A method designing program boundary controls for multidimensional distributed-parameter systems (Q1913079)

The authors consider problems in designing a multidimensional distributed control which changes the state of a distributed parameter object by acting on the boundary of the object. The substitution method is used to design this distributed control. The substitution method is extended and substantiate for two- and three-dimensional spatial objects in which the control is distributed along the boundary of a two- or three-dimensional region. The authors present the mathematical statement of the control problem and describe procedures for solving it. They give numerical examples of the solution of control problems for two- and three-dimensional spatial objects the state of which is described by the heat conduction equation, including objects in stationary (time-invariant) regimes.