Radoslav Paulen

Slovak University of Technology in Bratislava · Institute of Information Engineering, Automation and Mathematics

The enormous technological growth increases the application of machine learning in the petrochemical industry. One of these applications is a soft-sensor design. A soft sensor represents a relatively efficient way of inferring hard-to-measure industrial variables (e.g., concentration). It takes a form of a mathematical model. Consequently, the sens...

We study the problem of data-based design of multi-model linear inferential (soft) sensors. The multi-model linear inferential sensors promise increased prediction accuracy yet simplicity of the model structure and training. The standard approach to the multi-model inferential sensor design consists in three separate steps: 1) data labeling (establ...

There is an increasing need to monitor industrial key variables by inferential (soft) sensors. This contribution deals with the challenge of increasing the accuracy of inferential sensors yet maintaining the simple (linear) structure. In order to fulfill these opposing requirements, we design a linear multi-model inferential sensor (MIS) that switc...

The potential of data-based modeling techniques gains importance in the chemical industry whereas the development of first-principles models requires too much effort due to the complex physics and chemistry. The data-based inferential (or soft, surrogate) sensors play a significant role in this field. Such sensors can accurately and frequently esti...

We investigate the problem of robust design of experiments (rDoE) in the context of nonlinear maximum-likelihood parameter estimation. It is assumed that an experimenter designs a series of experiments with the possibility of a re-design after a particular experiment run. We present a novel rDoE approach that uses multi-stage decision making in ord...

We study approaches to the robust model-based design of experiments in the context of maximum-likelihood estimation. These approaches provide robustification of model-based methodologies for the design of optimal experiments by accounting for the effect of the parametric uncertainty. We study the problem of robust optimal design of experiments in t...

Inferential (or soft) sensors are used in industry to infer the values of imprecisely and rarely measured (or completely unmeasured) variables from variables measured online (e.g., pressures, temperatures). The main challenge, akin to classical model overfitting, in designing an effective inferential sensor is the selection of a correct structure o...

Inferential (or soft) sensors are used in industry to infer the values of imprecisely and rarely measured (or completely unmeasured) variables from variables measured online (e.g., pressures, temperatures). The main challenge, akin to classical model overfitting, in designing an effective inferential sensor is the selection of a correct structure o...

Inferential (or soft) sensors are used in industry to infer the values of imprecisely and rarely measured (or completely unmeasured) variables from variables measured online (e.g., pressures, temperatures). The main challenge, akin to classical model overfitting, in designing an effective inferential sensor is to select a correct structure represen...

Nowadays, the quality of industrial data has a significant impact on the performance of modern (advanced) controllers. The industrial data is usually corrupted by statistically deviated measurements (outliers). This contribution studies methods for the reduction of outliers in the industrial dataset, such as Hotelling's T2 distribution, minimum cov...

The trade‐off between optimality and complexity has been one of the most important challenges in the field of robust model predictive control (MPC). To address the challenge, we propose a flexible robust MPC scheme by synergizing the multi‐stage and tube‐based MPC approaches. The key idea is to exploit the nonconservatism of the multi‐stage MPC and...

Inferential (or soft) sensors are used in industry to infer the values of imprecisely and rarely measured (or completely unmeasured) variables from variables measured online (e.g., pressures, temperatures). The main challenge, akin to classical model overfitting, in designing an effective inferential sensor is to select a correct structure represen...

This paper is about a set-membership based state- and parameter estimation approach for nonlinear dynamic systems under the assumption that all measurement errors are bounded. In detail, we propose an outer approximation method, where the set of states and parameters that is consistent with the incoming measurement bounds is over-approximated by an...

The trade-off between optimality and complexity has been one of the most important challenges in the field of robust Model Predictive Control (MPC). To address the challenge, we propose a flexible robust MPC scheme by synergizing the multi-stage and tube-based MPC approaches. The key idea is to exploit the non-conservatism of the multi-stage MPC an...

