Yu.P. Kornushin

Bauman Moscow State Technical University, Kaluga Branch (Kaluga, Россия)

Formulation of the problem. The problem of synthesis of optimal programmed controls for nonlinear plants is considered. The desired control transfers the object from a given initial state to a given final state, within a given time interval; a limitation is imposed on the control in terms of the amount of energy spent on its formation. The optimality criterion is a quadratic functional. 

Purpose. To develop a method and algorithm for the synthesis of optimal program controls for controlling the final state (terminal control) of a wide class of nonlinear affine objects that have nonlinear characteristics of an analytical form in the mathematical model, or reduce to them.

Results. A new synthesis method is proposed, which allows constructing program control in an analytical form. To achieve the result, the following actions are sequentially performed (synthesis algorithm): the conditions for solving the problem are determined in the presence of a constraint; linearization of the mathematical model of the control object is performed according to the Newton - Kantorovich scheme, which reduces the original nonlinear differential equations to an iterative sequence of linearized equations; a new formulation of the synthesis problem is performed by the optimality criterion and the constraint, as a quadratic optimization problem with an equality-type constraint; the parameterization of the mathematical model of the control object, the constraint and the optimality criterion is carried out using the apparatus of matrix operators; the critical values of the constraint are found and the synthesis of the optimal program control is carried out directly.

Practical significance. The proposed algorithm can be used in the design of electromechanical complexes and systems, control of the orientation and rotation of solar batteries of spacecraft, telescopes, determination and prediction of the position of an object in space, maintenance of the required temperature regime of communication and control equipment, consumption and replenishment of energy resources, guidance of observation equipment to certain areas the starry sky, in motion and navigation systems, the position of spacecraft in a given orbit. 

Kornushin Yu.P. Synthesis of optimal software controls with a control constraints for nonlinear objects using the matrix operator method. Nonlinear World. 2021. V. 19. № 4. 2021. P. 21−31. DOI: https://doi.org/10.18127/j20700970-202104-03 (In Russian)

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