Transformation Using Neural-Based Identification for Controlling Singularly- Perturbed Eigenvalue-Preserved Reduced Order Systems

This paper introduces a new hierarchy for controlling dynamical systems. The new control hierarchy uses supervised neural network to identify certain parameters of the transformed system matrix [ A ]. Then, Linear Matrix Inequality (LMI) is used to determine the permutation matrix [P] so that a complete system transformation {[ B~ ], [ C ], [ D~ ]} is performed. The transformed model is then reduced using singular perturbation method, and various feedback control schemes are applied to enhance system performance, including PID control, state feedback control using pole assignment, state feedback control using LQR optimal control, and output feedback control. The comparative experimental results between system transformation without using LMI and state transformation via using LMI shows clearly the superiority in system modeling and control using the proposed LMI-based control method. The new control methodology simplifies the system model and thus uses simpler controllers to produce the desired response. Index Terms Linear Matrix Inequality (LMI), LQR Optimal Control, Neural Networks, Order Model Reduction, Output Feedback Control, PID Control, Parameter Estimation, Pole Placement, Singular Perturbation Methods, State Feedback Control, System Identification.