Combining a backstepping controller with a local stabilizer

TL;DR

This paper proposes a hybrid control strategy combining backstepping and local stabilization to address nonlinear systems where classical backstepping cannot achieve global stability, ensuring practical stability of an attractor.

Contribution

It introduces a novel hybrid feedback design that overcomes structural obstacles preventing classical backstepping from achieving global stabilization.

Findings

Hybrid controller achieves practical stability of a designated attractor.

Applicable to nonlinear systems with structural design obstacles.

Demonstrated effectiveness on a specific nonlinear system.

Abstract

We consider nonlinear control systems for which there exist some structural obstacles to the design of classical continuous stabilizing feedback laws. More precisely, it is studied systems for which the backstepping tool for the design of stabilizers can not be applied. On the contrary, it leads to feedback laws such that the origin of the closed-loop system is not globally asymptotically stable, but a suitable attractor (strictly containing the origin) is practically asymptotically stable. Then, a design method is suggested to build a hybrid feedback law combining a backstepping controller with a locally stabilizing controller. The results are illustrated for a nonlinear system which, due to the structure of the system, does not have a priori any globally stabilizing backstepping controller.