Data-driven iterative learning control for nonlinear multivariate systems using transpose adaptive filtering

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 $n_i$-input-$n_o$-output systems, the approach necessitates conducting $n_i\times n_o$ 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.