Supervisory acceleration of convergence for homogeneous systems

ABSTRACT

The rate of convergence to the origin for a chain of integrators stabilised by homogeneous feedback is accelerated by a supervisory switching of control parameters. The proposed acceleration algorithm ensures a fixed-time convergence for otherwise exponentially or finite-time stable homogeneous closed-loop systems. Bounded disturbances are taken into account. The results are especially useful in the case of exponentially stable systems widespread in practice. The proposed switching strategy is illustrated by computer simulation.

KEYWORDS:

• Homogeneous systems
• finite-time stability
• fixed-time stability

Disclosure statement

No potential conflict of interest was reported by the authors.

Notes

1. For example, $\underset{\_}{\sigma }\left(s\right)=\left\{\begin{array}{cc}\hfill n^{-\frac{r_{max}}{\rho }}{s}^{r_{max}}& \hfill \text{if}s\le n^{\frac{1}{\rho }}\\ \hfill n^{-\frac{r_{min}}{\rho }}{s}^{r_{min}}& \hfill \text{if}s>n^{\frac{1}{\rho }}\end{array}\right.,\bar{\sigma }\left(s\right)=\sqrt{n}\left\{\begin{array}{cc}\hfill s^{r_{min}}& \hfill \text{if}s\le 1\\ \hfill s^{r_{max}}& \hfill \text{if}s>1\end{array}\right..$

Additional information

Funding

This work was partially supported by ANR [Grant Number ANR-15-CE23-0007] (Project Finite4SoS); the Government of Russian Federation [Grant Number 074-U01]; the Ministry of Education and Science of Russian Federation [Project Number 14.Z50.31.0031].