Optimal control of systems with transportation lags

Simultaneous use of first-order partial differential equations and ordinary differential equations, instead of differential-difference equations, is presented to define systems involving transportation lag processes. Variational analysis is carried out for the system to obtain an optimal control law which minimizes a specified objective function, and the strong maximum condition which has to be satisfied by the optimal control is derived and discussed. The theory developed is rather general and may be applied to a class of systems wider than those defined by differential-difference equations.