  We study the prospects of probing the anomalous $tHq$~($q= u, c$) couplings
via SS2L or 3L signatures at the High Luminosity (HL-LHC) run of the 14 TeV
CERN collider. We focus on signals of the $tH$ associated production followed
by the decay modes $t\to b\ell^{+}\nu_{\ell}$ and $H\to WW^{\ast}$, and
$t\bar{t}$ production followed by the decay modes $t\to b\ell^{+}\nu_{\ell}$
and $\bar{t}\to H(\to WW^{\ast})\bar{q}$, where $\ell=e, \mu$. Based on two
types of $H\to WW^{\ast}$ decay topologies, one assuming the semileptonic decay
mode $H\to WW^{\ast}\to \ell^{+}\nu jj $ and the other the fully leptonic decay
mode $H\to WW^{\ast}\to \ell^{+}\nu \ell^{-}\bar{\nu}$, we perform a full
simulation for signals and backgrounds. It is shown that, at the future HL-LHC,
the branching ratio $Br(t\to uh)~(Br(t\to ch))$ can be probed to
$1.17~(1.56)\times 10^{-3}$ for the same-sign di-lepton channel and to
$7.1~\times 10^{-4}~(1.39~\times 10^{-3})$ for the 3L channel at $3\sigma$
sensitivity.
