optimal control

Solution of a Problem of Spacecraft’s Orbit Optimal Reorientation Using Quaternion Equations of Orbital System of Coordinates Orientation

Authors: Pankratov I. A., Sapunkov Y. G., Chelnokov Y. N.

The problemof optimal reorientation of the spacecraft’s orbit is solved with the help of the Pontryagin maximum principle and quaternion equations. Control (thrust vector, orthogonal to the orbital plane) is limited inmagnitude. Functional, which determines a quality of control process, is weighted sum of time and impulse (or square) of control. We have formulated a differential boundary problems of reorientation of spacecraft’s orbit. Optimal control laws, transversality conditions, not containing Lagrange multipliers, examples of numerical solution of the problem are given.

Analytical Solution of Equations of Near-circular Spacecraft’s Orbit Orientation

Authors: Pankratov I. A.

The problem of optimal reorientation of spacecraft’s orbit with a limited control, orthogonal to the plane of spacecraft’s orbit, is considered. An approximate analytical solution of differential equations of near-circular spacecraft’s orbit orientation by control, that is permanent on adjacent parts of the active spacecraft’s motion, is obtained.

Using Galerkin Method for Solving Linear Optimal Control Problems

Authors: Pankratov I. A.

The linear optimal control problem is considered. Duration of the controlled process is fixed. It is necessary to minimize the functional, that characterizes the energy consumption. A method of constructing an approximate solution based on the Galerkin method is proposed. Examples of numerical solutions of the problem are given.

The problem of optimal control for singularly perturbed system with delay with integral quadratic constraints

Authors: Grebennikova I. V.

The control problem for the singularly perturbed system with delay with indeterminate initial conditions and integral quadratic constraints on the control resources according to the minimax criterion is considered. Procedure is proposed for construction initial approximation of control response for minimax problem of control. 

About a problem of spacecraft's orbit optimal reorientation

Authors: Pankratov I. A., Sapunkov Y. G., Chelnokov Y. N.

 The problem of optimal reorientation of the spacecraft's orbit is solved with the help of the Pontryagin maximum principle and quaternion equations. Control (thrust vector, orthogonal to the orbital plane) is limited in magnitude. Functional, which determines a quality of control process is weighted sum of time and module (or square) of control. We have formulated a differential boundary problems of reorientation of spacecraft's orbit.

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