We study approaches to robust model-based design of experiments in the context of maximum-likelihood estimation. These approaches provide robustification of model-based methodologies for the design of optimal experiments by accounting for the effect of the parametric uncertainty. We study the problem of robust optimal design of experiments in the f...

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 pra...

We address the question of how to reduce the inevitable loss of performance that is incurred by robust multi-stage NMPC due to the lack of knowledge compared to the case where the exact plant model (no uncertainty) is available. Multi-stage NMPC in the usual setting over-approximates a continuous parametric uncertainty set by a box and includes the...

A novel robust nonlinear model predictive control scheme (NMPC) based on the multi-stage formulation is introduced in this paper. The scenario tree of Multi-stage NMPC is often built by assuming parametric uncertainty and by considering the minimum and maximum values of the parameters. This can augment the uncertainty set and can result in a perfor...

A novel non-conservative robust nonlinear model predictive control scheme (NMPC) based on the multi-stage formulation is introduced for the case of an ellipsoidal uncertainty set. Multi-stage NMPC models uncertainty by a tree of discrete scenarios. In the case of a continuous-valued uncertainty, the scenario tree is usually built for all combinatio...

Inferential sensors are used in industry to infer the values of the imprecisely and infrequently measured (or completely unmeasured) variables from measured variables (e.g., pressures, temperatures). This work deals with the design of inferential sensors suitable for an advanced process control of a depropanizer column of the Slovnaft refinery in B...

Design space is a key concept in pharmaceutical quality by design, providing better understanding of manufacturing processes and enhancing regulatory flexibility. It is of paramount importance to develop computational techniques for providing quantitative representations of a design space, in accordance with the ICH Q8 guideline. The focus is on Ba...

This paper is concerned with guaranteed parameter estimation for discrete-time nonlinear systems subject to bounded uncertainties. The proposed approach is based on polytopic set parameterizations. Similar to other estimation and filtering approaches, the presented algorithm is based on two operations, propagation of the polytopic uncertainty throu...

This paper deals with the optimal operation of a continuously operated laboratory membrane separation plant. The goal is to find an economically optimal regime of operation using the transmembrane pressure (TMP) and the operating temperature as adjustable set-points for the low-level controllers. The main challenge is to identify the optimum in the...

Dual control is a technique that addresses the trade-off between probing (excitation signals) and control actions, which results in a better estimation of the unknown parameters and therefore in a better (tracking or economic) performance. Multi-stage NMPC is a robust-control scheme that represents the uncertainty using a scenario tree that is ofte...

This paper is concerned with set-membership estimation in nonlinear dynamic systems. The problem entails characterizing the set of all possible parameter values such that given predicted outputs match their corresponding measurements within prescribed error bounds. Most existing methods to tackle this problem rely on outer-approximation techniques,...

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 pra...

A model-based optimal experiment design (OED) of nonlinear systems is studied. OED represents a methodology for optimizing the geometry of the parametric joint-confidence regions (CRs), which are obtained in an a posteriori analysis of the least-squares parameter estimates. The optimal design is achieved by using the available (experimental) degree...

This paper studies a dynamic real-time optimization in the context of model-based time-optimal operation of batch processes under parametric model mismatch. In order to tackle the model-mismatch issue, a receding-horizon policy is usually followed with frequent re-optimization. The main problem addressed in this study is the high computational burd...

This paper studies a dynamic real-time optimization in the context of model-based time-optimal operation of batch processes under parametric model mismatch. In order to tackle the model-mismatch issue, a receding-horizon policy is usually followed with frequent re-optimization. The main problem addressed in this study is the high computational burd...

We address the problem of robust nonlinear model predictive control (NMPC) under plant-model mismatch in the absence of full-state measurements. We propose an approach that is based on the use of a model-error model (MEM) to handle the estimation errors and the structural plant-model mismatch in a Multi-stage NMPC framework. The MEM which consists...

This paper presents a scheme for dual robust control of batch processes under parametric uncertainty. The dual-control paradigm arises in the context of adaptive control. A trade-off should be decided between the control actions that (robustly) optimize the plant performance and between those that excite the plant such that unknown plant model para...

