Supervisory-based quantised hands-off control for a class of uncertain systems with nonlinear sector

Abstract

This article is concerned with the problem of stabilising nonlinear uncertain systems subject to signal quantisation using nonlinear sector design. The boundary of nonlinear sector decided by the behaviour of the system showing an input-to-state stability is equivalent to $\mathcal{K}\mathcal{L}$-stability. A novel control design based on supervisory-based quantised hands-off control is introduced. With this, the true state of the nonlinear plant is estimated and the quantised control steers the trajectory of the system inside the nonlinear sector in finite time and further to the origin asymptotically. The proposed approach is validated through an illustrative example to demonstrate its theoretical effectiveness.

Keywords:

• $[\mathcal{K}\mathcal{,}\mathcal{K}\mathcal{L}]$ sector
• control-Lyapunov function
• supervisory control
• static and dynamic quantisation
• Hands-off control

Disclosure statement

No potential conflict of interest was reported by the author(s).

Data availability statement

The authors confirm that the data supporting the findings of this study are available within the article.

Additional information

Funding

The authors thank to Vellore Institute of Technology, Vellore, India for providing VIT SEED GRANT (RGEMS) Sanctioned Order No.: SG20230106 for carrying out this research work.