Global tracking for a class of uncertain nonlinear systems with unknown sign-switching control direction by output feedback

Abstract

This paper addresses the design of a sliding mode controller for a class of high-order uncertain nonlinear plants with unmatched state-dependent nonlinearities and unknown sign of the high frequency gain, i.e., the control direction is assumed unknown. Differently from most previous studies, the control direction is allowed to switch its sign. We show that it is possible to obtain global exact tracking using only output-feedback by coupling a relay periodic switching function with a norm state observer. One significant advantage of the new scheme is its robustness and improved transient response under arbitrary changes of the control direction which have been theoretically demonstrated for jump variations and successfully tested by simulations. The proposed controller is also evaluated with a DC motor control experiment.

Keywords:

• uncertain nonlinear systems
• unknown control direction
• Nussbaum gain
• sliding mode control
• variable structure systems
• output-feedback
• global exact tracking

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. For each fixed y(z), ψ_i(y, t) (ψ_o(z, t)) is uniformly bounded in t.

2. For each fixed y, ϕ₀(y, t) is uniformly bounded in t.

3. For a, b, p, q ∈ ⁺, with 1/p + 1/q = 1, one has that ab ≤ a^p/p + b^q/q (Young's inequality). Here, we have considered $a={\bar{\gamma }}_2$, b = [(1 + 1/ε₁)Π]^1/m, p = 1 + ε₂ and q = (ε₂ + 1)/ε₂.

Additional information

Funding

The authors gratefully acknowledge the financial support by CAPES, FAPERJ and CNPq from Brazil.