Abstract
In this paper, the optimal control problem for a distributed parameter system described by a liner high order partial differential equation is formulated with a performance index of the final energy of the system.
It is pointed out that a class of scalar-formed high order partial differential equation can be effectively reduced to a vector-formed lower order partial differential equation, by introducing a new state vector composed of variables which are enough to assign the total energy of the controlled system.
Also pointed out is that a high order system with complex boundary conditions, such as a homogeneous but time-variant condition or a non-homogeneous condition involving controls, can be transformed to a system with simpler boundary conditions such as a time-invariant or a homogeneous one, respectively, by introducing the extended definition of operators. Then, Dynamic Programming technique is used to derive the optimal condition, which proves to include the already known results given by Russel and Komkov.
