# Adaptive backstepping control for FOS with nonsmooth nonlinearities

## TL;DR

This paper introduces an adaptive backstepping control method for fractional order systems with nonsmooth nonlinearities like input saturation and dead zone, ensuring asymptotic tracking despite these challenges.

## Contribution

It presents a novel approach that decomposes control input to handle nonsmooth nonlinearities, transforming the problem into disturbance and saturation compensation within a fractional order adaptive backstepping framework.

## Key findings

- Effective asymptotic tracking achieved despite nonsmooth nonlinearities
- Bound estimation of disturbances improves control robustness
- Simulation results validate the proposed control strategy

## Abstract

This paper proposes an original solution to input saturation and dead zone of fractional order system. To overcome these nonsmooth nonlinearities, the control input is decomposed into two independent parts by introducing an intermediate variable, and thus the problem of dead zone and saturation transforms into the problem of disturbance and saturation afterwards. With the procedure of fractional order adaptive backstepping controller design, the bound of disturbance is estimated, and saturation is compensated by the virtual signal of an auxiliary system as well. In spite of the existence of nonsmooth nonlinearities, the output is guaranteed to track the reference signal asymptotically on the basis of our proposed method. Some simulation studies are carried out in order to demonstrate the effectiveness of method at last.