An optimal control approach to national settlement system planning

R. Mehra
1976 1976 IEEE Conference on Decision and Control including the 15th Symposium on Adaptive Processes  
In this paper, an optimal control approach to a problem in national settlement system planning is presented. The problem description is the same as considered by MacKinnon [6] and by Evtushenko and MacKinnon [41 . It is The initial state x(0) = x is also specified. The objective 0 function to be minimized with respect to u(t) , t = 0, ..., T -1 is J measures the deviation of actual populations x(t) from certain desired population levels g(t). The backward linkage model (1,2) will be considered
more » ... will be considered in Section IV. An Optimal Control Solution By adjoining the constraints to the cost function using appropriate multipliers, we define the Lagrangian function (3) where IT = [I,. . . ,I] is a 1 x n vector of all ones. Here X(t) , v(t), n(t) and p are dual or shadow-price variable for constraints (I), (3) , (4) and (2) , satisfying constraints n(t) 5 0 and p 2 0 and having the same dimension as the constraining equation. By rearranging terms, Eq. (6) can be written as,
doi:10.1109/cdc.1976.267755 fatcat:2wyjuk3zxfbntl5sjvpafgeonq