Multi-stage nonlinear model predictive control (msNMPC) is a robust control strategy based on the description of the uncertainty propagation through a dynamic system via a scenario tree and is one of the least conservative approaches to robust control. The computational complexity of the msNMPC, however, grows with respect to the number of uncertai...

This paper presents a scheme for dual robust control of batch processes under parametric uncertainty. The dual-control paradigm arises in the context of adaptive control. A trade-off should be decided between the control actions that (robustly) optimize the plant performance and between those that excite the plant such that unknown plant model para...

We are concerned with moving-horizon guaranteed parameter estimation (MH-GPE) of non-linear systems in a context of bounded measurement error. The problem consists of approximating the set of all possible parameter values such that the predicted values of plant outputs match their corresponding measurements within prescribed error bounds. The princ...

The problem of set-membership state estimation is studied under a bounded measurement noise for linear multi-output systems. Parallelotopes are considered as state-bounding sets for the representation of uncertainty, which is taken into account by a robust controller. Two estimation approaches are compared; the well-known Recursive Optimal Parallel...

The aim of this study is to analyze and improve APC control of a depropanizer distillation column at the Slovnaft company. The process is modelled within the gPROMS ModelBuilder environment which is a suitable tool for the process modeling, control, and optimization. Selected control configurations are studied: LV, LB, DV, LD, and Ryskamp. A steady...

This paper is concerned with guaranteed parameter estimation of non-linear dynamic systems in a context of bounded measurement error. The problem consists of approximating the set of all possible parameter values such that the predicted values of plant outputs match their corresponding measurements within prescribed error bounds. Efficient algorith...

The problem of guaranteed parameter estimation (GPE) consists in enclosing the set of all possible parameter values, such that the model predictions match the corresponding measurements within prescribed error bounds. One of the bottlenecks in GPE algorithms, commonly exploiting set inversion, is the construction of enclosures for the image-set of...

This paper is concerned with computing enclosures for the constrained reachable set of uncertain nonlinear dynamic systems. Our main contribution is a nontrivial extension of the generalized differential inequality, proposed in Villanueva et al. (2015), for the case that an a priori enclosure, of the reachable set is available. A practical implemen...

In this paper the problem of robust output-feedback Model Predictive Control (MPC) is considered. Uncertainty in the state estimates obtained from noisy measurements is bounded using set-membership techniques as we consider the noise to be bounded. Robustness of the MPC controller is achieved in a min-max sense. We use parallelotopic bounding for t...

Demand for prepared Cyber-physical systems (CPSs) engineers is growing in the Industry 4.0 economy and universities should respond accordingly. This article identifies trends in preparing the CPSs workforce of the future by reviewing educational curricula and research on CPSs of universities around the world. The research finds three main approache...

This work deals with modelling and control of a depropanizer distillation column of the Slovnaft refinery. The goal is to analyze different control structures and to suggest an effective one for the plant taking into account various disturbances. We use the gPROMS ModelBuilder environment to design the mathematical model of the process. Here, we ex...

In this paper, optimal strategy based on Pontryagin's minimum principle is presented for batch membrane separation of lactose-salt water solution, whilst minimizing costs. Optimal control problem comprises a weighted combination of the processing time and diluant consumption, i.e., the overall processing cost of separation. Process model is derived...

A model-based optimal experiment design (OED) of nonlinear systems is studied. OED represents a methodology for optimizing the geometry of the parametric joint-confidence regions (CRs), which are obtained in an a posteriori analysis of the least-squares parameter estimates. The optimal design is achieved by using the available (experimental) degree...

The problem of guaranteed parameter estimation (GPE) consists in enclosing the set of all possible parameter values, such that the model predictions match the corresponding measurements within prescribed error bounds. One of the bottlenecks in GPE algorithms is the construction of enclosures for the image-set of factorable functions. In this paper,...

