  Binary nonlinearization of AKNS spectral problem is extended to the cases of
higher-order symmetry constraints. The Hamiltonian structures, Lax
representations, $r$-matrices and integrals of motion in involution are
explicitly proposed for the resulting constrained systems in the cases of the
first four orders. The obtained integrals of motion are proved to be
functionally independent and thus the constrained systems are completely
integrable in the Liouville sense.
