Hamiltonian Formalism in Team Control Problems
- 8 Downloads
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.
Unable to display preview. Download preview PDF.
- 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