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It has been shown recently that the normal branch of a DGP braneworldscenario self-accelerates if the induced gravity on the brane is modified inthe spirit of $f(R)$ modified gravity. Within this viewpoint, we investigatecosmological viability of the Hu-Sawicki type modified induced gravity.Firstly, we present a dynamical system analysis of a general $f(R)$-DGP model.We show that in the phase space of the model, there exist three standardcritical points; one of which is a de Sitter point corresponding toaccelerating phase of the universe expansion. The stability of this pointdepends on the effective equation of state parameter of the curvature fluid. Ifwe consider the curvature fluid to be a canonical scalar field in theequivalent scalar-tensor theory, the mentioned de Sitter phase is unstable,otherwise it is an attractor, stable phase. We show that the effective equationof state parameter of the model realizes an effective phantom-like behavior. Acosmographic analysis shows that this model, which admits a stable de Sitterphase in its expansion history, is a cosmologically viable scenario.

On the cosmological viability of the Hu-Sawicki type modified induced gravity