An indirect numerical method is presented that solves a class of optimal control problems that have a singular arc occurring after an initial nonsingular arc. This method iterates on the subset of initial costate variables that enforce the junction conditions for switching to a singular arc, and the time of switching off of the singular arc to a final nonsingular arc, to reduce a terminal error function of the final conditions to zero. This results in the solution to the two-point boundary-value problem obtained using the minimum principle and some necessary conditions for singular arcs. The main advantage of this method is that the exact solution to the two-point boundary-value problem is obtained. The main disadvantage is that the sequence of controls for the problem must be known to apply this method. Two illustrative examples are presented.
[1]
H. Robbins.
A generalized legendre-clebsch condition for the singular cases of optimal control
,
1967
.
[2]
H. Gardner Moyer,et al.
3 Singular Extremals
,
1967
.
[3]
Louis G. Birta,et al.
The TEF/Davidon-Fletcher-Powell method in the computation of optimal controls
,
1969
.
[4]
D. H. Jacobson,et al.
A New Necessary Condition of Optimality for Singular Control Problems
,
1969
.
[5]
Air-to-Air Missile Trajectories for Maximization of Launch Range
,
1970
.
[6]
D. Jacobson,et al.
Computation of optimal singular controls
,
1970
.