Constrained bilinear systems

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˙=(A+Σ_iⁿu_iB_i)x are characterized by the fact that the controls can be expressed as polynomial functions of fewer parameters, i.e. u_i=g_i (υ₁, υ₂,...,υ_k) where g_i are polynomials and k\n\n\t\t