Feedback Optimal Control in Low-Thrust Interplanetary Trajectory Design

Document Type : Original Article

Authors

1 Dipartimento di Matematica, Universit`a di Milano Bicocca, and Astronomy Department, Cairo University.

2 Dipartimento di Ingegneria Aerospaziale, Politecnico di Milano.

Abstract

The feedback optimal control problem in low-thrust interplanetary trajectory design 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. This technique can be applied to any planet-to-planet transfer; it has been successfully tested here for the classical Earth-Mars low-thrust transfer.

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