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arXiv · 2508.13726

Singularity-free prescribed performance guaranteed control for perturbed system

Yiwei Liu
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Abstract

This paper addresses the prescribed performance control (PPC) challenge for high-order nonlinear systems affected by mismatched disturbances. The research aims to prevent singularity issues arising from error boundary violations during abrupt changes in reference trajectories. We introduce a novel transformation function with infinite-order differentiability at connection points, advancing beyond mere continuous differentiability. Utilizing this transformation function, we develop a comprehensive transformation strategy that ensures: (1) errors remain within prescribed boundaries when reference trajectories are smooth, and (2) errors return to prescribed boundaries within a specified timeframe following abrupt changes in reference trajectories. Additionally, the complexity explosion issue inherent in backstepping design is effectively resolved. Simulation results corroborate the validity of the proposed theoretical advancements.

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Yiwei Liu. 2025-08-19. Singularity-free prescribed performance guaranteed control for perturbed system. https://arxiv.org/abs/2508.13726

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