Name
Title | ||
|---|---|---|
Direct trajectory optimization and costate estimation of finite-horizon and infinite-horizon optimal control problems using a Radau pseudospectral method |
Abstract | ||
|---|---|---|
A method is presented for direct trajectory optimization and costate estimation of finite-horizon and infinite-horizon optimal
control problems using global collocation at Legendre-Gauss-Radau (LGR) points. A key feature of the method is that it provides
an accurate way to map the KKT multipliers of the nonlinear programming problem to the costates of the optimal control problem.
More precisely, it is shown that the dual multipliers for the discrete scheme correspond to a pseudospectral approximation
of the adjoint equation using polynomials one degree smaller than that used for the state equation. The relationship between
the coefficients of the pseudospectral scheme for the state equation and for the adjoint equation is established. Also, it
is shown that the inverse of the pseudospectral LGR differentiation matrix is precisely the matrix associated with an implicit
LGR integration scheme. Hence, the method presented in this paper can be thought of as either a global implicit integration
method or a pseudospectral method. Numerical results show that the use of LGR collocation as described in this paper leads
to the ability to determine accurate primal and dual solutions for both finite and infinite-horizon optimal control problems. |
Year | DOI | Venue |
|---|---|---|
2011 | 10.1007/s10589-009-9291-0 | Computational Optimization and Applications |
Keywords | Field | DocType |
Optimal control,Trajectory optimization,Collocation methods,Nonlinear optimization,Nonlinear programming | Chebyshev pseudospectral method,Mathematical optimization,Adjoint equation,Optimal control,Trajectory optimization,Mathematical analysis,Gauss pseudospectral method,Pseudospectral optimal control,Legendre pseudospectral method,Karush–Kuhn–Tucker conditions,Mathematics | Journal |
Volume | Issue | ISSN |
49 | 2 | 0926-6003 |
Citations | PageRank | References |
42 | 3.68 | 3 |
Authors | ||
7 | ||
Name | Order | Citations | PageRank |
|---|---|---|---|
| Divya Garg | 1 | 116 | 8.87 |
| Michael A. Patterson | 2 | 240 | 18.28 |
| Camila Francolin | 3 | 147 | 12.52 |
| Christopher L. Darby | 4 | 42 | 3.68 |
| Geoffrey T. Huntington | 5 | 201 | 15.92 |
| William W. Hager | 6 | 1603 | 214.67 |
| Anil V. Rao | 7 | 341 | 29.35 |