Paper Info
Title
Pseudospectral methods for solving infinite-horizon optimal control problems
Abstract
An important aspect of numerically approximating the solution of an infinite-horizon optimal control problem is the manner in which the horizon is treated. Generally, an infinite-horizon optimal control problem is approximated with a finite-horizon problem. In such cases, regardless of the finite duration of the approximation, the final time lies an infinite duration from the actual horizon at t=+∞. In this paper we describe two new direct pseudospectral methods using Legendre–Gauss (LG) and Legendre–Gauss–Radau (LGR) collocation for solving infinite-horizon optimal control problems numerically. A smooth, strictly monotonic transformation is used to map the infinite time domain t∈[0,∞) onto a half-open interval τ∈[−1,1). The resulting problem on the finite interval is transcribed to a nonlinear programming problem using collocation. The proposed methods yield approximations to the state and the costate on the entire horizon, including approximations at t=+∞. These pseudospectral methods can be written equivalently in either a differential or an implicit integral form. In numerical experiments, the discrete solution exhibits exponential convergence as a function of the number of collocation points. It is shown that the map ϕ:[−1,+1)→[0,+∞) can be tuned to improve the quality of the discrete approximation.
Year
DOI
Venue
2011
10.1016/j.automatica.2011.01.085
Automatica
Keywords
Field
DocType
Optimal control,Pseudospectral methods,Nonlinear programming
Chebyshev pseudospectral method,Monotonic function,Mathematical optimization,Optimal control,Mathematical analysis,Nonlinear programming,Gauss pseudospectral method,Pseudospectral optimal control,Legendre pseudospectral method,Mathematics,Collocation
Journal
Volume
Issue
ISSN
47
4
0005-1098
Citations 
PageRank 
References 
17
1.43
6
Authors
3
Name
Order
Citations
PageRank
Divya Garg11168.87
William W. Hager21603214.67
Anil V. Rao334129.35