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Data-driven iterative learning control for nonlinear multivariate systems using transpose adaptive filtering
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DOI：10.1016/j.ejcon.2025.101273.png)
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Abstract
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This paper presents a novel data-driven iterative learning control (ILC) algorithm for stabilized multivariable nonlinear dynamical systems. The proposed algorithm incorporates two data-driven learning mechanisms: an adaptive feedforward algorithm that models perturbed dynamics as an unknown linear time-varying system and minimizes RMS errors with respect to an LTI reference model, followed by a second learning mechanism for fast convergence in trajectory tracking. For multivariate systems, the non-commutative nature of the cascade of systems necessitates the use of the right inverse for adaptive model matching to promote error convergence. To address challenges in adaptive filtering, a transposition-based technique is introduced to obtain the right inverse for square and over-actuated systems. For ni-input- no-output systems, the approach necessitates conducting ni×no experiments. An efficient algorithm is proposed to reduce this requirement by reorganizing impulse response matrix components. The effectiveness of the proposed methods is demonstrated through both simulations and experiments.
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