Abstract: An optimal control system for canceling the undesired responses of a linear istributed-parameter system in response to an input stimulus. The control system is optimally distributed and its design is based on the extension of the Pontryagin's maximum principle for a lumped-parameter system to a distributed-parameter system. The technique is to transform the stimulus-to-undesired-output transfer function of the distributed-parameter system into a multidimensional discrete state-space model, and to require a performance criterion to be defined. Theorems have been established to give conditions for asymptotic stability of the closed-loop distributed-parameter system, and to set up weighting factors for the performance criterion. An optimal distributed-control system can force the states of the distributed system to behave according to the prescribed performance criterion regardless of the boundary and initial conditions.