Costate Computation by a Chebyshev Pseudospectral Method

Gong, Qi; Ross, I. Michael; Fahroo, Fariba

doi:10.2514/1.45154

Cited by 29 publications

(11 citation statements)

References 25 publications

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“…We can see that the time histories of the states and controls are almost the same as those in [26] and [27].…”

Section: Numerical Examplesmentioning

confidence: 63%

“…Since the partial derivatives of F are supposed to be continuous, F satisfies the local Lipschitz conditions with respect to its arguments. Therefore, we have kF N (x 3 N (t);u 3 N (t);t) 0 F (x(t);ũ(t);t)k kF N (x 3 N (t);u 3 N (t);t) 0 F (x 3 N (t);u 3 N (t);t)k + kF(x 3 N (t);u 3 N (t);t) 0 F (x(t);ũ(t);t)k CN 01 jF(x 3 N (t);u 3 N (t);t)j1 + kF(x 3 N (t);u 3 N (t);t) 0 F (x(t);u 3 N (t);t)k + kF(x(t);u 3 N (t);t) 0 F (x(t);ũ(t);t)k CN 01 jF(x 3 N (t);u 3 N (t);t)j 1 + K1kx 3 N 0xk + K2ku 3 N 0ũk (27) where K1 and K2 are the Lipschitz constants of the function F with respect to the first two variables, they are independent of N . Obviously, the right hand side of (27) tends to 0 when N 0 !…”

Section: Theoretical Resultsmentioning

confidence: 99%

“…Example 1: We first consider a minimum fuel orbit transfer problem discussed in [26], [27]. The problem is to minimize In Table I, we give the comparison of J N obtained via three methods.…”

Section: Numerical Examplesmentioning

confidence: 99%

See 2 more Smart Citations

An Efficient Chebyshev Algorithm for the Solution of Optimal Control Problems

Qin

Zhang

2011

IEEE Trans. Automat. Contr.

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“…We can see that the time histories of the states and controls are almost the same as those in [26] and [27].…”

Section: Numerical Examplesmentioning

confidence: 63%

Section: Theoretical Resultsmentioning

confidence: 99%

See 1 more Smart Citation

An Efficient Chebyshev Algorithm for the Solution of Optimal Control Problems

Qin

Zhang

2011

IEEE Trans. Automat. Contr.

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“…Various direct methods, including the collocation method of discrete state variables and control variables [24], the differential inclusion method in which only state variables are discretized [25], and the numerical integration method in which only control variables are discretized [26], have been presented to deal with trajectory optimization problems. In recent years, the pseudo spectral method has attracted great attention of many researchers [27], which has in theory been confirmed that the pseudo spectral method converted nonlinear programming problems are equivalent to the first order necessary conditions of optimal control problem [28].…”

Section: Low Thrust Trajectory Optimizationmentioning

confidence: 98%

A survey on orbital dynamics and navigation of asteroid missions

Baoyin

2014

Acta Mech Sin

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Asteroid exploration is currently one of the most concerned topics among international space agencies. Orbital dynamics and navigation are obviously crucial for asteroid exploration. This paper aims to give a brief review on the dynamics, control and navigation of asteroid reconnaissance orbits, including the heliocentric transfer orbit and near asteroid orbit. The developments in optimization techniques of the transfer segment are discussed in detail. We surveyed global researches in this field and made comments on several important progresses. The final section proposed a prospective of future studies with emphasis on the key techniques of these issues in the asteroid exploration missions.

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“…Thus, we have derived a Riemann-Stieltjes-generalized Pontryagin principle via a new application of the covector mapping principle [11][12][13][14] summarized in Fig. 4.…”

Section: B Riemann-stieltjes Generalization Of Pontryagin's Principlementioning

confidence: 99%

Riemann–Stieltjes Optimal Control Problems for Uncertain Dynamic Systems

Ross

Proulx

Karpenko

et al. 2015

Journal of Guidance, Control, and Dynamics

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Motivated by uncertain parameters in nonlinear dynamic systems, we define a nonclassical optimal control problem where the cost functional is given by a Riemann-Stieltjes "functional of a functional." Using the properties of Riemann-Stieltjes sums, a minimum principle is generated from the limit of a semidiscretization. The optimal control minimizes a Riemann-Stieltjes integral of the Pontryagin Hamiltonian. The challenges associated with addressing the noncommutative operations of integration and minimization are addressed via cubature techniques leading to the concept of hyper-pseudospectral points. These ideas are then applied to address the practical uncertainties in control moment gyroscopes that drive an agile spacecraft. Ground test results conducted at Honeywell demonstrate the new principles. The Riemann-Stieltjes optimal control problem is a generalization of the unscented optimal control problem. It can be connected to many independently developed ideas across several disciplines: search theory, viability theory, quantum control and many other applications involving tychastic differential equations.

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Costate Computation by a Chebyshev Pseudospectral Method

Cited by 29 publications

References 25 publications

An Efficient Chebyshev Algorithm for the Solution of Optimal Control Problems

An Efficient Chebyshev Algorithm for the Solution of Optimal Control Problems

A survey on orbital dynamics and navigation of asteroid missions

Riemann–Stieltjes Optimal Control Problems for Uncertain Dynamic Systems

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