Optimal control of a dynamic system using perfect measurements of its states

On the synthesis of optimal dynamic systems under condition of uncertainty

“…According to Definition 2.5, the value of the control action u 0 (t * , x 0 ) is equal to the initial value of the optimal program for the position (t * , x 0 ), which can be found before the start of the control process. The next value of the control action u 0 t * + h, x * (t * + h) is obtained from the optimal program u 0 (t * , x 0 ) by the dual linear programming method by correcting the previous optimal support [2,8,9].…”

“…An algorithm for the operation of an optimal Regulator was described in [8] and was based on: 1) the discreteness of control actions; 2) the reduction of the problem of constructing a sequence of optimal programs to linear programming problems (LP); 3) the dual method (of LP) [9].…”

“…Let u 0 g (t|τ, z), t ∈ T (τ) be the optimal guaranteed program for problem (3.2) for position (τ, z), and X τ be the set of all states z ∈ R n for which there are guaranteed programs for the problem (3.1). The problem of constructing an extreme discrete feedback, as well as the problem (2.1) in the class of discrete control actions is reduced to the linear programming problem and solved by a dual method [3,9,10].…”