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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]

In this paper, we consider a class of nonlinear time-delay optimal control problems with canonical equality and inequality constraints. We propose a new computational approach, which combines the control parameterization technique with a hybrid time-scaling strategy, for solving this class of optimal control problems. The proposed approach involves approximating the control variables by piecewise constant functions, whose heights and switching times are decision variables to be optimized. Then, the resulting problem with varying switching times is transformed, via a new hybrid time-scaling strategy, into an equivalent problem with fixed switching times, which is much preferred for numerical computation. Our new time-scaling strategy is hybrid in the sense that it is related to two coupled time-delay systems-one defined on the original time scale, in which the switching times are variable, the other defined on the new time scale, in which the switching times are fixed. This is different from the conventional time-scaling transformation widely used in the literature, which is not applicable to systems with time-delays. To demonstrate the effectiveness of the proposed approach, we solve four numerical examples. The results show that the costs obtained by our new approach are lower, when compared with those obtained by existing optimal control methods. [ABSTRACT FROM AUTHOR]

Abstract The control parameterization method used together with the time-scaling transformation is an effective approach to approximating optimal control problems into optimal parameter selection problems when no time delays are involved. The approximate problems can then be solved by gradient-based optimization algorithms. However, the time-scaling transformation, which works well for optimizing variable switching times of the approximate piecewise constant/linear control functions obtained after the application of the control parameterization method, is not applicable to optimal control problems with time delays. In this paper, we consider a class of nonlinear optimal control problems with multiple time delays subject to canonical equality and inequality constraints. Our aim is to develop a novel transformation procedure that converts a given time-delay system into an equivalent system – defined on a new time horizon – in which the control switching times are fixed, but the dynamic system contains multiple variable time delays expressed in terms of the durations between the switching times for each of the approximate control functions in the original time horizon. On this basis, we show that an optimal control policy for the equivalent system can be obtained efficiently using gradient-based optimization techniques. This optimal control policy can then be used to determine the optimal switching times and optimal control variables for the original system. We conclude the paper by solving two example problems. [ABSTRACT FROM AUTHOR]