High Order Optimal Feedback Control of Lunar Landing and Rendezvous Trajectories
AbstractOptimal feedback control is classically based on
linear approximations, whose accuracy drops off
rapidly in highly nonlinear dynamics. 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 the dependency of the
spacecraft state on initial conditions and
environmental parameters to be represented by high
order Taylor polynomials. The resulting polynomials
can be manipulated to obtain the high order
expansion of the solution of two-point boundary
value problems. Based on the reduction of
the optimal control problem to an equivalent two-point
boundary value problem, differential algebra
is used in this work to compute the high order
expansion of the solution of the optimal control
problem about a reference trajectory. New optimal
control laws for displaced initial states are
then obtained by the mere evaluation of polynomials.
P. Di Lizia, R. Armellin, F. Bernelli-Zazzera, M. Berz,
in: CEAS 2011 The International Conference of the European Aerospace Societies, (2011)
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