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A numerical method for computing optimal controls in feedback and digital forms and its application to the blowing‐venting control system of manned submarines
Author(s) -
Font R.,
Pedregal P.,
Periago F.
Publication year - 2012
Publication title -
optimal control applications and methods
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.458
H-Index - 44
eISSN - 1099-1514
pISSN - 0143-2087
DOI - 10.1002/oca.2024
Subject(s) - computation , optimal control , nonlinear system , scheme (mathematics) , computer science , submarine , state (computer science) , numerical analysis , control theory (sociology) , state variable , basis (linear algebra) , ordinary differential equation , mathematical optimization , differential equation , control (management) , mathematics , engineering , algorithm , artificial intelligence , mathematical analysis , physics , quantum mechanics , marine engineering , thermodynamics , geometry
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.