Abstract: There is a lot of large-scale system with delay in industrial engineering, it's optimal decision is always difficult. On the basis of the optimization study of the production scheme and control，the dynamic programming model of a kind of large-scale system with delay is summarized and it's optimiza-tion algorithm is studied. The principle of optimality under condition is proposed, so the dynamic programming is extended to the optimization of the system with delay. The recursive algorithm of delay dynamic differential programming is pre-sented and it’s convergence under some conditions is proved. This algorithm is used in the coordinate-lever of the optimal hierarchical control of the water plant and the simula-tion demonstrates its availability and efficiency. The result ob-tained is important for energy-saving. The model and the algo-rithm mentioned may be used in a more wide range.

Key words: Optimal hierarchical control, Delay dynamic differential programming, Large-scale system with delay, Principle of optimality under condition