ALGORITHM FOR SOLUTION OF LINEAR QUADRATIC OPTIMIZATION PROBLEM WITH CONSTRAINT IN THE FORM OF EQUALITIES ON CONTROL IN A CERTAIN PART OF THE TIME INTERVAL
Keywords:
linear quadratic optimization problem, Euler-Lagrange equation, control action, optimal program trajectory, the system of linear algebraic equationAbstract
In this paper the linear quadratic optimization problem is considered. In current problem there is a CONSTRAINT in the form of equalities on the control actions in a known part of the time interval.
Constructing extended functional, the corresponding Euler-Lagrange equations are described. Solving these equations, control actions and the corresponding trajectory on each part of the time interval are constructed, i.e. on the part where there is no limitation on control and vertical external force, on the part the control has a limitation. The results are illustrated by the example of vertical movement and hovering of a flying object at a certain height under action.
