Necessary conditions for the optimal control of a system with time-varying transport lags

Necessary conditions to be satisfied if the control of a system with time-varying transport lags is to be optimal, are derived. These correspond to the Euler-Lagrange equations, the first corner condition, and the transversality condition of the calculus of variations. The systems considered can be nonlinear, have a multivariable control, and contain a number of different transport lags. The states and controls of the system are assumed to be unbounded.