Direct Trajectory Optimization by a Chebyshev Pseudospectral Method ; Journal of Guidance, Control, and Dynamics, v. 25, 2002 ; pp. 160-166

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 N t h degree Lagrange polynomial approxiniations for the state and control variables with the values of these variables at the Chebyshev-GaussLobatto (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.

[1]  Gamal N. Elnagar,et al.  The pseudospectral Legendre method for discretizing optimal control problems , 1995, IEEE Trans. Autom. Control..

[2]  S. Orszag,et al.  Theory and applications of spectral methods , 1984 .

[3]  J. Betts.  Survey of Numerical Methods for Trajectory Optimization , 1998 .

[4]  B. Conway,et al.  Collocation Versus Differential Inclusion in Direct Optimization , 1998 .

[5]  I. Michael Ross,et al.  Second Look at Approximating Differential Inclusions , 2001 .

[6]  Greg Knowles,et al.  An Introduction to Applied Optimal Control , 1982 .

[7]  Gamal N. Elnagar,et al.  Pseudospectral Chebyshev Optimal Control of Constrained Nonlinear Dynamical Systems , 1998, Comput. Optim. Appl..

[8]  C. Canuto.  Spectral methods in fluid dynamics , 1991 .

[9]  R. V. Dooren,et al.  A Chebyshev technique for solving nonlinear optimal control problems , 1988 .

[10]  D. Hull.  Conversion of optimal control problems into parameter optimization problems , 1996 .

[11]  C. Hargraves,et al.  DIRECT TRAJECTORY OPTIMIZATION USING NONLINEAR PROGRAMMING AND COLLOCATION , 1987 .

[12]  O. V. Stryk,et al.  Numerical Solution of Optimal Control Problems by Direct Collocation , 1993 .

[13]  Alex Solomonoff,et al.  A fast algorithm for spectral differentiation , 1992 .

[14]  I. Michael Ross,et al.  Costate Estimation by a Legendre Pseudospectral Method , 1998 .

[15]  A. L. Herman,et al.  Direct optimization using collocation based on high-order Gauss-Lobatto quadrature rules , 1996 .

[16]  Jacques Vlassenbroeck,et al.  A chebyshev polynomial method for optimal control with state constraints , 1988, Autom..