Nonlinear \(H_\infty\) control via measurement feedback using neural network

  • Rochdi Bachir Bouiadjra
  • Mohamed Fayçal Khelfi
  • Mohammed Salem
  • Moussa Sedraoui
Technical Paper


In this paper, we solve the nonlinear \(H_\infty\) optimal control with output feedback via the neural network (NN)–least squares method for the affine nonlinear system. The approach is based on successive approximate solution of two Hamilton–Jacobi–Isaacs (HJI) equations, which appear in the \(H_\infty\) optimal output feedback control. Successive approximation (SA) approach combined with neural network (NN) for updating control and disturbance inputs in the case of state-feedback control is first proposed to solve an HJI equation with two players. The obtained solution is then used to solve, with the SA-NN approach for updating disturbance input, an HJI equation with one player in the output feedback control problem. Simulations on the Translational oscillator with rotational actuator mechanical system are presented to illustrate the effectiveness of the proposed method.


Nonlinear \(H_\infty\) control Output feedback Hamilton–Jacobi–Isaacs equation Successive approximation Neural-network approximation 



The authors would like to thank the referees and the editor for the detailed comments that have helped significantly improve the quality of presentation.


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Copyright information

© The Brazilian Society of Mechanical Sciences and Engineering 2016

Authors and Affiliations

  1. 1.Computer Science DepartmentUniversity Mustapha Stambouli of MascaraMascaraAlgeria
  2. 2.Laboratory of Research in Industrial Computing and NetworksUniversity Ahmed Benbella Oran 1OranAlgeria
  3. 3.Laboratoire des télécommunicationsUniversité 8 Mai 1945 GuelmaGuelmaAlgeria

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