Solution of one control problem for a dynamical system in partial derivatives

For a second-order dynamic system in partial derivatives with three boundary conditions, the problem of constructing control and state functions in analytical form is solved by the cascade decomposition method. Two criteria of complete controllability are obtained. The first criterion is based on the surjectivity property of a certain matrix. The second criterion is identical to the Kalman criterion. A class of functions is identified that determine the analytical form of control and state functions. A method for constructing control and state functions in analytical form is developed.