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Direct and indirect methods in optimal control with state constraints and the climbing trajectory of an aircraft
Author(s) -
Cots Olivier,
Gergaud Joseph,
Goubinat Damien
Publication year - 2017
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.2347
Subject(s) - optimal control , shooting method , control theory (sociology) , maximum principle , boundary value problem , lift (data mining) , thrust , mathematics , state (computer science) , trajectory , lagrange multiplier , trajectory optimization , climbing , boundary (topology) , state variable , mathematical optimization , computer science , control (management) , engineering , mathematical analysis , aerospace engineering , physics , algorithm , astronomy , artificial intelligence , data mining , thermodynamics , structural engineering
Summary In this article, the minimum time and fuel consumption of an aircraft in its climbing phase are studied. The controls are the thrust and the lift coefficient and state constraints are taken into account: air slope and speed limitations. The application of the maximum principle leads to parameterize the optimal control and the multipliers associated with the state constraints with the state and the costate and leads to describe a multipoint boundary value problem, which is solved by multiple shooting. This indirect method is the numerical implementation of the maximum principle with state constraints and it is initialized by the direct method, both to determine the optimal structure and to obtain a satisfying initial guess. The solutions of the boundary value problems we define give extremals, which satisfy necessary conditions of optimality with at most 2 boundary arcs. Note that the aircraft dynamics has a singular perturbation but no reduction is performed.