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45
Model Predictive Control: Past, Present and Future
 Computers and Chemical Engineering
, 1997
"... More than 15 years after Model Predictive Control (MPC) appeared in industry as an effective means to deal with multivariable constrained control problems, a theoretical basis for this technique has started to emerge. The issues of feasibility of the online optimization, stability and performance a ..."
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Cited by 135 (6 self)
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More than 15 years after Model Predictive Control (MPC) appeared in industry as an effective means to deal with multivariable constrained control problems, a theoretical basis for this technique has started to emerge. The issues of feasibility of the online optimization, stability and performance are largely understood for systems described by linear models. Much progress has been made on these issues for nonlinear systems but for practical applications many questions remain, including the reliability and efficiency of the online computation scheme. To deal with model uncertainty "rigorously" an involved dynamic programming problem must be solved. The approximation techniques proposed for this purpose are largely at a conceptual stage. Among the broader research needs the following areas are identified: multivariable system identification, performance monitoring and diagnostics, nonlinear state estimation, and batch system control. Many practical problems like control objective prior...
Perspectives on system identification
 In Plenary talk at the proceedings of the 17th IFAC World Congress, Seoul, South Korea
, 2008
"... System identification is the art and science of building mathematical models of dynamic systems from observed inputoutput data. It can be seen as the interface between the real world of applications and the mathematical world of control theory and model abstractions. As such, it is an ubiquitous ne ..."
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Cited by 91 (3 self)
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System identification is the art and science of building mathematical models of dynamic systems from observed inputoutput data. It can be seen as the interface between the real world of applications and the mathematical world of control theory and model abstractions. As such, it is an ubiquitous necessity for successful applications. System identification is a very large topic, with different techniques that depend on the character of the models to be estimated: linear, nonlinear, hybrid, nonparametric etc. At the same time, the area can be characterized by a small number of leading principles, e.g. to look for sustainable descriptions by proper decisions in the triangle of model complexity, information contents in the data, and effective validation. The area has many facets and there are many approaches and methods. A tutorial or a survey in a few pages is not quite possible. Instead, this presentation aims at giving an overview of the “science ” side, i.e. basic principles and results and at pointing to open problem areas in the practical, “art”, side of how to approach and solve a real problem. 1.
A Clustering Technique for the Identification of Piecewise Affine Systems
, 2001
"... We propose a new technique for the identification of discretetime hybrid systems in the PieceWise Affine (PWA) form. This problem can be formulated as the reconstruction of a possibly discontinuous PWA map with a multidimensional domain. In order to achieve our goal, we provide an algorithm that ..."
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Cited by 61 (8 self)
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We propose a new technique for the identification of discretetime hybrid systems in the PieceWise Affine (PWA) form. This problem can be formulated as the reconstruction of a possibly discontinuous PWA map with a multidimensional domain. In order to achieve our goal, we provide an algorithm that exploits the combined use of clustering, linear identification, and pattern recognition techniques. This allows to identify both the affine submodels and the polyhedral partition of the domain on which each submodel is valid avoiding gridding procedures. Moreover, the clustering step (used for classifying the datapoints) is performed in a suitably defined feature space which allows also to reconstruct different submodels that share the same coefficients but are defined on different regions. Measures of confidence on the samples are introduced and exploited in order to improve the performance of both the clustering and the final linear regression procedure.
Nonlinear Predictive Control Using Local Models  Applied To A Batch Fermentation Process
 PRACTICE
, 1994
"... The problem of controlling processes that operate within a wide range of operating conditions is addressed. The operation of the process is decomposed into a set of operating regimes, and simple local statespace model structures are developed for each regime. These are combined into a global model ..."
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Cited by 28 (3 self)
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The problem of controlling processes that operate within a wide range of operating conditions is addressed. The operation of the process is decomposed into a set of operating regimes, and simple local statespace model structures are developed for each regime. These are combined into a global model structure using an interpolation method. Unknown local model parameters are identified using empirical data. The control problem is solved using a model predictive controller based on this model representation. As an example, a simulated batch fermentation reactor is studied. The modelbased controller's performance is compared to the performance with an exact process model, and a linear model. It is experienced that a nonlinear model with good prediction capabilities can be constructed using elementary and qualitative process knowledge combined with a sufficiently large amount of process data.
On MultiObjective Identification Of TakagiSugeno Fuzzy Model Parameters
 IN: IFAC WORLD CONGRESS
, 2002
"... The problem of identifying the parameters of the constituent local linear models of TakagiSugeno fuzzy models is considered. In order to address the tradeoff between global model accuracy and interpretability of the local models as linearizations of a nonlinear system, two multiobjective identi ..."
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Cited by 12 (0 self)
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The problem of identifying the parameters of the constituent local linear models of TakagiSugeno fuzzy models is considered. In order to address the tradeoff between global model accuracy and interpretability of the local models as linearizations of a nonlinear system, two multiobjective identification algorithms are studied. Particular attention is paid to the analysis of conflicts between objectives, and we show that such information can be easily computed from the solution of the multiobjective optimization. This information is useful to diagnose the model and tune the weighting/priorities of the multiobjective optimization. Moreover, the result of the conflict analysis can be used as a constructive tool to modify the fuzzy model structure (including membership functions) in order to meet the multiple objectives. The methods are illustrated on an experimental lungs respiration application.
