Direct trajectory optimization by a Chebyshev pseudospectral method

By Fariba Fahroo, I. Michael Ross. Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334), 2000

620 citations recorded by the source corpus.

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.

Subfields: Aerospace Engineering

View Paper: https://www.semanticscholar.org/paper/1fec0ea1b3e11fec6f44575eae626ff5705d768b

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In Aerospace Engineering

Citations in the corpus

A review of pseudospectral optimal control: From theory to flight (2012, positive): “Proposition 1 generalizes the results obtained for the “big two” techniques, namely the Legendre[34] and Chebyshev[45, 46] pseudospectral methods.”
Pseudospectral Optimal Control and Its Convergence Theorems (2008, methodology): “During the 1990s, PS methods were introduced for solving optimal control problems [7, 6, 9, 8]; and since then, have gained considerable attention [10, 14, 16, 19, 30, 31].”
Convex programming approach to powered descent guidance for mars landing (2007, methodology): “Remark 7: Other basis functions such as Chebyshev polynomials [11,12,27] can also be used.”
A Powered Descent Guidance Algorithm for Mars Pinpoint Landing (2005, methodology): “Remark 10 Once can use other basis functions such as Chebyshev polynomials [8, 22].”
Homotopic approach and pseudospectral method applied jointly to low thrust trajectory optimization (2012, methodology): “The pseudospectral method [26–46] is a popular direct method, which parameterizes the state and control variables by orthogonal polynomials such as Legendre polynomial [30–37], Chebyshev polynomial [29–41], and Jacobi polynomial [42,43], and approximates dynamics at various Gauss quadrature points, ”
On the convergence of nonlinear optimal control using pseudospectral methods for feedback linearizable systems (2007, methodology): “Over the last decade, the PS methods have been used to solve a broad class of industrial-strength optimal control problems, for instance, low-thrust orbit transfers [10], impulsive orbit transfers [14], ascent guidance [12, 13], etc.”
Optimization-Based Collision Avoidance (2017, background): “Motivated by [52], we do not directly minimize τF ; instead, observing that τF = NTopt, we will treat the discretization time Topt as a decision variable, giving rise to the following cost function:”
Direct trajectory optimization based on a mapped Chebyshev pseudospectral method (2013, methodology): “And three requirements for the methods are figured out in Ref.16.”
Wavelet Collocation Method for Optimal Control Problems (2009, methodology): “3 The collocation methods developed to solve nonlinear optimal control problems generally fall into two categories, local collocation[12,13] and global orthogonal collocation [14-17].”