Design of Automatic Optimization Control of Methanol and Diethylene Glycol Recovery Units

The Pathwise-Determined Maximum Principle and Symmetric Integrals

“…The problem of the deterministic optimal control is to build the control u(t) and trajectory x(y) such that to minimize the cost functional over conditions and some constraints and control constraints, which can be formally written as here U is the class of admissible controls (see [2][3][4]).…”

“…The rest of this paper is devoted to the study of the maximum principle for problems A1 and B1. In what follows, it is assumed everywhere that the functions F 0 (t, y, u) , G 0 (x, y) , B(t, y, u) satisfy the conditions of the deterministic maximum principle (see [3]), that is, they have partial derivatives (F 0 ) � z , (G 0 ) � x , (G 0 ) � y , (B) � y , continuous together with their derivatives in all their arguments It is known that in the case of the Wiener process V(s) = W(s) the solution to problem B1 is found using the stochastic maximum principle. But we follow [7] in assuming that the choice of nonanticipating control is a certain restriction, so we can use the Lagrange multipliers L. Then, in order to construct a nonanticipating control, instead of optimization problem (3.3), (3.4), we will use the problem with the Lagrange multiplier: minimize…”