Fuzzy Identification from a Grey Box Modeling Point of View
 Fuzzy Model Identification
, 1997
"... Introduction The design of mathematical models of complex realworld (and typically nonlinear) systems is essential in many fields of science and engineering. The developed models can be used, e.g., to explain the behavior of the underlying system as well as for prediction and control purposes. A c ..."
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Cited by 10 (0 self)
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Introduction The design of mathematical models of complex realworld (and typically nonlinear) systems is essential in many fields of science and engineering. The developed models can be used, e.g., to explain the behavior of the underlying system as well as for prediction and control purposes. A common approach for building mathematical models is socalled black box modeling (Ljung, 1987; Soderstrom and Stoica, 1989), as opposed to more traditional physical modeling (or white box modeling), where everything is considered known a priori from physics. Strictly speaking, a black box model is designed entirely from data using no physical or verbal insight whatsoever. The structure of the model is chosen from families that are known to be very flexible and successful in past applications. This also means that the model parameters lack physical or verbal significance; they are tuned just to fit the observed data as well as possible. The term "black box modeling" is
A Constructive Learning Algorithm for Local Model Networks
 in `Proceedings of the IEEE Workshop on ComputerIntensive Methods in Control and Signal Processing
, 1995
"... Local Model Networks are flexible architectures for the representation of complex nonlinear dynamic systems. The local nature of the representation leads to a modular network which can integrate a variety of paradigms (neural nets, statistics, fuzzy systems and a priori mathematical models), but be ..."
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Cited by 9 (3 self)
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Local Model Networks are flexible architectures for the representation of complex nonlinear dynamic systems. The local nature of the representation leads to a modular network which can integrate a variety of paradigms (neural nets, statistics, fuzzy systems and a priori mathematical models), but because of the power of the local models, the architecture is less sensitive to the curse of dimensionality than other local representations, such as Radial Basis Function networks. The concept of `locality' is a difficult one to define, and tends to vary over a problem's input space, so a constructive structure identification algorithm is presented which automatically defines a suitable model structure on the basis of the observed data from the process being identified. Local learning algorithms are introduced for the local model parameter optimisation, which save computational effort and produce more interpretable and robust models. 1. Introduction Computationally intensive learning systems...
Local Model Networks and Local Learning
 in Fuzzy Duisburg, '94
, 1994
"... : The Local Model Networks (networks composed of locally accurate models, where the output is interpolated by smooth locally active basis functions) described in this paper provide a solid basis for practical modelling tasks. The architecture benefits from being able to incorporate Fuzzy, Neural Net ..."
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Cited by 7 (3 self)
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: The Local Model Networks (networks composed of locally accurate models, where the output is interpolated by smooth locally active basis functions) described in this paper provide a solid basis for practical modelling tasks. The architecture benefits from being able to incorporate Fuzzy, Neural Network and conventional System Identification methodology and experience. The advantages of the architecture are described, and the tradeoff between Local and Global Learning is investigated. The Local Learning method is computationally less expensive and was found to lead to smoother and more interpretable solutions than global learning. The results are illustrated with a robot actuator modelling problem. 1. Introduction Modelling nonlinear dynamic systems from observed data and a priori engineering knowledge is a major area of science and engineering. In recent years a great deal of work has appeared in new areas like Fuzzy Modelling and Neural Networks to complement the previous work in st...
Genetic Programming for Model Selection of TSKFuzzy Systems
, 2001
"... This paper compares a genetic programming approach with a greedy partition algorithm (LOLIMOT) for structure identification of local linear neurofuzzy models. The crisp linear conclusion part of a TakagiSugenoKang (TSK) fuzzy rule describes the underlying model in the local region specified in th ..."
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Cited by 6 (0 self)
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This paper compares a genetic programming approach with a greedy partition algorithm (LOLIMOT) for structure identification of local linear neurofuzzy models. The crisp linear conclusion part of a TakagiSugenoKang (TSK) fuzzy rule describes the underlying model in the local region specified in the premise. The objective of structure identification is to identify an optimal partition of the input space into Gaussian, axisorthogonal fuzzy sets. The linear parameters in the rule consequent are then estimated by means of a local weighted least squares algorithm. LOLIMOT is an incremental treeconstruction algorithm that partitions the input space by axisorthogonal splits. In each iteration it greedily adds the new model that minimizes the classification error. Genetic programming performs a global search for the optimal partition tree and is therefore able to backtrack in case of suboptimal intermediate split decisions. We compare the performance of both methods for function approximation of a highly nonlinear two dimensional test function and an engine characteristic map.
Robust Identification of TakagiSugenoKang Fuzzy Models using Regularization
"... The identification of fuzzy models can sometimes be a difficult problem, often characterized by lack of data in some regions, collinearities and other data deficiencies, or a suboptimal choice of model structure. Regularization is suggested as a general method for improving the robustness of standa ..."
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Cited by 5 (2 self)
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The identification of fuzzy models can sometimes be a difficult problem, often characterized by lack of data in some regions, collinearities and other data deficiencies, or a suboptimal choice of model structure. Regularization is suggested as a general method for improving the robustness of standard parameter identification algorithms leading to more accurate and wellbehaved fuzzy models. The properties of the method are related to the bias/variance tradeoff, and illustrated with a semirealistic simulation example. 1 Introduction The problem of identifying fuzzy models is often an illconditioned one, in the sense that there may be insufficient information in the empirical data to identify the model's parameters with sufficient accuracy. Fuzzy models, such as the TakagiSugenoKang model [24], are often characterized by a fuzzy partitioning of the system's operating range and a simple local model within each region. Poor accuracy or undesirable behavior of the identified model is ...