# Approximation-based adaptive fixed-time tracking control for uncertain high-order nonlinear systems subject to time-varying parameters and unknown input nonlinearity

## TL;DR

This paper introduces a new control method for nonlinear systems with uncertain parameters and unknown input nonlinearities, ensuring tracking within a fixed time.

## Contribution

The novel contribution is an adaptive neural network-based fixed-time tracking control scheme for uncertain high-order nonlinear systems.

## Key findings

- The proposed control strategy ensures tracking error converges to a small neighborhood of zero within fixed time.
- The method maintains boundedness of all closed-loop system signals despite input nonlinearities.
- Simulation results validate the effectiveness of the theoretical approach.

## Abstract

In this paper, the fixed-time tracking control (FTTC) problem is discussed for a type of uncertain high-order nonlinear systems. Compared with the existing works, the studied system is affected by time-varying parameters and unknown input nonlinearity. By applying neural network (NN) approximation method together with the adaptive control method, the fixed-time control theory, the backstepping control method, and the Nussbaum gain function (NGF) technique, an adaptive NN-based FTTC scheme is presented to achieve fixed time tracking. Especially, the NGF is utilized to handle the unknown control gain caused by unknown input nonlinearity. Furthermore, some adaptive control laws are formulated to estimate unknown parameters. Under the influence of different input nonlinearity, it can be inferred that the designed control strategy guarantees that the tracking error converges to a small neighborhood of zero within a fixed time, while also maintaining the boundedness of all signals of the closed-loop system. Finally, three simulation cases are presented to validate the availability of the theoretical results.