An optimal PID control algorithm for training feedforward neural networks

Xingjian Jing, Li Cheng

Research output: Journal article publicationJournal articleAcademic researchpeer-review

70 Citations (Scopus)


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.
Original languageEnglish
Article number6185668
Pages (from-to)2273-2283
Number of pages11
JournalIEEE Transactions on Industrial Electronics
Issue number6
Publication statusPublished - 1 Jan 2013


  • Feedforward neural networks
  • linear matrix inequality (LMI)
  • proportional integral and derivative (PID) controller
  • robust learning

ASJC Scopus subject areas

  • Control and Systems Engineering
  • Computer Science Applications
  • Electrical and Electronic Engineering


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