# Stable approach based diagonal recurrent quantum neural networks for identification of nonlinear systems

## TL;DR

A new quantum neural network model is developed to better identify complex nonlinear systems with guaranteed stability and improved performance.

## Contribution

The novel DRQNN-LS model combines quantum learning with Lyapunov stability for robust nonlinear system identification.

## Key findings

- DRQNN-LS outperforms other models in RMSE, MSE, and FIT metrics on nonlinear systems.
- The model demonstrates robustness in chaotic and real-world system modeling.
- Lyapunov-based adaptive learning ensures stable convergence and efficient tuning.

## Abstract

Identification of nonlinear dynamics from input-output data is crucial in many fields where conventional linear models fail to capture nonlinear dynamics of complex systems. Although recurrent neural network architectures have the potential to deal with these problems, they often face limitations in stability, memory capacity, and convergence efficiency. Recent developments in quantum neural networks (QNNs) offer a promising alternative due to their inherent parallelism and high-dimensional processing power. However, the application of QNNs in dynamic nonlinear modeling is still underexplored, especially with regard to stability-guaranteed learning strategies. To address this gap, a novel Diagonal Recurrent Quantum Neural architecture with Lyapunov Stability (DRQNN-LS) has been developed, which combines the structural simplicity of diagonal recurrent networks harnessing the capabilities of quantum learning algorithms and the mathematical rigor of Lyapunov stability theory. Stable convergence and efficient parameter tuning are ensured by deriving adaptive learning rates through Lyapunov analysis. The proposed model is evaluated through three scenarios: a mathematical nonlinear system, a chaotic Henon map, and a practical DC motor system. Comparative analysis with other models demonstrates the exceptional capabilities of DRQNN-LS in terms of the RMSE, MSE, and FIT metrics. The obtained responses validate the effectiveness and robustness of DRQNN-LS for modeling highly nonlinear and real-world systems.