Direct multiple shooting transcription with polynomial algebra for optimal control problems under uncertainty

Cristian Greco, Marilena Di Carlo, Massimiliano Vasile, Richard Epenoy

Research output: Contribution to journalArticle

Abstract

This paper proposes a novel approach to the solution of optimal control problems under uncertainty (OCPUUs). OCPUUs are first cast in a general formulation that allows the treatment of uncertainties of different nature, and then solved with a new direct transcription method that combines multiple shooting with generalised polynomial algebra to model and propagate extended sets. The continuity conditions on extended sets at the boundary of two adjacent segments are directly satisfied by a bounding approach. The Intrusive Polynomial Algebra aNd Multiple shooting Approach (IPANeMA) developed in this work can handle optimal control problems under a wide range of uncertainty models, including nonparametric, epistemic, and imprecise probability ones. In this paper, the approach is applied to the design of a robust low-thrust trajectory to a Near-Earth Object with uncertain initial conditions. It is shown that the new method provides more robust and reliable trajectories than the solution of an analogous deterministic optimal control problem.
Original languageEnglish
Number of pages34
JournalActa Astronautica
Early online date16 Dec 2019
DOIs
Publication statusE-pub ahead of print - 16 Dec 2019

Fingerprint

Multiple Shooting
Polynomial Algebra
Transcription
Algebra
Optimal Control Problem
Polynomials
Uncertainty
Trajectories
Trajectory
Imprecise Probabilities
Generalized Polynomials
Nonparametric Model
Model Uncertainty
Initial conditions
Adjacent
Earth (planet)
Formulation
Range of data

Keywords

  • optimal control under uncertainty
  • robust control
  • generalised multiple shooting
  • intrusive polynomial algebra
  • low-thrust trajectory optimisation

Cite this

@article{cc868f0703ad4e40a6fa4cc7a3b19e6b,
title = "Direct multiple shooting transcription with polynomial algebra for optimal control problems under uncertainty",
abstract = "This paper proposes a novel approach to the solution of optimal control problems under uncertainty (OCPUUs). OCPUUs are first cast in a general formulation that allows the treatment of uncertainties of different nature, and then solved with a new direct transcription method that combines multiple shooting with generalised polynomial algebra to model and propagate extended sets. The continuity conditions on extended sets at the boundary of two adjacent segments are directly satisfied by a bounding approach. The Intrusive Polynomial Algebra aNd Multiple shooting Approach (IPANeMA) developed in this work can handle optimal control problems under a wide range of uncertainty models, including nonparametric, epistemic, and imprecise probability ones. In this paper, the approach is applied to the design of a robust low-thrust trajectory to a Near-Earth Object with uncertain initial conditions. It is shown that the new method provides more robust and reliable trajectories than the solution of an analogous deterministic optimal control problem.",
keywords = "optimal control under uncertainty, robust control, generalised multiple shooting, intrusive polynomial algebra, low-thrust trajectory optimisation",
author = "Cristian Greco and {Di Carlo}, Marilena and Massimiliano Vasile and Richard Epenoy",
year = "2019",
month = "12",
day = "16",
doi = "10.1016/j.actaastro.2019.12.010",
language = "English",
journal = "Acta Astronautica",
issn = "0094-5765",

}

Direct multiple shooting transcription with polynomial algebra for optimal control problems under uncertainty. / Greco, Cristian; Di Carlo, Marilena; Vasile, Massimiliano; Epenoy, Richard.

In: Acta Astronautica, 16.12.2019.

Research output: Contribution to journalArticle

TY - JOUR

T1 - Direct multiple shooting transcription with polynomial algebra for optimal control problems under uncertainty

AU - Greco, Cristian

AU - Di Carlo, Marilena

AU - Vasile, Massimiliano

AU - Epenoy, Richard

PY - 2019/12/16

Y1 - 2019/12/16

N2 - This paper proposes a novel approach to the solution of optimal control problems under uncertainty (OCPUUs). OCPUUs are first cast in a general formulation that allows the treatment of uncertainties of different nature, and then solved with a new direct transcription method that combines multiple shooting with generalised polynomial algebra to model and propagate extended sets. The continuity conditions on extended sets at the boundary of two adjacent segments are directly satisfied by a bounding approach. The Intrusive Polynomial Algebra aNd Multiple shooting Approach (IPANeMA) developed in this work can handle optimal control problems under a wide range of uncertainty models, including nonparametric, epistemic, and imprecise probability ones. In this paper, the approach is applied to the design of a robust low-thrust trajectory to a Near-Earth Object with uncertain initial conditions. It is shown that the new method provides more robust and reliable trajectories than the solution of an analogous deterministic optimal control problem.

AB - This paper proposes a novel approach to the solution of optimal control problems under uncertainty (OCPUUs). OCPUUs are first cast in a general formulation that allows the treatment of uncertainties of different nature, and then solved with a new direct transcription method that combines multiple shooting with generalised polynomial algebra to model and propagate extended sets. The continuity conditions on extended sets at the boundary of two adjacent segments are directly satisfied by a bounding approach. The Intrusive Polynomial Algebra aNd Multiple shooting Approach (IPANeMA) developed in this work can handle optimal control problems under a wide range of uncertainty models, including nonparametric, epistemic, and imprecise probability ones. In this paper, the approach is applied to the design of a robust low-thrust trajectory to a Near-Earth Object with uncertain initial conditions. It is shown that the new method provides more robust and reliable trajectories than the solution of an analogous deterministic optimal control problem.

KW - optimal control under uncertainty

KW - robust control

KW - generalised multiple shooting

KW - intrusive polynomial algebra

KW - low-thrust trajectory optimisation

UR - https://www.sciencedirect.com/journal/acta-astronautica

U2 - 10.1016/j.actaastro.2019.12.010

DO - 10.1016/j.actaastro.2019.12.010

M3 - Article

JO - Acta Astronautica

JF - Acta Astronautica

SN - 0094-5765

ER -