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Construction of an attainability set for the Brockett integrator. (Russian, English) Zbl 1106.49035
Prikl. Mat. Mekh. 68, No. 5, 707-724 (2004); translation in J. Appl. Math. Mech. 68, No. 5, 631-646 (2004).
The Brockett integrator [R. W. Brockett, “Differential Geometric Control Theory”, R. W. Brockett, et al. (eds.), Boston: Birkhäuser, 181–191 (1983; Zbl 0503.00014)] is one of the first classical examples of the system for which the control problem solution requires the nonlinear (discontinuous) control law to be introduced. The authors apply some results of the optimal control theory [L. S. Pontryagin, V. G. Boltyanskij, R. V. Gamkrelidze and E. F. Mischenko, “Mathematical theory of optimal processes”, Nauka, Moscow (1969; Zbl 0179.14001)] and solve the problem on attainability sets construction for nonlinear dynamical system known as the nonholonomous Brockett integrator. It is proved that the attainability set boundary is characterized by the optimal trajectory points constructed for the control problem with integral quality exponent prescribing the figure area limited by the motion trajectory of controlled system.

MSC:
49K15 Optimality conditions for problems involving ordinary differential equations
49K35 Optimality conditions for minimax problems
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