Generalized quasi-spectral model predictive static programming method using Gaussian quadrature collocation

A new generalized quasi-spectral model predictive static programming (GS-MPSP) method is proposed to efficiently solve a class of terminal-constrained optimal control problems with specified or free terminal time. A spectral representation method is used to model the profile of the control vector, t...

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Bibliographic Details
Published in:Aerospace science and technology Vol. 106; p. 106134
Main Authors: Zhou, Cong, Yan, Xiaodong, Tang, Shuo
Format: Journal Article
Language:English
Published: Elsevier Masson SAS 01.11.2020
Subjects:
Gaussian quadrature collocation
Model predictive static programming (MPSP)
Quasi-spectral
Trajectory planning
Gaussian quadrature collocation
Model predictive static programming (MPSP)
Trajectory planning
Quasi-spectral
ISSN:1270-9638, 1626-3219
Online Access:Get full text
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Summary:A new generalized quasi-spectral model predictive static programming (GS-MPSP) method is proposed to efficiently solve a class of terminal-constrained optimal control problems with specified or free terminal time. A spectral representation method is used to model the profile of the control vector, then an infinite-dimensional optimization problem in a continuous-time framework is transformed into a small-dimensional static programming problem minimizing a certain performance index. Using the Gauss quadrature collocation method, the computation of the sensitivity matrix can be converted to the solution of a group of linear equations and algebraic summation at a few collocation nodes. Subsequently, the spectral coefficients and terminal time are efficiently obtained to eliminate terminal output deviations by solving the static programming problem. A simulation case with a scenario of intercepting a high-speed target with a specified impact angle in the midcourse phase was conducted. The results indicate that the proposed GS-MPSP approach has increased computational efficiency compared to traditional methods.
ISSN:1270-9638
1626-3219
DOI:10.1016/j.ast.2020.106134