  The concept of Hilbert space fragmentation (HSF) has recently been put
forward as a routine to break quantum ergodicity. While HSF widely exists in
dynamical constraint models, it is still challenging to tune HSF. Here, we
propose a scheme to tune HSF in a one-dimensional tilted lattice of interacting
spinless fermions with periodically driven tunneling. The dynamics is governed
by effective Hamiltonians with kinetic constraints, which appear as
density-dependent tunneling in the weak-tunneling perturbation expansion. The
kinetic constraint can be tuned via changing the driving frequency, and three
different kinds of strong HSF can be engineered. In general, the system is
strongly constrained and exhibits a strong HSF. Two partial resonance
frequencies are analytically given by a time-dependent perturbation theory for
Floquet systems, at which some kinetic constraints are released and the system
exhibits another two different strong HSF. We demonstrate the perturbation
analysis with exact numerical simulation of the entanglement entropy, the
density correlation functions and the saturated local density profiles. Our
result provides a promising way to control HSF through Floquet engineering.
