# An Adaptive Control Scheme Based on Non-Interference Nonlinearity Approximation for a Class of Nonlinear Cascaded Systems and Its Application to Flexible Joint Manipulators

## TL;DR

This paper introduces a new adaptive control method for complex nonlinear systems, showing improved performance in simulations and experiments.

## Contribution

A novel nonlinearity approximation scheme with a simplified structure for adaptive control of cascaded systems.

## Key findings

- The proposed controller outperforms radial basis function network control in simulations and experiments.
- The method achieves stability even with unmodeled uncertainties through a squared-error correction procedure.
- The controller is validated on a flexible joint system, demonstrating robustness and simplicity.

## Abstract

Control design for the nonlinear cascaded system is challenging due to its complicated system dynamics and system uncertainty, both of which can be considered some kind of system nonlinearity. In this paper, we propose a novel nonlinearity approximation scheme with a simplified structure, where the system nonlinearity is approximated by a steady component and an alternating component using only local tracking errors. The nonlinearity of each subsystem is estimated independently. On this basis, a model-free adaptive control for a class of nonlinear cascaded systems is proposed. A squared-error correction procedure is introduced to regulate the weight coefficients of the approximation components, which makes the whole adaptive system stable even with the unmodeled uncertainties. The effectiveness of the proposed controller is validated on a flexible joint system through numerical simulations and experiments. Simulation and experimental results show that the proposed controller can achieve better control performance than the radial basis function network control. Due to its simplicity and robustness, this method is suitable for engineering applications.