Legendre Pseudospectral Approximations of Optimal Control Problems

By I. Michael Ross, Fariba Fahroo. 2003

292 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/bd7a639933759e360089a083e3c67c9bd81fdc34

How researchers see this paper

The researchers whose trusted networks rank it highest, strongest advocate first. Every researcher gets a different order.

Citations in the corpus

Optimal Cross-Wind Towing and Power Generation with Tethered Kites (2007, methodology): “Studies of convergence behavior and application of the method can be found in [30].”
On the convergence of nonlinear optimal control using pseudospectral methods for feedback linearizable systems (2007, methodology): “1 Pseudospectral methods are not limited to dynamical systems in normal form; in fact, they are applicable to far more general nonlinear systems; see, for example, [24, 25, 29] and the references therein.”
On Discrete-Time Optimality Conditions for Pseudospectral Methods (2006, unknown): “The most widely used PS method is the Legendre PS method 22,34,35 that is based on the Legendre-Gauss-Lobatto (LGL) node points.”
Algorithm 902: GPOPS, A MATLAB software for solving multiple-phase optimal control problems using the gauss pseudospectral method (2010, methodology): “Examples of COTS software include SOCS [Betts and Huffman 1997], DIRCOL [von Stryk 2000], GESOP [Jansch et al. 1994], OTIS [Vlases et al. 1990], DIDO [Ross and Fahroo 2001], DIRECT [Williams 2008], and MISER [Goh and Teo 1988], while examples of open-source optimal control software include DYNOP”
Optimal trajectory planning for trains – A pseudospectral method and a mixed integer linear programming approach (2013, background): “All those approximations are relevant to optimal control problems, e.g., the differential equations of the optimal control problem can then be approximated by algebraic equations (Ross and Fahroo, 2003).”
Direct Trajectory Optimization and Costate Estimation via an Orthogonal Collocation Method (2006, methodology): “Additionally, a costate estimation procedure that uses the Legendre pseudospectral method was developed in [13,14].”
Homotopic approach and pseudospectral method applied jointly to low thrust trajectory optimization (2012, methodology): “Actually, this correspondence was termed ‘covector or costates mapping’ in [31–39] and various versions of this equivalence were presented there in different frameworks, such as LGL, LG, and LGR.”
A review of pseudospectral optimal control: From theory to flight (2012, unknown): “Proposition 1 generalizes the results obtained for the “big two” techniques, namely the Legendre[34] and Chebyshev[45, 46] pseudospectral methods.”