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access icon free Adaptive predictive control of periodic non-linear auto-regressive moving average systems using nearest-neighbour compensation

  • Author(s): Chenguang Yang 1 ; Hongbin Ma 2 ; Mengyin Fu 2
    • View affiliations
    • Affiliations: 1: School of Computing and Mathematics, Plymouth University, Drake Circus, Plymouth Devon PL4 8AA, UK;
      2: Key Laboratory of Intelligent Control and Decision of Complex Systems, Beijing Institute of Technology, Beijing 100081, People's Republic of China
  • Source: Volume 7, Issue 7, 02 May 2013, p. 936 – 951
    DOI:  10.1049/iet-cta.2012.0809 , Print ISSN 1751-8644, Online ISSN 1751-8652
© The Institution of Engineering and Technology
Received 11/10/2012, Accepted 01/02/2013, Revised 05/01/2013, Published

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.

Inspec keywords: autoregressive moving average processes; uncertain systems; periodic control; nonlinear control systems; control system synthesis; adaptive control; closed loop systems; compensation; time-varying systems; asymptotic stability; delays; discrete time systems; predictive control

Other keywords: periodic nonlinear autoregressive moving average systems; uncertain periodic parameters; semiparametric uncertainties; guaranteed boundedness stability; nonparametric uncertainties; one-step update law; noncausalness problem; discrete-time NARMA systems; n-step parameter update law; unknown periodic time delays; asymptotic tracking performance; nearest neighbour compensation; future output prediction; nonlinear uncertain effect compensation; adaptive predictive control law; closed-loop signal; uncertain nonlinear parameters; parametric uncertainties

Subjects: Optimal control; Nonlinear control systems; Stability in control theory; Other topics in statistics; Time-varying control systems; Distributed parameter control systems; Control system analysis and synthesis methods; Discrete control systems; Self-adjusting control systems

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