A numerical method for computing optimal controls in feedback and digital forms and its application to the blowing‐venting control system of manned submarines

Abstract

SUMMARYOn 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.

Multi‐verse optimizer based PI‐type active disturbance rejection generalized predictive control parameter tuning for ship motion

“…Veremey designed a filter to realize the control law optimization of the ships 7 . Font devised a computing optimal control, and employed it in the submarine control system 8 . Islam proposed robust integral backstepping and terminal synergetic control, and employed it in ship motion control 9 …”

“…7 Font devised a computing optimal control, and employed it in the submarine control system. 8 Islam proposed robust integral backstepping and terminal synergetic control, and employed it in ship motion control. 9 Based on PID, Han proposed active disturbance rejection control (ADRC) [10][11][12] method in 1997.…”

Mejora de la maniobrabilidad de submarinos tripulados mediante control óptimo de tanques de lastre

“…Los resultados muestran que con un adecuado control el soplado diferencial de los tanques puede contribuir de manera sustantiva a mejorar la estabilidad y seguridad de este tipo de maniobras. Parte de los resultados de simulación incluidos en este capítulo han sido publicados en [FGPMP12,FPP].…”