We consider three optimal control problems (linear terminal, bilinear and quadratic functionals) with respect to the special bilinear system with a matrix of rank 1. For the terminal problem we received two versions of conditions on the initial data of the system and functional in which the maximum principle becomes the sufficient optimality condition. At the same time the problem becomes very simple: the optimal control is determined in the process of integration phase or conjugate system (one Cauchy problem).

1. Srochko V.А. Iterative methods for solving optimal control problems (in Russian). Moscow, Fizmatlit, 2000. 160 p.

2. Srochko V.А., Antonik V.G. Methods for solving multiextremal problems of optimal control (in Russian), Irkutsk, IGU, 2012. 105 p.

3. Srochko V.А., Antonik V.G., Aksenyushkina E.V. Sufficient optimality conditions based on functional increment formulas in control problems (in Russian). Izvestia IGU, Ser. Matematika, 2014, vol. 8, pp. 125-140.

4. Khailov E. N. On extremal controls in homogeneous bilinear system (in Russian). Trudy MIAN, 1998, vol. 220, pp. 217-235.

5. Khailov E. N. Solving of optimal control problems with a terminal functional for bilinear systems (in Russian). Vestnik MGU, ser. 15, 1998, no 1, pp. 26-30.

6. Swierniak A. Some Control Problems for Simplest Differential Models of Proliferation Cycle. Applied Math. and Computer Science, 1994, vol. 4, no 2, pp. 223-232.

7. Swierniak A. Cell Cycle as an Object of Control. Journal of Biological Systems, 1995, vol. 3, no 1, pp. 41-54.