Adaptive fuzzy backstepping dynamic surface control for output-constrained non-smooth nonlinear dynamic system

Output-constrained backstepping dynamic surface control (DSC) is proposed for the purpose of output constraint and precise output positioning of a strict feedback single-input, single-output dynamic system in the presence of deadzone and uncertainty. A symmetric barrier Lyapunov function (BLF) is employed to meet the output constraint requirement using DSC as an alternative method of backstepping control that is adopted mainly to deal with the BLF’s constraint control. However, using the ordinary DSC method with the BLF limits the selection of the control gain whereas this limitation does not exist in the backstepping structure. To remove this limitation, we propose a partial backstepping DSC method in which backstepping control is added only in the first recursive DSC design step. For precise positioning, an inverse deadzone method and adaptive fuzzy system are introduced to handle unknown deadzone and unmodeled nonlinear functions. We show that the semiglobal boundedness of the overall closed-loop signals is guaranteed, the tracking error converges within the prescribed region, and precise positioning performance is ensured. The proposed control scheme is experimentally evaluated using a robot manipulator.

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