Construction of precise solutions in special type nonlinear time optimal control problem

The question of precise solutions construction in the nonlinear time optimal control problem of special type is considered. These results are strengthening the known results of M. Athans, P. Falb and R. Laccosse [1, 2] for controlled systems with invariant norm. The statement of the problem for controlled systems with integral invariant is due to A. M. Letov [3]. Some estimates for optimal time in the nonlinear controlled special type systems were found on the basis of the above results. Theoretical foundation of investigation is consideration pair of polar reciprocal convex bodies, one of which is control region of the object. Two-dimensional example of time optimal control for the bilinear system is investigated.