Abstract | ||
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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 |
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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 Garg | 1 | 116 | 8.87 |
William W. Hager | 2 | 1603 | 214.67 |
Anil V. Rao | 3 | 341 | 29.35 |