Hida theory for Shimura varieties of Hodge type

In this article, we generalize the work of H.Hida and V.Pilloni to construct $p$-adic families of $mu$-ordinary modular forms on Shimura varieties of Hodge type $Sh(G,X)$ associated to a Shimura datum $(G,X)$ where $G$ is a connected reductive group over $mathbb{Q}$ and is unramified at $p$, such that the adjoint quotient $G^mathrm{ad}$ has no simple factors isomorphic to $mathrm{PGL}_2$.