Abstract
The determination of various parameters or control input signals satisfying particular performance criteria is often addressed with optimization techniques where one aims at minimizing certain quantity, which may be implicitly dependent on the dynamic response of a system. Such an approach requires an efficient and reliable method of gradient calculation. The adjoint method is an effective procedure specifically designed for such calculations. This paper presents a discrete Hamiltonian–based adjoint method which allows one to find the gradient of the performance index in multibody systems’ optimization. Hamilton’s equations of motion are discretized by means of trapezoidal rule and incorporated into a discrete system of adjoint equations. Explicit formula for the gradient of the cost functional is derived and exploited in an exemplary optimal control problem.
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Acknowledgments
This work has been supported by National Science Center under grant No. 2018/29/B/ST8/00374. The first author would also like to acknowledge the support of the Institute of Aeronautics and Applied Mechanics funds for scientific research.
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Maciąg, P., Malczyk, P., Frączek, J. (2020). The Discrete Hamiltonian-Based Adjoint Method for Some Optimization Problems in Multibody Dynamics. In: Kecskeméthy, A., Geu Flores, F. (eds) Multibody Dynamics 2019. ECCOMAS 2019. Computational Methods in Applied Sciences, vol 53. Springer, Cham. https://doi.org/10.1007/978-3-030-23132-3_43
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DOI: https://doi.org/10.1007/978-3-030-23132-3_43
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