Dual control seeks to explicitly deal with the trade-off between the excitation of the controlled system by probing actions, which lead to a more accurate estimation of the unknown parameters of the plant model, and performance (set-point tracking, economic optimality , etc.) of the controlled system under the imperfect knowledge of the plant beha...

This paper introduces set-membership nonlinear regression (SMR), a new approach to nonlinear regression under uncertainty. The problem is to determine the subregion in parameter space enclosing all (global) solutions to a nonlinear regression problem in the presence of bounded uncertainty on the observed variables. Our focus is on nonlinear algebra...

The multi-stage MPC approach models the evolution of state trajectories for different realizations of the uncertainty as a scenario tree and considers the availability of feedback information explicitly in the predictions and in the computation of the control moves. Since the structure of the feedback policy is not restricted, multi-stage MPC is le...

In this paper we present an implicit dual robust nonlinear model predictive control (NMPC) in the framework of (bounded-error) guaranteed parameter estimation and multi-stage NMPC, which uses a scenario tree to represent propagation of parametric model uncertainty through a dynamic system. The proposed implicit dual control scheme excites the syste...

This paper presents a scheme for dual robust control of batch processes under parametric uncertainty. Some recently proposed approaches can be used to tackle this problem, however, this will be done at the price of conservativeness or significant computational burden. In order to increase computational efficiency, we propose a scheme that uses para...

In this paper an approach is studied to guaranteed (set-membership) state estimation for robust output-feedback model predictive control (MPC) with hard input and state constraints. Uncertainties are assumed to arise in a dynamic system from unknown initial conditions of state variables and due to unknown-but-bounded measurement noise. The uncertai...

This paper studies a dynamic real-time optimization in the context of model-based time-optimal operation of batch processes under parametric model mismatch. A class of batch membrane separation processes is in the scope of the presented applications. In order to tackle the model-mismatch issue, a receding-horizon policy is usually followed with fre...

In this paper, a time-optimal strategy is implemented for batch membrane separation of lactose-salt solution. Parameters of the flow-rate model are estimated by solving a dynamic optimization problem that minimizes the difference between experimental and simulated system outputs. The estimated flow-rate models are used to formulate an optimal contr...

In this paper, a time-optimal strategy is implemented for batch membrane separation of lactose-salt solution. Parameters of the flow-rate model are estimated by solving a dynamic optimization problem that minimizes the difference between experimental and simulated system outputs. The estimated flow-rate models are used to formulate an optimal contr...

This paper studies a dynamic real-time optimization in the context of model-based time-optimal operation of batch processes under parametric model mismatch. A class of batch membrane separation processes is in the scope of the presented applications. In order to tackle the model-mismatch issue, a receding-horizon policy is usually followed with fre...

This paper presents a scheme for dual robust control of batch processes under parametric uncertainty. Some recently proposed approaches can be used to tackle this problem, however, this will be done at the price of conservativeness or significant computational burden. In order to increase computational efficiency, we propose a scheme that uses para...

In this paper an approach is studied to guaranteed (set-membership) state estimation for robust output-feedback model predictive control (MPC) with hard input and state constraints. Uncertainties are assumed to arise in a dynamic system from unknown initial conditions of state variables and due to unknown-but-bounded measurement noise. The uncertai...

In this paper we present an implicit dual robust nonlinear model predictive control (NMPC) in the framework of (bounded-error) guaranteed parameter estimation and multi-stage NMPC, which uses a scenario tree to represent propagation of parametric model uncertainty through a dynamic system. The proposed implicit dual control scheme excites the syste...

The multi-stage MPC approach models the evolution of state trajectories for different realizations of the uncertainty as a scenario tree and considers the availability of feedback information explicitly in the predictions and in the computation of the control moves. Since the structure of the feedback policy is not restricted, multi-stage MPC is le...

Several approaches for robustification of model-based methodologies for the design of optimal experiments have been presented in the past, mainly in the context of maximum-likelihood estimation in order to account for the effect of the nominal values of parameters being far from the true values. In this contribution we study the problem of robust o...

