This paper presents a general purpose neighboring optimal guidance algorithm that is capable of driving a dynamical system along a specified nominal, optimal path. This goal is achieved by minimizing the second differential of the objective function along the perturbed trajectory. This minimization principle leads to deriving all the corrective maneuvers, in the context of a closed-loop guidance scheme. Several time-varying gain matrices, referring to the nominal trajectory, are defined, computed offline, and stored in the onboard computer. Original analytical developments, based on optimal control theory, in conjunction with the use of a normalized time scale, constitute the theoretical foundation for three relevant features: (i) a new, efficient law for the real-time update of the time of flight (the so called time-to-go), (ii) a new termination criterion, and (iii) a new analytical formulation of the sweep method. This new guidance, termed variable–time–domain neighboring optimal guidance, is rather general, avoids the usual numerical difficulties related to the occurrence of singularities for the gain matrices, and is exempt from the main disadvantages of similar algorithms proposed in the past. For these reasons, the variable–time–domain neighboring optimal guidance has all the ingredients for being successfully applied to problems of practical interest.

Variable-time-domain neighboring optimal guidance, part 1: Algorithm structure / Pontani, Mauro; Cecchetti, Giampaolo; Teofilatto, Paolo. - In: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. - ISSN 0022-3239. - 166:1(2015), pp. 76-92. [10.1007/s10957-014-0676-6]

Variable-time-domain neighboring optimal guidance, part 1: Algorithm structure

PONTANI, MAURO;CECCHETTI, GIAMPAOLO;TEOFILATTO, Paolo
2015

Abstract

This paper presents a general purpose neighboring optimal guidance algorithm that is capable of driving a dynamical system along a specified nominal, optimal path. This goal is achieved by minimizing the second differential of the objective function along the perturbed trajectory. This minimization principle leads to deriving all the corrective maneuvers, in the context of a closed-loop guidance scheme. Several time-varying gain matrices, referring to the nominal trajectory, are defined, computed offline, and stored in the onboard computer. Original analytical developments, based on optimal control theory, in conjunction with the use of a normalized time scale, constitute the theoretical foundation for three relevant features: (i) a new, efficient law for the real-time update of the time of flight (the so called time-to-go), (ii) a new termination criterion, and (iii) a new analytical formulation of the sweep method. This new guidance, termed variable–time–domain neighboring optimal guidance, is rather general, avoids the usual numerical difficulties related to the occurrence of singularities for the gain matrices, and is exempt from the main disadvantages of similar algorithms proposed in the past. For these reasons, the variable–time–domain neighboring optimal guidance has all the ingredients for being successfully applied to problems of practical interest.
2015
2nd-order sufficient conditions for optimality; neighboring optimal guidance; optimal space trajectories; perturbative guidance; control and optimization; management science and operations research; applied mathematics
01 Pubblicazione su rivista::01a Articolo in rivista
Variable-time-domain neighboring optimal guidance, part 1: Algorithm structure / Pontani, Mauro; Cecchetti, Giampaolo; Teofilatto, Paolo. - In: JOURNAL OF OPTIMIZATION THEORY AND APPLICATIONS. - ISSN 0022-3239. - 166:1(2015), pp. 76-92. [10.1007/s10957-014-0676-6]
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/997857
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