Abstract A high order optimal control strategy is proposed in this work, based on the use of differential algebraic techniques. In the frame of orbital mechanics, differential algebra allows to represent, by high order Taylor polynomials, the dependency of the spacecraft state on initial conditions and environmental parameters. The resulting polynomials can be manipulated to obtain the high order expansion of the solution of two-point boundary value problems. Since the optimal control problem can be reduced to a two-point boundary value problem, differential algebra is used to compute the high order expansion of the solution of the optimal control problem about a reference trajectory. Whenever perturbations in the nominal conditions occur, new optimal control laws for perturbed initial and final states are obtained by the mere evaluation of polynomials. The performances of the method are assessed on lunar landing, rendezvous maneuvers, and a low-thrust Earth–Mars transfer.
Highlights Differential algebra is introduced and used to Taylor expand ODE flows. The minimum-energy optimal control problem is reduced to a TPBVP. A high order method to expand the solution in the boundary conditions is presented. The control of lunar landing, rendezvous, and low-thrust transfers is addressed. The accuracy of the method with respect to the uncertainty level is discussed.
High order optimal control of space trajectories with uncertain boundary conditions
Acta Astronautica ; 93 ; 217-229
2013-07-04
13 pages
Aufsatz (Zeitschrift)
Elektronische Ressource
Englisch
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