In this work, a line-up competition algorithm (LCA) is applied to solve the dynamic optimization problems derived from unsteady chemical systems. The problems are first converted ito nonlinear programming problems using the concept of control vector parametrization. The parameters embedded in the converted problems then are selected by LCA. To improve numerical accuracy, the normal (Gaussian) sampling policy is introduced to replace the uniform sampling policy used in basic LCA. Variable step input (VSI) and variable ramp input (VRI) are respectively considered to rebuild the control policy in solutions. Some typical examples are provided to demonstrate the robustness and efficiency of this modification.

This work presents a numerical method to solve the optimal control problem with time‐delayed arguments and a fixed terminal time. A series of auxiliary states obtained from the linearly truncated Taylor series expansion are used to represent the status of a time‐delayed state at different time intervals. The backward iterative dynamic programming (IDP) technique can thus be directly employed to solve the delay‐free optimal control problem with augmented states. Five numerical examples are provided, demonstrating the proposed method's effectiveness in solving the time‐delayed optimal control problems. Copyright © 2000 John Wiley & Sons, Ltd.

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