Use of piecewise-linear continuous optimal-control for time-delay systems

By using piecewise linear continuous control, rather than piecewise constant control, excellent control can be obtained with the use of a relatively small number of stages. For nonlinear systems, the use of a multipass method in iterative dynamic programming (IDP) is convenient and effective in obtaining convergence to the optimum. However, a good initial control policy, which can be readily obtained by the use of Taylor series approximation and piecewise constant control, may be necessary. Computational experience with a two-stage CSTR system shows the viability of using IDP for typical chemical engineering systems with time delays.