Certainty equivalence adaptation combined with super-twisting sliding-mode control

ABSTRACT

In this paper, a Lyapunov-based control concept is presented that combines variable structure and adaptive control. The considered system class consists of nonlinear single input systems which are affected by matched structured and unstructured uncertainties. Resorting to the certainty equivalence principle, the controller exploits advantages of both the sliding-mode and the adaptive control methodology. It is demonstrated that the gains of the discontinuous control action may be reduced remarkably when compared with pure sliding-mode-based approaches. The efficiency of the presented concept is demonstrated in detail, using results of numerical simulations.

KEYWORDS:

• Adaptive control
• sliding mode control
• Lyapunov methods

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Acknowledgments

The authors kindly acknowledge support by the German Academic Exchange Service (DAAD) with financial means of The German Federal Ministry for Education and Research (BMBF). The authors also express their gratitude to Jaime Moreno Pérez for his valuable comments.

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. For brevity we shall drop the arguments of G₁, g₂ for the following calculations.