Jacobi pseudospectral method for solving optimal control problems

By Paul Williams. 2004

95 citations recorded by the source corpus.

Subfields: Aerospace Engineering, Numerical Analysis

View Paper: https://www.semanticscholar.org/paper/465b7769fad3e7a07616b17ec1c72effa63b9f86

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In Aerospace Engineering

In Numerical Analysis

Citations in the corpus

Pseudospectral methods for solving infinite-horizon optimal control problems (2011, background): “…(1995), Elnagar and Razzaghi (1997), Fahroo and Ross (2008), Garg et al. (2009), Garg et al. (2010), Huntington (2007), Rao et al. (2010) and Williams (2004) Pseudospectral methods are a class of direct collocation methods where the optimal control problem is transcribed to a nonlinear…”
AN OVERVIEW OF THREE PSEUDOSPECTRAL METHODS FOR THE NUMERICAL SOLUTION OF OPTIMAL CONTROL PROBLEMS (2017, unknown): “Let X denote the matrix formed from the coefficients xij in (4).”
Riemann–Stieltjes Optimal Control Problems for Uncertain Dynamic Systems (2015, background): “Typical choices in PS optimal control theory are these “big two” methods [12] because other polynomial basis functions do not have desirable properties for optimal control applications [19,20].”
Algorithm 902: GPOPS, A MATLAB software for solving multiple-phase optimal control problems using the gauss pseudospectral method (2010, background): “…problems [Elnagar et al. 1995; Elnagar and Kazemi 1998; Vlassenbroeck and Doreen 1988; Fahroo and Ross 2000, 2001; Ross and Fahroo 2004b; Rao 2003; Williams 2004a, 2004b, 2005; Ross and Fahroo 2004a, 2004b; Ross and Fahroo 2008a, 2008b; Benson 2004; Benson et al. 2006; Huntington 2007; Kameswaran…”
A review of pseudospectral optimal control: From theory to flight (2012, unknown): “The quest for improvement [47, 76] over Legendre polynomials has not gone beyond the Chebyshev PS method; thus, these “big two” methods constitute the state of the art.”
Homotopic approach and pseudospectral method applied jointly to low thrust trajectory optimization (2012, methodology): “The pseudospectral method [26–46] is a popular direct method, which parameterizes the state and control variables by orthogonal polynomials such as Legendre polynomial [30–37], Chebyshev polynomial [29–41], and Jacobi polynomial [42,43], and approximates dynamics at various Gauss quadrature points, ”