The extended linear complementarity problem

In this paper we define the Extended Linear Complementarity Problem (ELCP), an extension of the well-known Linear Complementarity Problem (LCP). We study the general solution set of an ELCP and we present an algorithm to find all its solutions. Finally we show that the ELCP can be used to solve some important problems in the max algebra

Forecasting day-ahead electricity prices in Europe: the importance of considering market integration

Motivated by the increasing integration among electricity markets, in this paper we propose two different methods to incorporate market integration in electricity price forecasting and to improve the predictive performance. First, we propose a deep neural network that considers features from connected markets to improve the predictive accuracy in a local market. To measure the importance of these features, we propose a novel feature selection algorithm that, by using Bayesian optimization and functional analysis of variance, evaluates the effect of the features on the algorithm performance. In addition, using market integration, we propose a second model that, by simultaneously predicting prices from two markets, improves the forecasting accuracy even further. As a case study, we consider the electricity market in Belgium and the improvements in forecasting accuracy when using various French electricity features. We show that the two proposed models lead to improvements that are statistically significant. Particularly, due to market integration, the predictive accuracy is improved from 15.7% to 12.5% sMAPE (symmetric mean absolute percentage error). In addition, we show that the proposed feature selection algorithm is able to perform a correct assessment, i.e. to discard the irrelevant features

Early age behaviour of concrete supercontainers for radioactive waste disposal

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A distributed accelerated gradient algorithm for distributed model predictive control of a hydro power valley

A distributed model predictive control (DMPC) approach based on distributed optimization is applied to the power reference tracking problem of a hydro power valley (HPV) system. The applied optimization algorithm is based on accelerated gradient methods and achieves a convergence rate of O(1/k^2), where k is the iteration number. Major challenges in the control of the HPV include a nonlinear and large-scale model, nonsmoothness in the power-production functions, and a globally coupled cost function that prevents distributed schemes to be applied directly. We propose a linearization and approximation approach that accommodates the proposed the DMPC framework and provides very similar performance compared to a centralized solution in simulations. The provided numerical studies also suggest that for the sparsely interconnected system at hand, the distributed algorithm we propose is faster than a centralized state-of-the-art solver such as CPLEX

Hybrid model predictive control for freeway traffic using discrete speed limit signals

HYCON2 Show day - Traffic modeling, Estimation and Control 13/05/2014 GrenobleIn this paper, two hybrid Model Predictive Control (MPC) approaches for freeway traffic control are proposed considering variable speed limits (VSL) as discrete variables as in current real world implementations. These discrete characteristics of the speed limits values and some necessary constraints for the actual operation of VSL are usually underestimated in the literature, so we propose a way to include them using a macroscopic traffic model within an MPC framework. For obtaining discrete signals, the MPC controller has to solve a highly non-linear optimization problem, including mixed-integer variables. Since solving such a problem is complex and difficult to execute in real-time, we propose some methods to obtain reasonable control actions in a limited computation time. The first two methods (-exhaustive and -genetic discretization) consist of first relaxing the discrete constraints for the VSL inputs; and then, based on this continuous solution and using a genetic or an exhaustive algorithm, to find discrete solutions within a distance of the continuous solution that provide a good performance. The second class of methods split the problem in a continuous optimization for the ramp metering signals and in a discrete optimization for speed limits. The speed limits optimization, which is much more time-consuming than the ramp metering one, is solved by a genetic or an exhaustive algorithm in communication with a non-linear solver for the ramp metering. The proposed methods are tested by simulation, showing not only a good performance, but also keeping the computation time reduced.Unión Europea FP7/2007–201