  We present a simple procedure to construct non-local conserved charges for
classical open strings on coset spaces. This is done by including suitable
reflection matrices on the classical transfer matrix. The reflection matrices
must obey certain conditions for the charges to be conserved and in involution.
We then study bosonic open strings on $AdS_5\times S^5$. We consider boundary
conditions corresponding to Giant Gravitons on $S^5$, $AdS_4\times S^2$
D5-branes and $AdS_5 \times S^3$ D7-branes. We find that we can construct the
conserved charges for the full bosonic string on a Maximal Giant Graviton or a
D7-brane. For the D5-brane, we find that this is possible only in a SU(2)
sub-sector of the open string. Moreover, the charges can not be constructed at
all for non-maximal Giant Gravitons. We discuss the interpretation of these
results in terms of the dual gauge theory spin chains.
