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

“…Prior to the control process, the controller exe cutes preparatory operations. Specifically, it calculates and stores (5) where τ l ∈ T h , ; are chosen times; and…”

“…sponding intervals of T l with the initial conditions The finite numbers among (7) are calculated and are stored. By integrating adjoint equation (6) in parallel on the intervals T l ( ) for with the use of (5), (i) the coprogram δ h (ϑ|τ) = , ϑ ∈ T n (τ) is calcu lated;…”

“…(ii) the direction of change in the coprogram Δδ h (ϑ|τ) = , ϑ ∈ T n (τ) is cal culated and stored; (iii) the numbers (8) are calculated; the finite numbers among them are ordered together with those in (7) and are stored:…”

“…For this purpose, Eq. (6) is integrated in parallel on the intervals T l with the use of numbers (5). The column d(τ 0 ) is removed from the matrix D |supp| (τ) in the case of II(a) and II(b), while the column d(τ * ) is added to the matrix D |supp| (τ) in the case of I(b) and II(b).…”

“…The method described in this paper can be implemented for dynamic systems of moderate dimension. To control systems of high dimension n, we can use the method of quasi decomposition of the fundamental matrix [5], which solves large optimal control problems with parameters of special structure. This method was implemented in [6][7][8] for systems with delay and for hyperbolic and parabolic systems.…”