Command Filtered Backstepping

TLDR

Backstepping design complexity grows with system order because each step requires computing command derivatives up to the plant’s order. This paper introduces command filters to eliminate the need for analytic derivatives in backstepping. The authors present a compensated tracking‑error formulation that preserves standard stability properties and provide a rigorous Tikhonov‑based proof of closed‑loop stability and performance.

Abstract

Implementation of backstepping becomes increasingly complex as the order of the system increases. This increasing complexity is mainly driven by the need to compute command derivatives at each step of the design, with the ultimate step requiring derivatives of the same order as the plant. This article addresses a modification that obviates the need to compute analytic derivatives by introducing command filters in the backstepping design. While the concept of the command filter has previously been introduced in the literature, the main contribution of this technical note is the rigorous analysis of the effect of the command filter on closed-loop stability and performance, and a proof of stability based on Tikhonov's theorem. The implementation approach includes a compensated tracking error that retains the standard stability properties of backstepping approaches.