INTERNATIONAL JOURNAL OF ROBUST AND NONLINEAR CONTROL Int. J. Robust Nonlinear Control 2014; 24:166–178 Published online 24 July 2012 in Wiley Online Library (wileyonlinelibrary.com). DOI: 10.1002/rnc.2881 A robust discrete-time adaptive control approach for systems with almost periodic time-varying parameters Khalid Abidi * ,† Department of Mechatronics, Bahcesehir University, Turkey SUMMARY A periodic adaptive control approach is proposed for a class of nonlinear discrete-time systems with time- varying parametric uncertainties which are almost periodic, and the only prior knowledge is the periodicity. The new adaptive controller updates the parameters and the control signal periodically in a pointwise manner over one entire period, in the sequel that achieves a bounded tracking convergence. The result is further extended to scenarios with unknown input gain, higher order dynamics, and tracking. Copyright © 2012 John Wiley & Sons, Ltd. Received 27 January 2012; Revised 16 April 2012; Accepted 3 July 2012 KEY WORDS: periodic adaptation; time-varying parameters; adaptive control; discrete-time system; non- linear process 1. INTRODUCTION Periodic adaptive control is a relatively new idea in the area of adaptive control theory. In periodic adaptive control, the parameters are periodic in nature and can vary either with respect to time or with respect to system states. In the classical adaptive control, the parametric adaptation mechanism essentially consists of a number of integrators, thus the adaptive control system is able to achieve asymptotic tracking convergence in the presence of constant parametric uncertainties, [1–3]. On the other hand, for dealing with a class of time-varying periodic unknown parameters, a method is introduced that is based on pointwise integration relying on the a priori knowledge of the periodicity of the parameters, [4–7]. Periodic variations are encountered in many real systems. These variations can exist in the system parameters, [8, 9], or as a disturbance to the system, [10–12]. This necessitates the effort in formulating an adaptive control scheme that can handle a class of systems with time-varying periodic unknown parameters or disturbances by taking into account the periodicity of the variations. In certain cases, the variations of parameters may not be exactly periodic and there can exist a bounded drift in every cycle. There can also be cases where there may exist unmodeled bounded uncertainties in the system. In these cases, robustness of the periodic adaptive control may be an issue. In [4] and [5], the parameters are assumed to be perfectly periodic and no discussion was made to ensure robustness in the case of parameter drift or unmodeled uncertainties. Robustness in adaptive control has been the subject of much research in both continuous-time and discrete-time, because modeling uncertainties may result in poor performance and even instability of the closed-loop system as observed in [13]. To enhance the robustness of the adaptive control *Correspondence to: Khalid Abidi, Department of Mechatronics, Bahcesehir University, Turkey. † E-mail: khalid.abidi@bahcesehir.edu.tr Copyright © 2012 John Wiley & Sons, Ltd.