Large-scale processes in the energy and process industries are networks of interconnected nonlinear subsystems with uncertain and slowly drifting dynamics. Block-oriented self-tuning schemes, such as Hammerstein-based regulators, handle this uncertainty recursively but tie the controller to a restrictive model structure. In this study, the identified block-oriented model is replaced by Koopman linear predictors estimated online, one per subsystem, in a lifted observable space through a recursive least-squares law with forgetting and bounded covariance. These adaptive predictors are integrated into a distributed, input-constrained Koopman model predictive controller, denoted AK-DMPC, whose local problems are convex quadratic programs solved in parallel with a single neighbor communication per sampling instant. Three results are established: (i) The identifier has bounded covariance, and its parameter error does not vanish but decays exponentially to a residual set whose radius is set by the lifting (closure) error and the parameter drift; (ii) the multistep prediction error is bounded by the estimation and closure errors propagated through the interconnection; and (iii) under a verifiable small-gain condition on the interconnection, the closed loop is input-to-state stable on an explicit region of the state space with respect to these errors. The network tracking error is therefore governed by the dictionary richness. Abrupt parameter jumps, which violate the slow-drift premise, are covered by a dwell-time corollary quantifying the excursion and the geometric recovery. Recursive feasibility is proved under standard terminal ingredients. On three interconnected nonlinear tanks with an abrupt valve fault, AK-DMPC lowers the network tracking error by $ 28\% $ and $ 58\% $ against a frozen Koopman controller and a decentralized linear controller, and it matches an adaptive Hammerstein self-tuning regulator in accuracy with threefold smoother control and a closed-loop stability certificate ($ \rho(A_{\mathrm{cl}})\approx0.54 $).
Citation: Tawfik Guesmi, Mourad Elloumi, Khalid Alqunun, Omar Naifar. Adaptive Koopman predictive control of large-scale interconnected nonlinear systems: A recursive lifting approach with small-gain guarantees[J]. AIMS Mathematics, 2026, 11(8): 27164-27202. doi: 10.3934/math.20261088
Large-scale processes in the energy and process industries are networks of interconnected nonlinear subsystems with uncertain and slowly drifting dynamics. Block-oriented self-tuning schemes, such as Hammerstein-based regulators, handle this uncertainty recursively but tie the controller to a restrictive model structure. In this study, the identified block-oriented model is replaced by Koopman linear predictors estimated online, one per subsystem, in a lifted observable space through a recursive least-squares law with forgetting and bounded covariance. These adaptive predictors are integrated into a distributed, input-constrained Koopman model predictive controller, denoted AK-DMPC, whose local problems are convex quadratic programs solved in parallel with a single neighbor communication per sampling instant. Three results are established: (i) The identifier has bounded covariance, and its parameter error does not vanish but decays exponentially to a residual set whose radius is set by the lifting (closure) error and the parameter drift; (ii) the multistep prediction error is bounded by the estimation and closure errors propagated through the interconnection; and (iii) under a verifiable small-gain condition on the interconnection, the closed loop is input-to-state stable on an explicit region of the state space with respect to these errors. The network tracking error is therefore governed by the dictionary richness. Abrupt parameter jumps, which violate the slow-drift premise, are covered by a dwell-time corollary quantifying the excursion and the geometric recovery. Recursive feasibility is proved under standard terminal ingredients. On three interconnected nonlinear tanks with an abrupt valve fault, AK-DMPC lowers the network tracking error by $ 28\% $ and $ 58\% $ against a frozen Koopman controller and a decentralized linear controller, and it matches an adaptive Hammerstein self-tuning regulator in accuracy with threefold smoother control and a closed-loop stability certificate ($ \rho(A_{\mathrm{cl}})\approx0.54 $).
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Tawfik Guesmi, Mourad Elloumi, Khalid Alqunun, Omar Naifar. Adaptive Koopman predictive control of large-scale interconnected nonlinear systems: A recursive lifting approach with small-gain guarantees[J]. AIMS Mathematics, 2026, 11(8): 27164-27202. doi: 10.3934/math.20261088
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