Singularity-free prescribed performance guaranteed control for perturbed system

TL;DR

This paper proposes a novel control method for high-order nonlinear systems that guarantees prescribed performance without singularities, even during abrupt reference changes, by introducing a new transformation function and strategy.

Contribution

It introduces a new transformation function with infinite differentiability and a comprehensive strategy to ensure prescribed performance without singularities in perturbed systems.

Findings

Errors stay within prescribed boundaries for smooth trajectories

Errors return to boundaries after abrupt reference changes

Simulation validates the theoretical control approach

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.