Meriam Chebre

Robust real-time optimization for the linear oil blending

In this paper we present a robust real-time optimization method for the online linear oil blending process. The blending process consists in determining the optimal mix of components so that the final product satisfies a set of specifications. We examine different sources of uncertainty inherent to the blending process and show how to address this uncertainty applying the Robust Optimization techniques. The polytopal structure of our problem permits a simplified robust approach. Our method is intended to avoid reblending and we measure its performance in terms of the blend quality giveaway and feedstocks prices. The difference between the nominal and the robust optimal values (the price of robustness) provides a benchmark for the cost of reblending which is difficult to estimate in practice. This new information can be used to adjust the level of conservatism in the model. We analyze the feasibility of a blend to be produced from a set of feedstocks when the heel of a previous blend is used in the composition of the new blend. Additional critical information for the control system is then produced.

Handling parameter ranking, equalities and bounds in adaptive control of blending systems

Abstract This paper presents solutions to handle ranking, equalities and bounds for the parameter estimates of a linear adaptive controller scheme used in the production of commercial fuels by blending. The control problem under consideration is a multi-variable output regulation problems with large uncertainties in the plant parameters. It can be solved using a specifically designed adaptive controller which combines constrained optimization and a closed-loop estimator of the plant parameters. As in numerous applications of adaptive control, while output convergence is usually guaranteed under feasibility assumptions, little is known about the asymptotic behavior of the parameter estimates themselves. Yet, from an application view-point, it is desired that these estimates satisfy some physical properties. In particular, parameters ranking, equalities and bounds are of practical importance and assert the consistency of the estimation. In this paper we expose techniques that guarantee this desired behavior.

Multiclass SVM with graph path coding regularization for face classification

We consider the problem of learning graphs in a sparse multiclass support vector machines framework. For such a problem, sparse graph penalty is useful to select the significant features and interpret the results. Classical ℓ1-norm learns a sparse solution without considering the structure between the features. In this paper, a structural knowledge is encoded as directed acyclic graph and a graph path penalty is incorporated to multiclass SVM. The learned classifiers not only improve the performance, but also help in the interpretation of the learned features. The performance of the proposed method highly depends on an initialization graph. Two generic ways to initialize the graph between the features are considered: one is built from similarities while the other one uses Graphical Lasso. The experiments of face classification task on Extended YaleB database verify that: i) graph regularization with multiclass SVM improves the performance and also leads to a more sparse solution compared to ℓ1-norm.

Optimization of dynamical systems with time-varying or input-varying delays

We study the optimization of dynamical systems exhibiting variable time delays. We consider time-varying delays, and delays implicitly defined by input variables as they appear in systems involving fluid transport phenomena. We establish the necessary optimality conditions. Simulations results are presented.

Prices of robustness and reblending in oil industry

Abstract In this paper we present a method to calculate the prices of robustness and reblending through a robust real-time optimization method for the on-line linear oil blending process. Our approach places this problem in a wider frame where different sources of uncertainty inherent to the blending process appear. The polytopal structure of our problem permits a robust approach that is simpler than the classical theory of Ben-Tal and Nemirovskii which needs convex programming tools. Our method is intended to avoid reblending and we measure its performance in terms of the blend quality giveaway and feedstocks prices. The difference between the nominal and the robust optimal values (the price of robustness) provides a benchmark for the cost of reblending which is difficult to estimate in practice. This new information can be used to adjust the level of conservatism in the model. Additional critical information for the control system is produced.

Optimal neighbourhood and model quality indicators

The construction of a good predicting model by learning algorithms does not necessarily imply a correct answer during the generalisation step. That is why one gives confidence intervals on the predicted value, often needing some hypothesis on the data’s density distribution. These hypothesis can hardly be verified when a little number of samples is given, which is the most frequent case in practice. We follow a local approach on the basis of an optimal neighbourhood choice. We use this neighbourhood to predict as well as to give some simple model quality indicators for any sample.