Direct Trajectory Optimization and Costate Estimation via an Orthogonal Collocation Method

By David A. Benson, Geoffrey T. Huntington, T. Thorvaldsen, Anil V. Rao. 2006

686 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/b3aad6e87f626a3d8a759bb13debc9158fbf3825

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In Aerospace Engineering

Citations in the corpus

Algorithm 902: GPOPS, A MATLAB software for solving multiple-phase optimal control problems using the gauss pseudospectral method (2010, methodology): “The GPM was chosen as the basis for the algorithm of this article because it has many useful numerical properties including the ability to generate highly accurate costates (adjoints) [Benson 2004; Benson et al. 2006; Hunting-ton 2007] of the continuous-time optimal control problem.”
AN OVERVIEW OF THREE PSEUDOSPECTRAL METHODS FOR THE NUMERICAL SOLUTION OF OPTIMAL CONTROL PROBLEMS (2017, neutral): “(7) Collocating the dynamics at the N LG points, we have DX = F(X,U) (8) Let XN+1 be the value of the state approximated at τN+1 = +1: XN+1,j = x N j (1) By the fundamental theorem of calculus, XN+1,j = x N j (1) = x N j (−1) + ∫ +1”
An hp‐adaptive pseudospectral method for solving optimal control problems (2011, methodology): “The most well developed pseudospectral methods are the the Gauss pseudospectral method (GPM) [9, 10], the Radau pseudospectral method [14, 15, 16] (RPM), and the Lobatto pseudospectral method [7] (LPM).”
An Introduction to Trajectory Optimization: How to Do Your Own Direct Collocation (2017, methodology): “For these methods, special care must be taken when handling boundary constraints [3, 23].”
Optimism-driven exploration for nonlinear systems (2015, methodology): “We use a pseudospectral trajectory optimization algorithm for MPC [9], and a Dirichlet process”
Pseudospectral methods for solving infinite-horizon optimal control problems (2011, methodology): “We refer to the LG collocation method developed in this section as the infinite-horizon version of the Gauss pseudospectral method (Benson, 2004; Benson et al., 2006; Garg et al., 2010; Huntington, 2007; Rao et al., 2010)”
Direct trajectory optimization based on a mapped Chebyshev pseudospectral method (2013, methodology): “Benson et al.6 used Gauss pseudospectral method to solve nonlinear optimal control problems.”
A unified framework for the numerical solution of optimal control problems using pseudospectral methods (2010, methodology): “, 1995; Fahroo & Ross, 2001), the Legendre–Gauss pseudospectralmethod (Benson et al., 2006; Rao et al., 2010), and the Legendre–Gauss–Radau pseudospectral method (Garg et al.”