Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Handbook of Mathematical Functions, With Formulas, Graphs, and Mathematical Tables,
Computational Optimization and Applications
Computational Optimization and Applications
ACM Transactions on Mathematical Software (TOMS)
Computational Optimization and Applications
Brief paper: Pseudospectral methods for solving infinite-horizon optimal control problems
Automatica (Journal of IFAC)
Convergence of the forward-backward sweep method in optimal control
Computational Optimization and Applications
An efficient overloaded method for computing derivatives of mathematical functions in MATLAB
ACM Transactions on Mathematical Software (TOMS)
Journal of Computational and Applied Mathematics
Mathematics and Computers in Simulation
On minimum-time paths of bounded curvature with position-dependent constraints
Automatica (Journal of IFAC)
Hi-index | 22.15 |
A unified framework is presented for the numerical solution of optimal control problems using collocation at Legendre-Gauss (LG), Legendre-Gauss-Radau (LGR), and Legendre-Gauss-Lobatto (LGL) points. It is shown that the LG and LGR differentiation matrices are rectangular and full rank whereas the LGL differentiation matrix is square and singular. Consequently, the LG and LGR schemes can be expressed equivalently in either differential or integral form, while the LGL differential and integral forms are not equivalent. Transformations are developed that relate the Lagrange multipliers of the discrete nonlinear programming problem to the costates of the continuous optimal control problem. The LG and LGR discrete costate systems are full rank while the LGL discrete costate system is rank-deficient. The LGL costate approximation is found to have an error that oscillates about the true solution and this error is shown by example to be due to the null space in the LGL discrete costate system. An example is considered to assess the accuracy and features of each collocation scheme.