We study some model control problems which arise in connection with optimal manipulation of dissipative quantum dynamics. It is shown that the problem of optimal control of quantum mechanical phenomenon in presence of dissipation can be reduced to the study of optimization problems associated with a class of constrained bilinear control systems. These bilinear systems x/spl dot/=(A+/spl Sigma//sub i//sup n/u/sub i/B/sub i/)x are characterized by the fact that the controls can be expressed as polynomial functions of fewer parameters, i.e. u/sub i/=g/sub i/ (/spl upsi//sub 1/, /spl upsi//sub 2/,...,/spl upsi//sub k/) where g/sub i/ are polynomials and k