Monotonic convergence and robustness of higher‐order gain‐adaptive iterative learning control

Abstract

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

Robust finite‐iteration tracking of discrete‐time systems in repetitive process setting via ILC scheme

“…and from ( 14), the entries a lk , l = 2, … , N, k = 1, … , N − 1, can be obtained. Further, from (14), it derives that…”

“…11 Meanwhile, a host of approaches have been widely adopted during the last few years for the convergence analysis of ILC dynamics. [12][13][14][15] Among these methods, the lifted-vector matrix technique is recognized as one of the most effective methods in the investigation of ILC convergence for systems, especially for discrete-time finite-length systems. To be specific, by utilizing this technique, the ILC dynamics can be expressed as an algebraic input-output transmission equation, and then the convergence of ILC dynamics is equivalent to the stability of the transmit matrix derived from the obtained algebraic input-output transmission system.…”

An Accelerated Error Convergence Design Criterion and Implementation of Lebesgue-p Norm ILC Control Topology for Linear Position Control Systems

“…e paper [39] found that even though the learning algorithm is theoretically convergent when it gets an enormous parameter value, the upper bound of the error during the initial stage of system operation often exceeds the allowable error range of practical engineering. To avoid the above defects of the λ norm, the papers [40,41] presented the convergence of PD iterative learning control algorithm in the sense of PD measurement in the definite upper norm [42,43]. It is found that the learning algorithm is convergent only in a subinterval of the system running time interval.…”