Discrete linear quadratic optimization problem with constraints in the form of equalities on control action

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.