Regional observability for Hadamard-Caputo time fractional distributed parameter systems

摘要

In this paper, regional (gradient) exact and approximate observability problems are studied on Hadamard-Caputo time fractional distributed parameter systems. Without any knowledge of the initial vector and its gradient, several equivalent criteria are first provided to achieve the regional observability. Based on these, characterizations for both ω−strategic and gradient ω-strategic zone sensors are developed. Then, by employing the Hilbert Uniqueness Method (HUM), we explicitly reconstruct the initial vector and its gradient respectively. A one-dimension example is finally included to illustrate our results.