An optimal linear feedback guidance scheme

Dreyfus, Stuart E.; Elliott, J. R.

doi:10.1016/0022-247x(64)90048-4

Cited by 5 publications

(2 citation statements)

References 3 publications

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“…The initial state of the system is specified by the condition x(t = to) = ?/ (4) and the terminal state is required to satisfy the vector equation = 0 (5) The control action u is to be selected from the admissible set U such that a specified function of the terminal conditions is minimized, i.e., = </>(xf, tf) = min (6) Following the maximum principle, 3 the multiplier vectors v and p are introduced and required to satisfy the differential equations …”

Section: Nominal Optimal Solutionmentioning

confidence: 99%

Neighboring optimal terminal control with discontinuous forcing functions.

McIntyre¹

1966

AIAA Journal

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The paper deals with an extension of the optimal guidance methods of Kelley and Breakwell to systems containing a bang-bang control component. The method consists of a rescaling of the time variable, which allows for small changes in the switching times, to compensate for the presence of initial errors and disturbing forces. Two example problems are analyzed which indicate that the linear or first-order approximation to the optimal guidance law is in good agreement with the exact law, provided that the disturbances and initial errors are small and the guidance logic is computed at a time slightly removed from the switching time. It is shown that a feedback mechanization is possible on time intervals that do not contain switches. In the vicinity of a switching time, however, a control scheme using the optimal guidance methods must operate on an open-loop basis.

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Section: Nominal Optimal Solutionmentioning

confidence: 99%

Neighboring optimal terminal control with discontinuous forcing functions.

McIntyre¹

1966

AIAA Journal

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“…The dynamic system and the ablation process are described by 1) a set of nonlinear ordinary differential equations of the form = fi(xj,Uk) i = 1, (1) where Xj = (xi, #2, • • ., x n ) the state vector; and u k = (uû % u r ) the control vector, 2) a set of initial state conditions of the form z»(fo) = xf, and 3) an optimal control u* (t), …”

mentioning

confidence: 99%

Guidance law and impact prediction for interplanetary vehicles.

Johnson

1968

Journal of Spacecraft and Rockets

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ENGINEERING NOTES 1235 quence, e.g., low-, high-, low-thrust. This result can be derived directly from the preceding theory. The field-free solution to the primer vector isThis is a straight line in three-dimensional space which passes through the origin if p(0) and p(0) are parallel (they must be parallel in the one-dimensional case). Thus, the magnitude of p, which is the distance from the line to the origin, is as shown in Fig. 2. Clearly, the switch functions Ki are largest at the beginning and end of the transfer corresponding to periods when high thrust is optimal. The optimal sequence, high-thrust, low-thrust, coast, low-thrust, high-thrust, follows directly. Notice that trajectories on which p(0) and p(0) are parallel require a coast in some region about p = 0. This is not, however, required if p(0) and p(0) are not parallel.

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Stagewise Newton, differential dynamic programming, and neighboring optimum control for neural-network learning

Mizutani

Dreyfus

Proceedings of the 2005, American Control Conference, 2005.

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An optimal linear feedback guidance scheme

Cited by 5 publications

References 3 publications

Neighboring optimal terminal control with discontinuous forcing functions.

Neighboring optimal terminal control with discontinuous forcing functions.

Guidance law and impact prediction for interplanetary vehicles.

Stagewise Newton, differential dynamic programming, and neighboring optimum control for neural-network learning

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