For a class of repetitive linear discrete time-invariant systems with higher relative degree, a higher-order gain-adaptive iterative learning control (HOGAILC) is developed while minimizing the energy increment of two adjacent tracking errors with the argument being the iteration-time-variable learning-gain vector (ITVLGV). By taking advantage of rows/columns exchanging transformation of matrix, the ITVLGV is achieved in an explicit form which is dependent upon the system Markov parameters and adaptive to the iterationwise tracking-error vector. Algebraic derivation demonstrates that the HOGAILC is strictly monotonously convergent. On the basis of the adaptive mode, a damping quasi-HOGAILC strategy is exploited while the uncertainties of the system Markov parameters exist. Rigorous analysis delivers that the damping quasi-scheme is strictly monotonically convergent and thus the HOGAILC mechanism is robust to a wider range of uncertainty of system parameters and the damping factor may relax the uncertainty range. Numerical simulations are made to illustrate the validity and the effectiveness. K E Y W O R D Sdamping factor, gain-adaptive iterative learning control, higher relative degree, iteration-time-variable learning-gain vector, strictly monotonic convergence, uncertainty 1 3960
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