Least Mean Square (LMS) Adaptive Algorithm

The Least Mean Square (LMS) adaptive algorithm is an iterative optimization method that minimizes the mean square error between the desired response and the filtered output signal. It estimates the gradient vector during iteration based on input signals and updates weight coefficients to achieve optimal adaptive filtering. As a stochastic gradient descent approach, LMS is notable for its computational simplicity—requiring no correlation function calculations or matrix operations. Typical implementations involve weight updates using a step-size parameter and instantaneous error feedback.

Neural Network-Based PID Control: Neural Network as Controller Rather Than PID Parameter Tuner

Neural network-based PID control does not use neural networks to tune PID parameters; instead, it employs a neural network directly as the controller, adjusting PID parameters indirectly by training the neural network's weight coefficients through backpropagation and optimization algorithms.