Direct trajectory optimization by a Chebyshev pseudospectral method

Author

Fahroo, Fariba ; Ross, I. Michael

Author_Institution

Dept. of Math., Naval Postgraduate Sch., Monterey, CA, USA

Volume

6

fYear

2000

fDate

2000

Firstpage

3860

Abstract

A Chebyshev pseudospectral method is presented in this paper for directly solving a generic optimal control problem with state and control constraints. This method employs Nth degree Lagrange polynomial approximations for the state and control variables with the values of these variables at the Chebyshev-Gauss-Lobatto (CGL) points as the expansion coefficients. This process yields a nonlinear programming problem (NLP) with the state and control values at the CGL points as unknown NLP parameters. Numerical examples demonstrate this method yields more accurate results than those obtained from the traditional collocation methods

Keywords

Chebyshev approximation; nonlinear programming; optimal control; path planning; spectral analysis; CGL points; Chebyshev pseudospectral method; Chebyshev-Gauss-Lobatto points; control constraints; direct trajectory optimization; high-degree Lagrange polynomial approximations; nonlinear programming problem; optimal control problem; state constraints; unknown NLP parameters; Chebyshev approximation; Cost function; Differential equations; Gaussian processes; Lagrangian functions; Mathematics; Nonlinear equations; Optimal control; Optimization methods; Polynomials;

fLanguage

English

Publisher

ieee

Conference_Titel

American Control Conference, 2000. Proceedings of the 2000

Conference_Location

Chicago, IL

ISSN

0743-1619

Print_ISBN

0-7803-5519-9

Type

conf

DOI

10.1109/ACC.2000.876945

Filename

876945