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Keywords:

  • digital controls;
  • closed-loop control system;
  • variational reformulation;
  • ballast tanks;
  • manned submarines;
  • blowing-venting operations

SUMMARY

On the basis of the classical variational reformulation of optimal control problems, we introduce a numerical scheme for solving those problems where the goal is the computation of optimal controls in feedback and digital forms defined on a discrete time mesh. The algorithm reduces the computation of such controls to solving a suitable nonlinear mathematical programming problem where the unknowns are the controls and slope of the state variable of the original problem. The motivation for this study comes from the real-world engineering problem which consists of maneuvering a manned submarine by using the blowing-venting control system of the ballast tanks of the vehicle. After checking the proposed algorithm in an academic example, we apply it to the maneuvering problem of submarines whose mathematical model includes a state law which is composed of a system of twenty-four nonlinear ordinary differential equations. Numerical results illustrate the performance of the numerical scheme. Copyright © 2012 John Wiley & Sons, Ltd.