This paper presents a convex approach to the design of optimal space trajectories while explicitly accounting for uncertainty. A covariance control problem aimed at driving a stochastic system from an initial probability distribution to a desired one at a final time is formulated to retrieve an optimal nominal trajectory and an additive state feedback controller that can compensate for exogenous in-flight disturbances. The feedback controller regulates the thrust magnitude and, consequently, the propellant mass consumption. As a result, mass is a random state variable with a significant variance if high disturbances are considered. The propagation of the mass variance is considered in the optimization to retrieve a control policy that is robust to mass uncertainties. Convexification strategies, including changes of variables, lossless relaxations, and successive linearization, are used to obtain a deterministic convex optimization problem solvable with low computational complexity. A numerical example consisting of a low-thrust transfer from the Earth to Mars is considered. Extensive Monte Carlo campaigns are carried out to assess the effectiveness and performance of the attained control policy.

Convex Approach to Covariance Control for Low-Thrust Trajectory Optimization with Mass Uncertainty / Benedikter, Boris; Zavoli, Alessandro; Wang, Zhenbo; Pizzurro, Simone; Cavallini, Enrico. - (2023). (Intervento presentato al convegno AIAA Science and Technology Forum and Exposition tenutosi a National Harbor, MD, USA) [10.2514/6.2023-2321].

Convex Approach to Covariance Control for Low-Thrust Trajectory Optimization with Mass Uncertainty

Benedikter, Boris;Zavoli, Alessandro;Pizzurro, Simone;Cavallini, Enrico
2023

Abstract

This paper presents a convex approach to the design of optimal space trajectories while explicitly accounting for uncertainty. A covariance control problem aimed at driving a stochastic system from an initial probability distribution to a desired one at a final time is formulated to retrieve an optimal nominal trajectory and an additive state feedback controller that can compensate for exogenous in-flight disturbances. The feedback controller regulates the thrust magnitude and, consequently, the propellant mass consumption. As a result, mass is a random state variable with a significant variance if high disturbances are considered. The propagation of the mass variance is considered in the optimization to retrieve a control policy that is robust to mass uncertainties. Convexification strategies, including changes of variables, lossless relaxations, and successive linearization, are used to obtain a deterministic convex optimization problem solvable with low computational complexity. A numerical example consisting of a low-thrust transfer from the Earth to Mars is considered. Extensive Monte Carlo campaigns are carried out to assess the effectiveness and performance of the attained control policy.
2023
AIAA Science and Technology Forum and Exposition
convex optimization; stochastic optimal control; space flight
04 Pubblicazione in atti di convegno::04b Atto di convegno in volume
Convex Approach to Covariance Control for Low-Thrust Trajectory Optimization with Mass Uncertainty / Benedikter, Boris; Zavoli, Alessandro; Wang, Zhenbo; Pizzurro, Simone; Cavallini, Enrico. - (2023). (Intervento presentato al convegno AIAA Science and Technology Forum and Exposition tenutosi a National Harbor, MD, USA) [10.2514/6.2023-2321].
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Utilizza questo identificativo per citare o creare un link a questo documento: https://hdl.handle.net/11573/1672740
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