Enhanced Quantum Kernel Self-Attention Network With Exponentially Weighted Laguerre Functions for Model Predictive Control

Abstract

The real-time applicability of Model Predictive Control (MPC) techniques has expanded due to significant advancements in both theoretical and high-performance computing. However, when linear models are applied to multivariable systems with strong nonlinearities and coupled dynamics, practically implementable MPC techniques still encounter issues, including excessive computational complexity, numerical ill-conditioning, and reduced performance. The absence of a methodical and effective strategy for selecting controller parameters that strikes a balance between tracking precision and computational efficiency under rapidly changing operational conditions is another challenge. To address these limitations, this manuscript proposes an Exponentially Weighted Laguerre function based Linear Time Varying Model Predictive Controller (EWLLTVMPC). The computational load is greatly reduced by using Laguerre functions to parameterize the control sequence, and numerical ill-conditioning due to large prediction horizons in multivariable systems is reduced by adding exponential weighting. In addition, the Quantum Kernel Self-Attention Network (QKSAN) model is employed to optimally tune the MPC controller parameters, enabling adaptive and high-performance control under diverse operating scenarios. The main goals of the proposed strategy are to reduce tracking error and control effort while maintaining closed-loop stability. A laboratory-scale Twin Rotor Multi-Input Multi-Output System (TRMS) is used to experimentally test the control optimization model, which is implemented in MATLAB. With RMSE values as low as 0.0057 rad for pitch and 0.0151 rad for yaw, the controller offers improved transient responsiveness. Experimental results demonstrate a 32% reduction in control effort for yaw tracking with little overshoots. The control signals retain their boundedness and smoothness in the face of external perturbations, demonstrating efficient actuator use and dependable performance. Thus, the proposed method shows improved performance compared to traditional Linear Time-Varying MPC, Recursive Least Squares Algorithm (RLSA), Halton Sampling Algorithm (HSA), and Convolutional Neural Network (CNN) approaches.