Global output feedback control of nonlinear time-delay systems with input matching uncertainty and unknown output function

ABSTRACT

This paper studies the problem of global output feedback control for nonlinear time-delay systems with input matching uncertainty and the unknown output function, whose nonlinearities are bounded by lower triangular linear unmeasured states multiplying the unknown constant, polynomial-of-output and polynomial-of-input growth rates. By constructing a new extended state observer and skillfully combining the dynamic gain method, backstepping method and Lyapunov–Krasovskii theorem, a delay-independent output feedback controller can be developed with only one dynamic gain. It is proved that all the signals of the closed-loop system are bounded, the states of the original system and the corresponding observer converge to zero, and the estimation of input matching uncertainty converges to its actual value. Two examples demonstrate the effectiveness of the control scheme.

Keywords:

• Nonlinear time-delay systems
• input matching uncertainty
• output function
• polynomial-of-output growth rate
• polynomial-of-input growth rate

Disclosure statement

No potential conflict of interest was reported by the authors.

ORCID

Jun Xia  http://orcid.org/0000-0002-1224-6142

Yujia Zhang  http://orcid.org/0000-0003-3991-7388

Chenguang Yang  http://orcid.org/0000-0001-5255-5559

Min Wang  http://orcid.org/0000-0001-7025-7651

Additional information

Funding

This work was supported by the Taishan Scholar Project of Shandong Province of China [Grant Number ts201712040] and by the National Natural Science Foundation of China [Grant Number 61673242].

Notes on contributors

Chao Guo

Chao Guo is a doctoral student at the Institute of Automation, Qufu Normal University. Her current research interests include nonlinear control and adaptive control.

Xue-Jun Xie

Xue-Jun Xie is a professor at the Institute of Automation, Qufu Normal University. His current research interests include stochastic nonlinear control systems and adaptive control.