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Reliability-aware zonotopic tube-based model predictive control of a drinking water network

Khoury Boutrous, Nejjari Fatiha, Puig Vicenç

International Journal of Applied Mathematics and Computer Science

2022

Vol. 32, no. 2

197--211

A robust economic model predictive control approach that takes into account the reliability of actuators in a network is presented for the control of a drinking water network in the presence of uncertainties in the forecasted demands required for the predictive control design. The uncertain forecasted demand on the nominal MPC may make the optimization process intractable or, to a lesser extent, degrade the controller performance. Thus, the uncertainty on demand is taken into account and considered unknown but bounded in a zonotopic set. Based on this uncertainty description, a robust MPC is formulated to ensure robust constraint satisfaction, performance, stability as well as recursive feasibility through the formulation of an online tube-based MPC and an accompanying appropriate terminal set. Reliability is then modelled based on Bayesian networks, such that the resulting nonlinear function accommodated in the optimization setup is presented in a pseudo-linear form by means of a linear parameter varying representation, mitigating any additional computational expense thanks to the formulation as a quadratic optimization problem. With the inclusion of a reliability index to the economic dominant cost of the MPC, the network users’ requirements are met whilst ensuring improved reliability, therefore decreasing short and long term operational costs for water utility operators. Capabilities of the designed controller are demonstrated with simulated scenarios on the Barcelona drinking water network.

Interpretacja sondowań dylatometrycznych (DMT) z wykorzystaniem analizy bayesowskiej

Rabarijoely S., Jabłonowski S., Falkowski T., Garbulewski K.

Przegląd Geologiczny

2008

Vol. 56, nr 4

322-329

Almost 250 years ago, T. Bayes outlined a statistical method which has become increasingly apparent and it allows scientists to combine new data with their existing knowledge and explained how should change beliefs in the light of new evidence. The paper addresses the applicability of Bayesian approach to the interpretation of DMT investigation carried out on the Campus SGGW at Warsaw. The first part of paper focuses on the geological and geotechnical conditions in the campus area and the theoretical foundation of Bayesian approach. The second part of paper includes the DMT tests with statistical analysis of soil parameters obtained. Finally, the application of Bayesian theory determines the distribution of characteristic DMTindexes in two geological layers of the SGGW Campus foundation. Examples of applying the Bayesian analysis demonstrate that it is a powerful and promising statistical tool in decision-making processes related to the selection of soil parameters in geotechnical design.