Model Predictive Control of Parabolic PDE Systems under Chance Constraints

Ruslan Voropai (), Abebe Geletu and Pu Li
Additional contact information
Ruslan Voropai: Group of Process Optimization, Institute for Automation and Systems Engineering, Technische Universität Ilmenau, P.O. Box 100565, 98684 Ilmenau, Germany
Abebe Geletu: German Research Chair, African Institute of Mathematical Sciences (AIMS), KN 3 Rd, Kigali, Rwanda
Pu Li: Group of Process Optimization, Institute for Automation and Systems Engineering, Technische Universität Ilmenau, P.O. Box 100565, 98684 Ilmenau, Germany

Mathematics, 2023, vol. 11, issue 6, 1-23

Abstract: Model predictive control (MPC) heavily relies on the accuracy of the system model. Nevertheless, process models naturally contain random parameters. To derive a reliable solution, it is necessary to design a stochastic MPC. This work studies the chance constrained MPC of systems described by parabolic partial differential equations (PDEs) with random parameters. Inequality constraints on time- and space-dependent state variables are defined in terms of chance constraints. Using a discretization scheme, the resulting high-dimensional chance constrained optimization problem is solved by our recently developed inner–outer approximation which renders the problem computationally amenable. The proposed MPC scheme automatically generates probability tubes significantly simplifying the derivation of feasible solutions. We demonstrate the viability and versatility of the approach through a case study of tumor hyperthermia cancer treatment control, where the randomness arises from the thermal conductivity coefficient characterizing heat flux in human tissue.

Keywords: model predictive control; partial differential equations; chance constraints; inner–outer approximation; hyperthermia cancer treatment (search for similar items in EconPapers)
JEL-codes: C (search for similar items in EconPapers)
Date: 2023
References: View references in EconPapers View complete reference list from CitEc
Citations:

Downloads: (external link)
https://www.mdpi.com/2227-7390/11/6/1372/pdf (application/pdf)
https://www.mdpi.com/2227-7390/11/6/1372/ (text/html)

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:gam:jmathe:v:11:y:2023:i:6:p:1372-:d:1094852

Access Statistics for this article

Mathematics is currently edited by Ms. Emma He

More articles in Mathematics from MDPI
Bibliographic data for series maintained by MDPI Indexing Manager ().