Direct trajectory optimization by a Chebyshev pseudospectral method
- Resource Type
- Conference
- Authors
- Fahroo, F.; Ross, I.M.
- Source
- Proceedings of the 2000 American Control Conference. ACC (IEEE Cat. No.00CH36334) American control conference American Control Conference, 2000. Proceedings of the 2000. 6:3860-3864 vol.6 2000
- Subject
- Robotics and Control Systems
Computing and Processing
Components, Circuits, Devices and Systems
Optimization methods
Chebyshev approximation
Polynomials
Optimal control
Lagrangian functions
Differential equations
Gaussian processes
Mathematics
Cost function
Nonlinear equations
- Language
- ISSN
- 0743-1619
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.