Optimal experiment design is usually performed as a search over a finitely-parameterized shape that (over-)approximates the confidence region of parameters of a model. In general, there exists no such shape to exactly enclose the confidence region of a nonlinear parameter estimation problem. Due to this fact, the design-of-experiment techniques are...

In this paper we study a model-based time-optimal operation of a batch diafiltration process in the presence of fouling where the fouling model is adapted on-line using the set-membership (guaranteed) parameter estimation. The membrane fouling poses one of the major problems in the field of membrane separation processes. The studied objective in th...

In large integrated production sites, an optimal allocation of the shared resources among different possibly competing production plants is key to a resource and energy efficient operation of the overall site. Typically, a large integrated production site can be regarded as a physically coupled system of systems (SoS), since it comprises many diffe...

In this paper we study a model-based time-optimal operation of a batch diafiltration process in the presence of fouling where the fouling model is adapted on-line using the set-membership (guaranteed) parameter estimation. The membrane fouling poses one of the major problems in the field of membrane separation processes. The studied objective in th...

In large integrated production sites, an optimal allocation of the shared resources among different possibly competing production plants is key to a resource and energy efficient operation of the overall site. Typically, a large integrated production site can be regarded as a physically coupled system of systems (SoS), since it comprises many diffe...

Dual control is a technique that solves the trade-off between using the input signal for the excitation of the system excitation signal (probing actions) and controlling it, which results in a better estimation of the unknown parameters and therefore in a better (tracking or economic) performance. In this paper we present a dual control approach fo...

n this paper, a choice of models for optimal control strategy is discussed for batch membrane processes. The system of lactose and salt in water is studied with the separation aim be- ing concentration of lactose and simultaneous removal of salt. The most crucial part of the model is dependence of permeation rate on concentrations of components. Tw...

The paper derives mathematical model and optimal operation of batch diafiltration processes with partial recirculation of retentate, i.e. batch closed-loop membrane processes. A generalized mathematical model of the process is developed in the form of a set of non-linear ordinary differential and algebraic equations. Two process variables are used...

Large interconnected production sites typically consist of many plants that are physically coupled by networks of sharedresources. An optimal site-wide allocation of shared resources is key to a resource-, energy-, and cost-optimal operation.Market-based coordination can find the site-wide optimum with limited data exchange between the subsystems a...

Download link: http://dx.doi.org/10.1016/j.compchemeng.2017.01.029 An approach to the design of experiments is presented in the framework of bounded-error (guaranteed) parameter estimation for nonlinear static and dynamic systems. The guaranteed parameter estimation determines nonasymptotic confidence limits on the unknown parameters of a mathema...

Price-based coordination can be used to coordinate (physically coupled) systems-of-systems (SoS) consisting of competing subsystems that are not willing to share every necessary detail that is required to compute the centralized solution. One example of such a SoS is a large integrated chemical production site that consists of a central site coordi...

The paper deals with parameter estimation of permeate flux model with fouling for the nanofiltration process. We propose a new technique towards fouling estimation with fouling model being an explicit function of concentration. The objective is to experimentally concentrate lactose in a lactose-salt solution at constant temperature and pressure usi...

This paper describes a hierarchical decomposition approach for the optimal operation of a sugar crystallization process. The process consists of two sections: the evaporation section, which operates continuously, and the crystallization section, which consists of crystallizers that operate in a semi-batch mode according to a predefined recipe. A re...

Site-wide allocation of shared resources among the units of (partially) autonomous plants can be realized by price-based coordination. In an iterative procedure, a central site-coordinator adjusts the transfer prices for shared resources based on the network (im)balance until the equilibrium price λ* is found which assures the achievement of networ...

This paper deals with the time-optimal operation and parameter estimation problem of a general diafiltration process in the presence of fouling. Fouling stands for one of the dominant problems in the membrane separation processes. The dynamic behavior of the fouled membrane is described by a general fouling model taken from literature. An Extended...