Abstract
Given is a team of m controlled motions with two types of members, a target set \(\mathcal {M}\) and an array \(\mathbf{E}_k(t)\) of external obstacles. The problem is for both types to simultaneously reach the target, avoiding the obstacles and the possible mutual collisions, while performing the overall process in minimal time. The problem solution is described in terms of the Hamiltonian formalism.
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Notes
- 1.
See R. Coleman, Calculus on normed vector spaces, Universitext, Springer, 2012.
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Kurzhanski, A.B. (2019). On the Problem of Optimization in Group Control. In: Kondratenko, Y., Chikrii, A., Gubarev, V., Kacprzyk, J. (eds) Advanced Control Techniques in Complex Engineering Systems: Theory and Applications. Studies in Systems, Decision and Control, vol 203. Springer, Cham. https://doi.org/10.1007/978-3-030-21927-7_3
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