<abstract xmlns="http://www.w3.org/1999/xhtml">

<p>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.</p>
</abstract>

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.

Reliability–Aware Zonotopic Tube–Based Model Predictive Control of a Drinking Water Network

International Journal of Applied Mathematics and Computer Science

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

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...

Reliability–Aware Zonotopic Tube–Based Model Predictive Control of a Drinking Water Network

Published Online: Jul 04, 2022

Page range: 197 - 211

Received: Nov 14, 2021

Accepted: May 10, 2022

DOI: https://doi.org/10.34768/amcs-2022-0015

Keywords
fault-tolerant control, reliability, robust MPC, zonotopes, Bayesian theory, drinking water network

© 2022 Boutrous Khoury et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Reliability–Aware Zonotopic Tube–Based Model Predictive Control of a Drinking Water Network

Published Online: Jul 04, 2022

Page range: 197 - 211

Received: Nov 14, 2021

Accepted: May 10, 2022

DOI: https://doi.org/10.34768/amcs-2022-0015

Keywordsfault-tolerant control, reliability, robust MPC, zonotopes, Bayesian theory, drinking water network

© 2022 Boutrous Khoury et al., published by Sciendo

This work is licensed under the Creative Commons Attribution-NonCommercial-NoDerivatives 3.0 License.

Keywords
fault-tolerant control, reliability, robust MPC, zonotopes, Bayesian theory, drinking water network