Title :
Discontinuous Galerkin optimal control for constrained nonlinear problems
Author :
Boucher, Randy ; Wei Kang ; Qi Gong
Author_Institution :
Dept. of Appl. Math., Naval Postgrad. Sch., Monterey, CA, USA
Abstract :
A new numerical technique is presented for solving optimal control problems. This paper introduces a direct method that calculates optimal trajectories by discretizing the system dynamics using Galerkin numerical techniques and approximates the cost function with quadrature. We show that for bang-bang optimal control problems, discontinuous element-based Galerkin techniques lead to improved solution accuracies. Also, we show that the Galerkin optimal control method has the potential to reduce the dimension of multi-scale problems. Using two examples, the Galerkin method described in this paper is shown to be a very accurate and highly versatile method.
Keywords :
Galerkin method; bang-bang control; function approximation; nonlinear control systems; optimal control; Galerkin numerical techniques; bang-bang optimal control problems; constrained nonlinear problems; cost function approximation; dimension reduction; discontinuous Galerkin optimal control; discontinuous element-based Galerkin techniques; multiscale problems; optimal trajectory calculation; system dynamics; Accuracy; Approximation methods; Cost function; Method of moments; Optimal control; Polynomials; Vectors; Constrained optimal control; Galerkin; pseudospectral;
Conference_Titel :
Control & Automation (ICCA), 11th IEEE International Conference on
Conference_Location :
Taichung
DOI :
10.1109/ICCA.2014.6870900