A ph mesh refinement method for optimal control |
| |
| Authors: | Michael A Patterson William W Hager Anil V Rao |
| |
| Affiliation: | 1. Department of Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL 32611, USA;2. Department of Mathematics, University of Florida, Gainesville, FL 32611, USA |
| |
| Abstract: | A mesh refinement method is described for solving a continuous‐time optimal control problem using collocation at Legendre–Gauss–Radau points. The method allows for changes in both the number of mesh intervals and the degree of the approximating polynomial within a mesh interval. First, a relative error estimate is derived based on the difference between the Lagrange polynomial approximation of the state and a Legendre–Gauss–Radau quadrature integration of the dynamics within a mesh interval. The derived relative error estimate is then used to decide if the degree of the approximating polynomial within a mesh should be increased or if the mesh interval should be divided into subintervals. The degree of the approximating polynomial within a mesh interval is increased if the polynomial degree estimated by the method remains below a maximum allowable degree. Otherwise, the mesh interval is divided into subintervals. The process of refining the mesh is repeated until a specified relative error tolerance is met. Three examples highlight various features of the method and show that the approach is more computationally efficient and produces significantly smaller mesh sizes for a given accuracy tolerance when compared with fixed‐order methods. Copyright © 2014 John Wiley & Sons, Ltd. |
| |
| Keywords: | optimal control collocation Gaussian quadrature variable‐order mesh refinement |
|
|
