Penalty shifting method on calculation of optimal linewise control of dam-detouring osimotic system for concrete dams with heterogemous

An optimal osmotic control problem for a concrete dam system

“…Here, the osmosis emerge in the mountain rocks on both sides of the dam is called the dam-detouring osmotic problem. This problem was discussed in our article [12]. It should be noted that the problem treated in [12] was only about its calculation.…”

“…This problem was discussed in our article [12]. It should be noted that the problem treated in [12] was only about its calculation. In the present paper, we shall deeply investigate the penalty shifting method with calculation of the optimal osmotic control, discuss the structure of an approximation program, and claim and prove the convergence of the method used for the dam system control in appropriate Hilbert space.…”

“…It should be emphasized that there is an quite difference between the two cases. Actually, the control problem we shall discuss in this paper is more peculiar than the problems discussed in the both references [12,10], and hence the results in this paper have both theoretical and practical significance for research on optimal control problems.…”

“…Penalty shifting method for digital approximation. This section is devoted to investigating applications of the penalty shifting method [12,13] to calculate the optimal control of osmotic systems for the basis of the dam. It has been seen that the optimal control problem (2.11) can be written as the minimization problem as follows:…”