Parameter Identification Problem for the Abstract State-Dependent Delay Differential Equation

In this manuscript, we deal with the first order identification problem for abstract state-dependent delay differential equation in a Banach space. The primary methods for identifying the results are a direct approach using Volterra integral equations for sufficiently regular data and an optimal control approach for less regular data. In optimal control approach, under certain hypotheses, the characterization of the limit of the sequence of approximate solutions demonstrates that it is a solution to the original identification problem. The abstract method finds relevance in various applications to partial differential equations (PDEs), providing further motivation for its exploration.