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This regularized optimal control problem with the cost (27) has continuous extremal controls and it is therefore well suited to a continuation procedure.
The overall continuation procedure is depicted on Fig. 16.
The continuation procedure aims at reducing progressively the infeasibility.
Fig. 16 Continuation procedure for solving ((mathcal {P}_{A})).
Fig. 13 Continuation procedure for ((mathcal {P}_{S})).
The numerical experiments show that this continuation procedure is very efficient.
Similar(29)
Continuation procedures are also valuable for high-thrust orbital transfer problems.
Similar continuation procedures have also been applied to the well-known Goddard's problem, and to its three-dimensional variants ([12, 14]).
Emphasis is placed on the effect of destabilizing loads and on the derivation of the solution methodologies required for tracking a highly nonlinear equilibrium path, namely: parameter continuation and arc-length continuation procedures.
Through this example, we illustrate how to analyze the (singular and regular) extremals of the problem with Lie and Poisson brackets, and how to elaborate numerical continuation procedures adapted to the solution structure.
The performance of the continuation procedures and the convergence of the multi-term extended Kantorovich method are examined through the solution of the two-dimensional Bratu Gelfand benchmark problem.
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