SNOPT: An SQP Algorithm for Large-Scale Constrained Optimization
SIAM Journal on Optimization
Nonlinear model predictive control of an inverted pendulum
ACC'09 Proceedings of the 2009 conference on American Control Conference
ACM Transactions on Mathematical Software (TOMS)
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
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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 @t@?[-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 @f:[-1,+1)-[0,+~) can be tuned to improve the quality of the discrete approximation.