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 on-line 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 on-line 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...

System identification is the art and science of building mathematical models of dynamic systems from observed input-output 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.

We propose a new technique for the identification of discrete-time hybrid systems in the Piece-Wise Affine (PWA) form. This problem can be formulated as the reconstruction of a possibly discontinuous PWA map with a multi-dimensional 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.

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 state-space 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 model-based controller's performance is compared to the performance with an exact process model, and a linear model. It is experienced that a non-linear model with good prediction capabilities can be constructed using elementary and qualitative process knowledge combined with a sufficiently large amount of process data.

Local Model Networks are flexible architectures for the representation of complex non-linear 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...

The problem of identifying the parameters of the constituent local linear models of Takagi-Sugeno 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 multi-objective 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 multi-objective optimization. This information is useful to diagnose the model and tune the weighting/priorities of the multi-objective 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.

Introduction The design of mathematical models of complex real-world (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 so-called 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

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 sub-optimal 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 well-behaved fuzzy models. The properties of the method are related to the bias/variance tradeoff, and illustrated with a semi-realistic simulation example. 1 Introduction The problem of identifying fuzzy models is often an ill-conditioned 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 Takagi-Sugeno-Kang 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 ...

This paper compares a genetic programming approach with a greedy partition algorithm (LOLIMOT) for structure identification of local linear neuro-fuzzy models. The crisp linear conclusion part of a Takagi-Sugeno-Kang (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, axis-orthogonal 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 tree-construction algorithm that partitions the input space by axis-orthogonal 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 non-linear two dimensional test function and an engine characteristic map.

This report is a review of the main neuro-control technologies. Two main kinds of neuro-control approaches are distinguished. One entails developing a single controller from a neural network and the other one embeds a number of controllers inside a neural network. The single neuro-control approaches are mainly system inverse: the inverse of the system dynamics is used to control the system in an open loop manner. The Multi-Layer Perceptron (MLP) is widely used for this purpose although there is no guarantee that it can succeed in learning to control the plant and that, more importantly, the unclear representation it achieves prohibits the analysis of its learned control properties. These problems and the fact that open loop control is not suitable for many systems highly restricts the usefulness of the MLP for control purposes. However, the non-linear modelling capability of the MLP could be exploited to enhance model based predictive control approaches since essentially, an accurate m...