Hamiltonian Formalism in Team Control Problems
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We consider the target control synthesis problem for a team of single-type plants performing a common motion to a target set under the condition that the team members do not collide with each other. In the process of motion, the team members must stay inside a virtual container forming a standard motion (tube) and avoiding the obstacles known in advance by reconfiguration. The general scheme for solving this problem, which reduces the original problem to a series of subproblems, is given, and Hamiltonian formalism is used for a detailed consideration of the subproblems of terminal control of ellipsoidal tubes, the container motions between moving external obstacles, and the evolution of the team inside the virtual container.
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- 8.Subbotina, N.N., Kolpakova, E.A., Tokmantsev, T.B., and Shagalova, L.G., Metod kharakteristik dlya uravneniya Gamil’tona-Yakobi-Bellmana (Method of Characteristics for the Hamiton-Jacobi-Bellman Equation), Yekaterinburg: RIO URO RAN, 2013.Google Scholar
- 11.Filippov, A.F., Differentsial’nye uravneniya s razryvnoi pravoi chast’yu (Differential Equations with Discontinuous Right-Hand Side), Moscow: Nauka, 1985.Google Scholar
- 13.Dem’yanov, V.F., Minimaks: differentsiruemost’ po napravleniyam (Minimax: Differentiability in Directions), Leningrad: Leningrad Gos. Univ., 1974.Google Scholar
- 16.Kurzhanski, A.B., Mitchell, I.M., and Varaiya, P., Optimization techniques for state-constrained control and obstacle problems, Proc. of the 6th IFAC Symposium NOLCOS-2004, Stuttgart, 2004, pp. 813–818.Google Scholar