optimal control

Quaternion Models and Algorithms for Solving the General Problem of Optimal Reorientation of Spacecraft Orbit

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

The problem of optimal reorientation of the spacecraft orbit is considered in quaternion formulation. Control (vector of the acceleration of the jet thrust) is limited in magnitude. To solve the problem it is required to determine the optimal orientation of this vector in space. It is necessary to minimize the duration of the process of reorientation of the spacecraft orbit. To describe the motion of the center of mass of the spacecraft we used quaternion differential equation of the orientation of the spacecraft orbit. The problem was solved using the maximum principle of L. S.

Approximation of Control for Singularly Perturbed System with Delay with Integral Quadratic Constraints

Authors: Grebennikova I. V., Kremlev A. G.

The purpose of the work is the development and theoretical substantiation of analytical approximate or asymptotic methods for solving optimal control problems for singularly perturbed systems with constant delay in phase variables under conditions of uncertainty with respect to the initial data. For achievement of a goal 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.

Applicathion the Pontryagin‘s Maximum Principle to Optimal Economics Models

Authors: Troshina S. V., Troshina N. Y.

In this paper three models of firm are considerd as the discrete optimal control problems. The algorithm for solution is based on Pontryagin‘s Maximum Principle. The paper contains numerical examples.

On Iterative Method of Constructing Optimal Control for Singularly Perturbed Systems with Delay with Quadratic Constraints

Authors: Grebennikova I. V., Kremlev A. G.

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. Iterative procedure of constructing control response that approximates the optimal solution with given accuracy with respect to a small positive parameter is proposed.

Approximate Solution of an Optimal Control Problem with Linear Nonhomogeneous Control System in Hilbert Space

Authors: Kurdyumov V. P.

For an optimal control problem with a linear differential equation in Hilbert space and quadratic criteria necessary and sufficient conditions of control functions optimality and approximate formulas of the expansions of these functions in eigenfunctions of the control system operator have been obtained.

On Iterative Method of Constructing Optimal Control for Singularly Perturbed Systems with Delay

Authors: Grebennikova I. V.

The control problem for the singularly perturbed system with delay according to the minimax criterion is considered. Iterative procedure of constructing control response that approximates the optimal solution with givenac curacy with respect toasmall positive parameter is proposed.

Investigation of the Problem of Optimal Correction of Angular Elements of the Spacecraft Orbit Using Quaternion Differential Equation of Orbit Orientation

Authors: Kozlov E. A., Chelnokov Y. N., Pankratov I. A.

In this paper we consider the problem of optimal correction of angular elements of the spacecraft orbit. Control (jet thrust vector orthogonal to the plane of the orbit) is limited by absolute value. The combined quality functional characterizes the amount of time and energy consumption. With the help of the Pontryagin maximum principle and quaternion differential equation of the spacecraft orbit orientation, we have formulated differential boundary value problem of correction of the angular elements of the spacecraft orbit.

Iterative Procedure of Constructing Optimal Solving in the Minimax Problem of Control for Singularly Perturbed System with Delay with Geometric Constraints

Authors: Grebennikova I. V., Kremlev A. G.

The control problem for the singularly perturbed system with delay with indeterminate initial conditions and geometric constraints on the control resources according to the minimax criterion is considered. Iterative procedure of constructing control response that approximates the optimal solution with given accuracy with respect to a small positive parameter is proposed.

Solving Kinematic Problem of Optimal Nonlinear Stabilization of Arbitrary Program Movement of Free Rigid Body

Authors: Chelnokov Y. N., Nelaeva E. I.

The kinematic problem of nonlinear stabilization of arbitrary program motion of free rigid body is studied. Biquaternion kinematic equation of perturbed motion of a free rigid body is considered as a mathematical model of motion. Instant speed screw of body motion is considered as a control. There are two functionals that are to be minimized. Both of them characterize the integral quantity of energy costs of control and squared deviations of motion parameters of a free rigid body from their program values.

Approximation of Control for Singularly Perturbed System with Delay with Geometric Constraints

Authors: Grebennikova I. V., Kremlev A. G.

The control problem for the singularly perturbed system with delay with indeterminate initial conditions and geometric constraints on the control resources according to the minimax criterion is considered. A limiting problem is formulated for which a specially selected quality functional is chosen. We propose the procedure for initial approximation construction of a control response in the control minimax problem.

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