Markov parameters identification and adaptive iterative learning control for linear discrete-time MIMO systems with higher-order relative degree

Abstract

For a kind of linear discrete-time-invariant multi-input-multi-output systems with a higher-order relative degree that repetitively operates within a finite time length, the paper exploits a Markov parameters identification method by making use of the multi-operation inputs and outputs obeying a criterion. Simultaneously, an adaptive iterative learning control scheme is architected by formulating the compensator with the sequentially identified Markov parameters and the tracking error in minimizing a performance index consisting of the quadratic tracking error of the next iteration and the compensation cost. Algebraic manipulations including the singular value decomposition of a matrix and the eigenvalues estimation conduct that the identification error of the Markov parameters is monotonically declining as the iteration goes on and a smaller identification ratio in the criterion delivers a faster decline rate. Meanwhile, a rigorous derivation achieves that under the assumption that the initial identification error is within an appropriate range the tracking error is monotonously convergent for the case when the relative degree is unit whilst the tracking error is asymptotically bounded for a positive level for the case where the relative degree is higher. Numerical simulations illustrate the validity and efficiency.