Nonlinear Decoupling Control With PI^λ D^μ Neural Network for MIMO Systems

Area of Science:

• Control Systems Engineering
• Artificial Intelligence
• Neural Networks

Background:

• Multi-input multi-output (MIMO) systems often exhibit strong coupling, complicating control.
• Traditional controllers may struggle with the dynamic complexity and coupling in MIMO systems.
• Neural network controllers offer adaptive capabilities but can face challenges with convergence and local optima.

Purpose of the Study:

• To propose a novel fractional order proportional-integral-differential neural network (PIDNN) controller for strongly coupled MIMO systems.
• To enhance controller performance by leveraging the long memory characteristics of fractional order calculus.
• To ensure controller stability and optimize initialization using advanced algorithms.

Main Methods:

• Introduction of a fractional order PID operator into the hidden layer neurons of a neural network.
• Application of Lyapunov theory to establish a sufficient condition for controller stability based on the learning rate.
• Initialization of the PI[Formula: see text]NN using the Beetle Swarm Optimization (BSO) algorithm to avoid local optima.
• Integration of fractional order calculus for improved control accuracy and convergence speed.

Main Results:

• The proposed fractional order PIDNN controller effectively eliminates coupling between system variables.
• Demonstrated superior control performance compared to existing methods in simulation examples.
• Achieved desirable control outcomes without the need for a specific system model.
• Validated the novelty of employing fractional order PI[Formula: see text] neurons in neural network controllers.

Conclusions:

• The fractional order PIDNN controller, optimized by BSO, presents a significant advancement for MIMO system control.
• The controller's design effectively addresses strong coupling and improves both accuracy and convergence.
• This work establishes a new paradigm by incorporating fractional order calculus into neural network-based control architectures.