Abstract
The paper studies a class of symmetric hyperbolic systems with boundary control. We prove the exact controllability of these systems. The exact controllability result is exploited to investigate the associated optimal control problem. For some special cases, we construct explicitly the optimal control law under the feedback form. Our construction illustrates the difficulty that we would meet for the boundary optimal control of hyperbolic systems. This difficulty does not appear if the control operator is bounded as has been observed in the existing literature.
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