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Zhu, Qiao; Xu, Jian-Xin; Yang, Shiping; Hu, Guang-Da

Adaptive backstepping repetitive learning control design for nonlinear discrete-time systems with periodic uncertainties. (English) Zbl 1330.93151

Int. J. Adapt. Control Signal Process. 29, No. 4, 524-535 (2015).
Summary: This paper addresses a tracking problem for uncertain nonlinear discrete-time systems in which the uncertainties, including parametric uncertainty and external disturbance, are periodic with known periodicity. Repetitive learning control (RLC) is an effective tool to deal with periodic unknown components. By using the backstepping procedures, an adaptive RLC law with periodic parameter estimation is designed. The overparameterization problem is overcome by postponing the parameter estimation to the last backstepping step, which could not be easily solved in robust adaptive control. It is shown that the proposed adaptive RLC law without overparameterization can guarantee the perfect tracking and boundedness of the states of the whole closed-loop systems in presence of periodic uncertainties. In addition, the effectiveness of the developed controller is demonstrated by an implementation example on a single-link flexible-joint robot.

Cited in 7 Documents

MSC:

93C55 Discrete-time control/observation systems
93C10 Nonlinear systems in control theory
68T05 Learning and adaptive systems in artificial intelligence
93C41 Control/observation systems with incomplete information

Keywords:

repetitive learning control; adaptive control; backstepping; nonlinear discrete-time systems; periodic uncertainties
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References:

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