Neural Network Based Adaptive Inverse Optimal Control for Non-Affine Nonlinear Systems

Muhammet Emre Sancı*, Gülay Öke Günel

*Corresponding author for this work

Research output: Contribution to journalArticlepeer-review


In this paper, a novel methodology is introduced for the inverse optimal control of non-affine, nonlinear and discrete-time systems. Although inverse optimal control of affine systems is studied in detail in technical literature, there is no adequate research about its implementation on non-affine systems. here are two main contributions of this work. Firstly using the input–output data of the system to be controlled its NARMA-L2 model is obtained using a multi-layer feedforward neural network, this step provides a conversion from a non-affine to affine system model. After the affine system model is obtained, the inverse optimal control law is applied. The second contribution of this paper is the computation of the inverse optimal control signal. The selection of the P matrix in the control law is crucial since its value directly affects the control performance. Here a novel method is proposed where an adaptive and optimal P matrix is computed online using a recurrent neural network to minimize a predefined cost function. The performance of the proposed control method is evaluated by simulations performed on benchmark problems. The robustness of the method is also tested by additional simulations where noise and disturbance is imposed on the system. The obtained results justify the applicability of the proposed approach.

Original languageEnglish
Article number46
JournalNeural Processing Letters
Issue number2
Publication statusPublished - Apr 2024

Bibliographical note

Publisher Copyright:
© The Author(s) 2024.


  • Adaptive control
  • Inverse optimal control
  • NARMA-L2 Model
  • Non-linear nonaffine systems


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