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A method designing program boundary controls for multidimensional distributed-parameter systems. (English. Russian original) Zbl 0845.93041
J. Comput. Syst. Sci. Int. 33, No. 6, 104-117 (1995); translation from Izv. Ross. Akad. Nauk, Tekh. Kibern. 1994, No. 1, 141-155 (1994).
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.

93C20 Control/observation systems governed by partial differential equations
93B40 Computational methods in systems theory (MSC2010)