Nonlinear constrained optimal control problem: a PSO–GA-based discrete augmented Lagrangian approach

  • M. A. Rahim
  • Haris M. KhalidEmail author
  • Amar Khoukhi
Original Article


This work deals with the optimal control problem which has been proposed to solve using the discrete augmented Lagrangian-based nonlinear programming approach. It is shown that this technique guarantees a satisfactory performance by minimizing the energy and maximizing the output. Further, a hybrid particle swarm and genetic algorithm-based approach is used to achieve the optimal value of Lagrange multipliers and required parameters. The designed scheme has been successfully tested through extensive simulation. The successful use of the proposed scheme encourages to other physical systems. The proposed scheme is evaluated extensively on a laboratory-scale coupled-tank system.


Optimal control Augmented Lagrangian Nonlinear programming Particle swarm optimization Genetic algorithm Control of two-tank system 


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Copyright information

© Springer-Verlag London Limited 2011

Authors and Affiliations

  1. 1.Faculty of Business AdministrationUniversity of New BrunswickFrederictonCanada
  2. 2.Department of Systems EngineeringKing Fahd University of Petroleum and MineralsDhahranSaudi Arabia

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