Mathematical control theory solution of an interactive accounting flows model

In this paper we have applied the mathematical control theory to the accounting network flows, where the flow rates are constrained by linear inequalities. The optimal control policy is of the “generalized bang-bang” variety which is obtained by solving at each instant in time a linear programming problem whose objective function parameters are determined by the “switching function” which is derived from the Hamiltonian function. The interpretation of the adjoint variables of the control problem and the dual evaluators of the linear programming problem demonstrates an interesting interaction of the cross section phase of the problem, which is characterized by linear programming, and the dynamic phase of the problem, which is characterized by control theory.