Adaptive uniform finite-/fixed-time convergent second-order sliding-mode control

ABSTRACT

This paper presents an adaptive gain algorithm for second-order sliding-mode control (2-SMC), specifically a super-twisting (STW)-like controller, with uniform finite/fixed convergence time, that is robust to perturbations with unknown bounds. It is shown that a second-order sliding mode is established as exact finite-time convergence to the origin if the adaptive gain does not have the ability to get reduced and converge to a small vicinity of the origin if the adaptation algorithm does not overestimate the control gain. The estimate of fixed convergence time of the studied adaptive STW-like controller is derived based on the Lyapunov analysis. The efficacy of the proposed adaptive algorithm is illustrated in a tutorial example, where the adaptive STW-like controller with uniform finite/fixed convergence time is compared to the adaptive STW controller with non-uniform finite convergence time.

KEYWORDS:

• Adaptive control
• sliding-mode control
• fixed-time convergence

Disclosure statement

No potential conflict of interest was reported by the authors.

Additional information

Funding

The authors thank the Mexican National Science and Technology Council (CONACyT) for financial support [grant number 232814], [grant number 129081].