Constructive Methods of Parametric and Functional Optimization

Realization of a bounded feedback in a nonlinear control problem

“…However, keeping the subsequent synthesis in mind, it is expedient to solve problem (9) by an adaptive (direct or dual) method [10], which, along with the optimal program control u t z h 0 ( | ), t T Î , provides the minimum support K op 0 0 ( ) -an important element to realize the optimal feedback control.…”

Optimal conditionally relative observation of non-stationary linear systems

“…Unlike the general linear programming problem, its elements are dynamic in nature. Below we will describe a dual method which is essentially a special rapid dynamic realization of the dual adaptive method of linear programming [12]. As in the case of the optimal control problem, the main time needed to solve optimal observation problems is spent in integrating the direct system; therefore, as in [11], the efficiency of the method is estimated in terms of a basic "time-consumption unit", namely, one integration of the direct system over the entire observation interval T.…”

“…To simplify the derivations, we shall assume that the numbers 6j,j ~ Jn and 6(0, t ~ Tb are different and non-zero (the general case was investigated in [12]). Number the finite ones in increasing order: 0 < ¢31 < ~2 < ... < ~k0.…”

“…The method is finite if the supports are regular in the iterations. A finite modification of the method may be constructed for any problem (3.1) [12].…”

Solving a class of linear optimal control problems with several control variables by the method of orienting curves

“…Linear optimal control problems with several control variables were investigated in many papers and books (see [2], [6], [71. [13], .…”