Sequential time scaling transformation technique for time-delay optimal control problem

The time-scaling transformation technique used within the computational framework of control parameterization serves as an effective method for the optimization of control switching time as well as the control value for time-delay optimal control problems. However, the conventional time-scaling transformation stipulates that the switching times for all control components must be identical, which may not be feasible in real-world scenarios. To address this limitation, we introduce the sequential time-scaling transformation technique for solving time-delay optimal control problems. By sequentially applying control parameterization and time-scaling transformation to each of the control variable, the new technique enables the configuration of a varying number of segments for the control, and the switching time for each control component can be adaptively selected. Numerical results demonstrate that our approach not only achieves superior cost performance but also offers enhanced flexibility in control strategy.