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.

In this study, the authors are concerned with the observer-based quantised H ∞ control problem for a class of discrete-time stochastic systems with random communication delays. The system under consideration involves signals quantisation, state-dependent disturbance as well as random communication delays. The measured output and the control input quantisation are considered simultaneously by using the sector bound approach, while the random communication delays from the sensor to the controller and from the controller to the plant are modelled by a linear function of the stochastic variable satisfying Bernoulli random binary distribution. It is aimed at designing an observer-based controller such that the dynamics of the closed-loop system is guaranteed to be exponentially stable in the mean square, and a prescribed H ∞ disturbance attenuation level is also achieved. Finally, a simulation example is given to illustrate the effectiveness of the proposed method.