• Fares Nafa Boumerdes university, Faculté de Technologie, Laboratoire d’Ingénierie des Sytémes et des Telecommunication, Cité FranzFanon, Boumerdes, Algeria
  • Aimad Boudouda Boumerdes university, Faculté de Technologie, Laboratoire d’Ingénierie des Sytémes et des Telecommunication, Cité FranzFanon, Boumerdes, Algeria
  • Billel Smaani Laboratoire Hyperfréquences et Semiconducteurs Constantine 1 university, B.P. 325 Route Ain El Bey, Constantine, Algeria



Adaptive, gradient descent, pendubot, sliding mode control, wavelets.


The control of underactuated mechanical systems (UMS) remains an attracting field where researchers can develop their control algorithms. To this date, various linear and nonlinear control techniques using classical and intelligent methods have been published in literature. In this work, an adaptive controller using sliding mode control (SMC) and wavelets network (WN) is proposed for a class of second-order UMS with two degrees of freedom (DOF).
This adaptive control strategy takes advantage of both sliding mode control and wavelet properties. In the main result, we consider the case of un-modeled dynamics of the above-mentioned UMS, and we introduce a wavelets network to design an adaptive controller based on the SMC. The update algorithms are directly extracted by using the gradient descent method and conditions are then settled to achieve the required convergence performance.
The efficacy of the proposed adaptive approach is demonstrated through an application to the pendubot.


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