An optimal PID control algorithm for training feedforward neural networks

The training problem of feedforward neural networks (FNNs) is formulated into a proportional integral and derivative (PID) control problem of a linear discrete dynamic system in terms of the estimation error. The robust control approach greatly facilitates the analysis and design of robust learning algorithms for multiple-input-multiple-output (MIMO) FNNs using robust control methods. The drawbacks of some existing learning algorithms can therefore be revealed clearly, and an optimal robust PID-learning algorithm is developed. The optimal learning parameters can be found by utilizing linear matrix inequality optimization techniques. Theoretical analysis and examples including function approximation, system identification, exclusive-or (XOR) and encoder problems are provided to illustrate the results.