High order optimal control of space trajectories with uncertain boundary conditions |
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| Institution: | 1. Politecnico di Milano, Dipartimento di Ingegneria Aerospaziale, Via La Masa 34, 20156 Milano, Italy;2. Department of Physics and Astronomy, Michigan State University, East Lansing, MI, USA;1. University of Basilicata, School of Engineering, 10, Ateneo Lucano Street, 85100 Potenza, Italy;2. National Research Council, Institute of Methodologies for Environmental Analysis (IMAA), c/da S.Loja, 85050 Tito Scalo (PZ), Italy;1. Science and Technology on Aerospace Flight Dynamics Laboratory, Beijing 100094, China;2. Beijing Aerospace Control Center, Beijing 100094, China;1. Politecnico di Milano, Polo Territoriale di Lecco, Via M. d′Oggiono 18/a, 23900 Lecco, Italy;2. Micos Engineering GmbH, Dübendorf (ZH), Switzerland;1. University of Naples Parthenope, Italy;2. University of Naples Federico II, Italy |
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| 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. |
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| Keywords: | Optimal control Space trajectories High-order methods Differential algebra Uncertain boundary conditions |
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