Adaptive predictive control of periodic non‐linear auto‐regressive moving average systems using nearest‐neighbour compensation. Issue 7 (1st May 2013) - Yang, Chenguang; Ma, Hongbin; Fu, Mengyin
Abstract : Many practical non‐linear systems can be described by non‐linear auto‐regressive moving average (NARMA) system models, whose stabilisation problem is challenging in the presence of large parametric uncertainties and non‐parametric uncertainties. In this work, to address this challenging problem for a wide class of discrete‐time NARMA systems, in which there are uncertain periodic parameters as well as uncertain non‐linear part with unknown periodic time delays, we develop adaptive predictive control laws using the key ideas of 'future outputs prediction' and 'nearest‐neighbour compensation', among which the former is carried out to overcome the non‐causalness problem and the latter novel idea is proposed to completely compensate for the effect of non‐linear uncertainties as well as unknown time delays. To achieve the desired asymptotic tracking performance in the presence of semi‐parametric uncertainties with time delays, an ' n ‐step parameter update law' is first designed, based on which an 'one‐step update law' is then elaborately constructed to obtain smoother closed‐loop signals. This study in general develops a systematic adaptive control framework for periodic NARMA systems with guaranteed boundedness stability and asymptotic tracking performance, which are established by rigorous theoretic proof and verified by simulation studies.