Feedback Optimal Control in Low-Thrust Interplanetary Trajectory Design with Drag

Astronomy and Astrophysics – Astronomy

Scientific paper

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Scientific paper

The feedback optimal control problem in low-thrust interplanetary trajectory design considering the effect of drag(the case of Poynting-Plummer-Danby drag) is studied in this paper. The problem is tackled by solving the Hamilton-Jacobi-Bellman equation via a generating function technique devised for linear systems. Instead of solving the classical optimal control problem, this technique allows us to derive closed loop control laws in the preliminary design phase.
The idea of the work consists in applying a globally diffeomorphic linearizing transformation that rearranges the original nonlinear two-body dynamics into a linear system of ordinary differential equations written in new variables. The generating function technique is then applied to this new dynamical system, the feedback optimal control is solved, and the variables are back transformed in the original ones. We circumvent in this way the problem of expanding the vector field and truncating higher-order terms because no accuracy is lost in the undertaken approach.

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