A Receding-Horizon $\mathcal {H}_\infty$ Model-Free Control for Application to Robot Manipulators
Abstract: Although robot manipulators are widely used in advanced industrial applications, their dynamics has very high complexity and uncertainties, making exact mathematical modeling difficult and preventing high-precision tracking control. Herein, we propose a practical high-performance model-free controller for robot manipulators that attenuates the undesirable side effects of a time-delayed state-based estimation (TDE) technique in terms of the receding-horizon $\mathcal {H}_\infty$ performance. By constructing tracking error dynamics with a sliding variable, the effects of TDE errors are identified and suppressed each time in terms of the fixed-horizon $\mathcal {H}_\infty$ performance. All initial states are shown to converge to a certain bounded set within a precomputed finite time. The proposed approach is beneficial for sudden transient responses and the temporarily unbounded TDE errors that cannot be handled by existing TDE-based controllers. Finally, the stability of the proposed controller is proven based on the comparison Lemma, and simulations and experiments show that its tracking performance and robustness are superior to those of conventional control algorithms.
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