DISCRETE LINEAR QUADRATIC OPTIMIZATION PROBLEM WITH CONSTRAINTS IN THE FORM OF EQUALITIES ON CONTROL ACTION

DISCRETE LINEAR QUADRATIC OPTIMIZATION PROBLEM WITH CONSTRAINTS IN THE FORM OF EQUALITIES ON CONTROL ACTION

F. A. Aliev, N. S. Hajiyeva

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Abstract

In the paper the discrete linear quadratic optimization problem, where, over a certain part of the time interval, some coordinates of the control actions are known constants. These equalities in the form of a penalty function with a certain weight are added to the quadratic functional and the corresponding discrete Euler-Lagrange equation is constructed, the solution of which is constructed using a discrete fundamental matrix. Then, an explicit expression of control actions over the entire time interval is given. The results are illustrated using the example of the vertical motion of a flying vehicle.

Keywords

linear quadratic optimization problem, discrete Euler-Lagrange equation, control action, optimal program trajectory, the system of linear algebraic equation, fundamental matrix, flying object.