Stable data‐driven Koopman predictive control: Concentrated solar collector field case study

• Published in: IET control theory & applications Vol. 17; no. 9; pp. 1116 - 1131
• Main Authors: Gholaminejad, Tahereh, Khaki‐Sedigh, Ali
• Format: Journal Article
• Language: English
• Published: Stevenage John Wiley & Sons, Inc 01-06-2023; Wiley
• Subjects: Closed loop systems; Control methods; Control stability; Control systems; Controllers; Datasets; data‐driven control; Design; Dynamical systems; Eigenvalues; Koopman operator; Linear operators; Linear systems; Linearity; Nonlinear control; Nonlinear dynamics; Nonlinear systems; Predictive control; Robust control; solar collector field; stability proof; Willems’ fundamental Lemma
• ISSN: 1751-8644; 1751-8652
• DOI: 10.1049/cth2.12442

Non‐linearity is an inherent feature of practical systems. Although there have been significant advances in the control of nonlinear systems, the proposed methods often require considerable computational resources or rely on local linearization around equilibrium points. The Koopman operator is an infinite‐dimensional linear operator that fully captures a system's non‐linear dynamics. However, one of the major problems is identifying a Koopman finite dimensional linear model for a nonlinear system. Initiated by the Willems’ fundamental Lemma, a class of data‐driven control methods has been developed for linear systems without the need to identify the system's matrices. Motivated by these two ideas, a data‐driven Koopman‐based predictive control scheme for non‐linear systems is proposed for unknown disturbed non‐linear systems utilising a finite‐length dataset. Then, considering the uncertainty in the Koopman state variables, a robust data‐driven Koopman predictive control structure is presented. Also, the results led to the design of a data‐driven Koopman predictive control strategy with terminal components to ensure the closed‐loop stability of nonlinear systems. The proposed scheme is tested on the distributed‐parameter model of the ACUREX solar collector field (located at Almería, Spain) to regulate the field outlet temperature around a desired value. Finally, simulation results show the effectiveness of the proposed approach.
In the present work, inspired by the Willems’ fundamental Lemma, without identifying linear system's matrices, a Koopman‐based data‐driven predictive control scheme for non‐linear systems is proposed. Also, a data‐driven Koopman predictive controller with uncertainty inclusion in the Koopman state variables, with closed‐loop stability guarantees is presented. The proposed data‐driven Koopman predictive controller is employed for the control of the ACUREX solar collector field distributed‐parameter model.