On the Use of Adjoint Gradients for Time-Optimal Control Problems Regarding a Discrete Control Parameterization: Extension for the Final Time Update
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As shown in [1], the adjoint method is well suited for finding the optimal control of a nonlinear dynamical system to carry out a prescribed task in the most efficient manner. There, the approach from [2] is utilized to transform the original infinite-dimensional optimization problem into a finite-dimensional one by a discrete control parameterization. This approach only provides the adjoint gradient with respect to parameters, e.g., the discrete control grid nodes, component dimensions, stiffness and damping coefficients, etc., in a suitable form. However, for an optimization problem with free final time, the gradient with respect to the final time is also needed, which has previously been computed by numerical differentiation. To further improve the efficiency of the gradient computation for such optimization tasks, this abstract outlines the crucial step required to provide this gradient information using the adjoint method. [1] Zallinger P., Pikuliński M., Malczyk P., Steiner W., Nachbagauer K., On the Comparison of Gradient Computations for Optimal Control Problems in Multibody Dynamics, 8th IMSD, Sevilla, 2026. submitted. [2] Lichtenecker D., Rixen D., Eichmeir P., Nachbagauer K., On the use of adjoint gradients for time-optimal control problems regarding a discrete control parameterization, Multibody System Dynamics, Vol. 59, No. 3, pp. 313-334, 2023.
