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The combination of the time-scaling transformation and control parameterization has proven to be an effective approach in addressing optimal control problems involving switching systems with predefined subsystem sequences. However, this approach has certain limitations. First, the number of control switchings is required to be no less than the number of subsystem switchings. Second, the switching of the subsystem must be accompanied by the switching of the control. Third, this scheme introduces many hyperparameters, leading to combinatorial explosion. To address these drawbacks, we introduce a novel computational approach such that the control switching can be independent of subsystem switching. The superiority of this novel approach can be clearly observed from the solutions obtained using the proposed method for solving two illustrative examples. [ABSTRACT FROM AUTHOR]

The control parameterization method used together with time-scaling transformation is an effective approach to transform optimal control problems into optimal parameter selection problems. The approximate problems can then be solved by gradient-based optimization methods. However, the conventional time-scaling transformation requires that all the control component functions switch simultaneously, which can be undesirable in practice. In this paper, we introduce a novel technique where the switching times for each of the control component functions can be adaptively selected. To demonstrate the effectiveness and flexibility of the proposed approach, two example problems with control input and terminal state constraints are solved using the method proposed. Numerical results show that the new method achieves much better objective values with some increase in computation time compared to the conventional time-scaling transformation technique. [ABSTRACT FROM AUTHOR]