The problem considered is that of using boundary heat flux control to steer the temperature in a rod from some given initial state to a prescribed final state. For rods of short to moderate length, it is well known that the control must satisfy a moment problem characterized by the eigenvalues of the system. For a long rod, viewed as one of semi-infinite length, the moment problem is replaced by an integral equation for the control. For sufficiently regular data, this integral equation can be solved explicitly for the desired control. The results further allow for the application of Tauberian theorems to relate the asymptotic time properties of the control to the asymptotic spatial properties of the final temperature state.
ASJC Scopus subject areas
- Control and Systems Engineering
- Computer Science Applications