1965
DOI: 10.1016/s0019-9958(65)90417-1
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Optimal trajectory, guidance, and conjugate points

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Cited by 22 publications
(18 citation statements)
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“…where zðtÞ is the Gaussian white noise with the correlation matrix zðt 1 Þzðt 2 Þ h i¼ H À1 dðt 1 À t 2 Þ: Derivation of Equation (14) for the covariance matrix of the linear Gaussian Markovian process (16) can be found, for example, in Reference [10]. The density of the probability distribution for the random process xðtÞ is determined by…”
Section: Reduction Of Dimensionality In Choosing Optimal Control Formentioning
confidence: 99%
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“…where zðtÞ is the Gaussian white noise with the correlation matrix zðt 1 Þzðt 2 Þ h i¼ H À1 dðt 1 À t 2 Þ: Derivation of Equation (14) for the covariance matrix of the linear Gaussian Markovian process (16) can be found, for example, in Reference [10]. The density of the probability distribution for the random process xðtÞ is determined by…”
Section: Reduction Of Dimensionality In Choosing Optimal Control Formentioning
confidence: 99%
“…Introduce the state subspace R contr ðt; D 1 ð0ÞÞ that is the set of current points xðtÞ of trajectories of system (16) provided that zðsÞ (for 04s4t) is a limited piecewise continuous arbitrary control input and that initial values xð0Þ satisfy the inequality xð0Þ T D þ 1 ð0Þxð0Þ > 0: Recall that DðT À tÞ ¼ D 1 ðtÞ; 04t4T : Introduce also the state subspace R x ðt; D 1 ð0ÞÞ in which the probability density for the random Gaussian vector xðtÞ is localized, provided that xðtÞ satisfies Equation (16) with zðsÞ represented by the Gaussian white noise with the correlation matrix zðs 1 Þzðs 2 Þ h i¼ H À1 dðs 1 À s 2 Þ: It is also assumed that the initial vector xð0Þ is the random Gaussian vector with the covariance matrix D 1 ð0Þ and that the random process zðsÞ (for 04s4t) and the random vector xð0Þ are independent.…”
Section: Proof Of Statement 1 Of Theoremmentioning
confidence: 99%
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“…Moreover, it is possible to derive a continuous linear feedback law [24] similar to those neighboring optimum feedback laws which are obtained using the backward sweep method to solve the linear boundary value problem (see e.g. [3], [21], [22], [23], Dyer, McReynolds [8], and Wood [31]). Because of the numerical instability, the use of such feedback laws is not recommended.…”
Section: Si~- C ~ Si B Cbmentioning
confidence: 99%
“…As it is known the boundedness of the solution of the matrix Riccati equation is equivalent to the "no-conjugate point to the final time" [1, 7,10].…”
Section: Introductionmentioning
confidence: 99%