Neural Network Radial Basis Function (RBF) Controller with PID Control Law in MATLAB Simulink

The given code defines a function that implements a neural network radial basis function (RBF) controller with a Proportional-Integral-Derivative (PID) control law.

The function takes in the current time, state variables, and control signals as inputs, along with a flag that indicates the purpose of the function call. The flag is used to determine whether to initialize the controller, update the controller, or calculate the controller outputs.

In the case 0, the function initializes the sizes of the system and sets the initial state variables, sample time, and simulation state consistency.

In the case 2, the function updates the controller based on the input control signals.

In the case 3, the function calculates the controller outputs based on the current time, state variables, control signals, and other parameters such as the number of RBF units (nn), PID controller gains (K_pid), learning rates (eta_pid), RBF centers (theta), and weight parameters (alfa, beta0, w0).

In cases 1, 4, and 9, the function returns an empty output as these cases are not handled.

The rest of the code defines the sub-functions for updating the discrete states and calculating the controller outputs. These sub-functions involve calculations related to RBF activation, weight updates, and Jacobian matrix calculations.

Overall, this function implements a neural network RBF controller with a PID control law and can be used for control applications in a simulation environment.