Article: Deep reinforcement learning LQR controller design for MIMO systems applied to gas production facility Journal: International Journal of Automation and Control (IJAAC) 2025 Vol.19 No.6 pp.669 - 704 Abstract: This paper addresses performance control in the synthesis of a stabilising controller for a gas production facility. The controller's performance is closely linked to the pole values defined during synthesis. However, it is highlighted that these calculated pole values may not always be applicable due to the system's physical constraints, such as the impossibility of reducing a biological chemical reaction from hours to microseconds. Initially, the controller is synthesised using an LQR controller with state estimators generated by a specific observer. An in-depth discussion of pole values is provided, referencing Hadamard's lemma, Gerschgorin discs, and the Nyquist stability criterion. To enhance stabilisation performance, Deep Reinforcement Learning is employed to modify the poles by adjusting LQR values in a learning environment. The results demonstrate a successful integration of Gerschgorin discs early in the synthesis process, followed by Deep Reinforcement Learning improvements, generating physically feasible pole values that significantly enhance controller performance. Inderscience Publishers - linking academia, business and industry through research

Title: Deep reinforcement learning LQR controller design for MIMO systems applied to gas production facility

Authors: Kamel Ben Slimane; Zied Tmar; Mongi Besbes

Addresses: RISC Lab - LR16ES07 ENIT, University of Tunis El Manar, Rommana 1068, Tunis, Tunisia ' RISC Lab - LR16ES07 ENIT, University of Tunis El Manar, Rommana 1068, Tunis, Tunisia; ISTIC, University of Carthage, Sidi Bou Said 1054, Tunis, Tunisia ' RISC Lab - LR16ES07 ENIT, University of Tunis El Manar, Rommana 1068, Tunis, Tunisia; ISTIC, University of Carthage, Sidi Bou Said 1054, Tunis, Tunisia

Abstract: This paper addresses performance control in the synthesis of a stabilising controller for a gas production facility. The controller's performance is closely linked to the pole values defined during synthesis. However, it is highlighted that these calculated pole values may not always be applicable due to the system's physical constraints, such as the impossibility of reducing a biological chemical reaction from hours to microseconds. Initially, the controller is synthesised using an LQR controller with state estimators generated by a specific observer. An in-depth discussion of pole values is provided, referencing Hadamard's lemma, Gerschgorin discs, and the Nyquist stability criterion. To enhance stabilisation performance, Deep Reinforcement Learning is employed to modify the poles by adjusting LQR values in a learning environment. The results demonstrate a successful integration of Gerschgorin discs early in the synthesis process, followed by Deep Reinforcement Learning improvements, generating physically feasible pole values that significantly enhance controller performance.

Keywords: stabilising controller; controller synthesis; pole placement; LQR control; linear quadratic regulator; Gerschgorin discs; deep reinforcement learning; MIMO systems; multiple inputs and multiple outputs.

DOI: 10.1504/IJAAC.2025.149525

International Journal of Automation and Control, 2025 Vol.19 No.6, pp.669 - 704

Received: 20 Jun 2024
Accepted: 01 Sep 2024
Published online: 05 Nov 2025 *

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Title: Deep reinforcement learning LQR controller design for MIMO systems applied to gas production facility

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