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

Area of Science:

• * Computational Science
• * Quantum Computing
• * Control Theory

Background:

• * Conventional linear models struggle with complex nonlinear dynamics found in many systems.
• * Recurrent neural networks offer potential but face challenges in stability and efficiency.
• * Quantum neural networks (QNNs) present an alternative with parallelism and high-dimensional processing.

Purpose of the Study:

• * To develop a stability-guaranteed learning strategy for dynamic nonlinear modeling using QNNs.
• * To introduce a novel Diagonal Recurrent Quantum Neural architecture with Lyapunov Stability (DRQNN-LS).
• * To enhance the stability, convergence, and efficiency of nonlinear system modeling.

Main Methods:

• * Integration of diagonal recurrent network structures with quantum learning algorithms.
• * Application of Lyapunov stability theory to ensure stable convergence and parameter tuning.
• * Derivation of adaptive learning rates through Lyapunov analysis for efficient parameter optimization.

Main Results:

• * DRQNN-LS demonstrated exceptional performance across three diverse scenarios: a mathematical nonlinear system, the chaotic Henon map, and a DC motor system.
• * Comparative analysis highlighted superior results for DRQNN-LS in RMSE, MSE, and FIT metrics.
• * The model exhibited robust and effective nonlinear dynamic modeling capabilities.

Conclusions:

• * DRQNN-LS offers a powerful and stable solution for identifying nonlinear dynamics from input-output data.
• * The integration of quantum computing and Lyapunov stability theory advances the field of dynamic system modeling.
• * The proposed architecture is validated for its effectiveness and robustness in complex, real-world applications.