource recovery systems is matched by an increasing demand in predictive capabilities. Mathematical models are excellent tools to meet this demand. However, obtaining reliable and fit-for-purpose models remain...

In the chemical industry, a large class of processes involving reactions can be described by partial differential equations that depend on time and on one or more spatial coordinates. Examples of such distributed reaction systems are tubular reactors and reactive separation columns. As in lumped reaction systems, the interaction between the differe...

This paper investigates the relations between three different properties, which are of importance in continuous-time optimal control problems: dissipativity of the underlying dynamics with respect to a specific supply rate, optimal operation at steady state, and the turnpike property. We show that dissipativity with respect to a steady state implie...

This article presents a kite control and optimization problem intended as a benchmark problem for advanced control and optimization. We provide an entry point to this exciting renewable energy system for researchers in control and optimization methods looking for a realistic test bench, and/or a useful application case for their theory. The benchma...

We discuss the design of sampled-data receding-horizon control schemes for continuous-time systems based on exact turnpike properties. We present sufficient convergence conditions that do not require any kind of terminal constraints or terminal penalties. We prove that, in the presence of state constraints, the existence of an exact turnpike implie...

The contribution of this article is to propose and experimentally validate an optimizing control strategy for power kites flying crosswind. The algorithm ensures the kite follows a reference path (control) and also periodically optimizes the reference path (efficiency optimization). The path-following part of the controller is capable of consistent...

Concentrations measurements are typically corrupted by noise. Data reconciliation techniques improve the accuracy of measurements by using redundancies in the material and energy balances expressed as relationships between measurements. Since in the absence of kinetic models these relationships cannot integrate information regarding past measuremen...

This work considers the numerical optimization of constrained batch and semi-batch processes, for which direct as well as indirect methods exist. Direct methods are often the methods of choice, but they exhibit certain limitations related to the compromise between feasibility and computational burden. Indirect methods, such as Pontryagin’s Minimum...

This contribution presents a kinetic model identification scheme that guarantees convergence to global optimality. The use of the extent-based incremental approach allows one to (i) identify each reaction individually, and (ii) reduce the number of parameters to identify via optimization to the ones that appear nonlinearly in the investigated rate...

This paper proposes a PMP-based solution scheme with parsimonious parameterization of sensitivity-seeking arcs in order to reduce the computational complexity of constrained dynamic optimization problems. We tested our method on a binary batch distillation column and a two-phase semi-batch reactor for the hydroformylation of 1-dodecene. The perform...

State estimation techniques are used for improving the quality of measured signals and for reconstructing unmeasured quantities. In chemical reaction systems, nonlinear estimators are often used to improve the quality of estimated concentrations. These nonlinear estimators, which include the extended Kalman filter, the receding-horizon nonlinear Ka...

This paper presents an overview of the recent developments of modifier-adaptation
schemes for real-time optimization of uncertain processes. These schemes have the ability to
reach plant optimality upon convergence despite the presence of structural plant-model mismatch.
Modifier Adaptation has its origins in the technique of Integrated System Opti...

The desire to operate chemical processes in a safe and economically optimal way has motivated the development of so-called real-time optimization (RTO) methods [1]. For continuous processes, these methods aim to compute safe and optimal steady-state setpoints for the lower-level process controllers. A key challenge for this task is plant-model mism...

This work considers the numerical optimization of constrained batch and semi-batch processes, for which direct as well as indirect methods exist. Direct methods are often the methods of choice, but they exhibit certain limitations related to the compromise between feasibility and computational burden. Indirect methods, such as Pontryagin’s Minimum...

This work considers the numerical optimization of constrained batch and semi-batch processes, for which direct as well as indirect methods exist. Direct methods are often the methods of choice, but they exhibit certain limitations related to the compromise between feasibility and computational burden. Indirect methods, such as Pontryagin’s Minimum...

Empirical model identification for biological systems is a challenging task due to the combined effects of complex interactions, nonlinear effects and lack of specific measurements. In this context, several researchers have provided tools for experimental design, model structure selection, and optimal parameter estimation, often packaged together i...

In the context of real-time optimization, modifier-adaptation schemes use estimates of the plant gradients to achieve plant optimality despite plant-model mismatch. Plant feasibility is guaranteed upon convergence, but not at the successive operating points computed by the algorithm prior to convergence. This paper presents a strategy for guarantee...

Model-based optimization methods suffer from the limited accuracy of the available process models. Because of plant-model mismatch, model-based optimal inputs may be suboptimal or, worse, unfeasible for the plant. Modifier adaptation (MA) overcomes this obstacle by incorporating measurements in the optimization framework. However, the standard MA f...

We discuss optimal load sharing of parallel gas compressors in the presence of plant-model mismatch. We
formulate this problem as a static real-time optimization task and propose to tackle it by means of modifier adaptation. Under mild assumptions, the chosen approach guarantees optimal operating conditions upon convergence. Furthermore, we discuss...

Model-based optimization methods suffer from the limited accuracy of the available process models. Because of plant-model mismatch, model-based optimal inputs may be suboptimal or, worse, unfeasible for the plant. Modifier adaptation (MA) overcomes this obstacle by incorporating measurements in the optimization framework. However, the standard MA f...

Path-following tasks, which refer to dynamic motion planning along pre-specified geometric references, are
frequently encountered in applications such as milling, robot-supported measurements, and trajectory planning for autonomous vehicles. Different convex and non-convex optimal control formulations have been proposed to tackle these problems for...