Constrained approximate boundary controllability

In this paper, constrained approximate boundary controllability for linear disturbed parameter dynamical systems described by partial differential equations of parabolic-type with mixed boundary conditions is considered. Using methods of spectral analysis for linear self-adjoint operators and general constrained controllability results, given by Son (1990), necessary and sufficient conditions for constrained approximate boundary controllability are formulated and proved. Moreover, in illustrative examples the constrained approximate boundary controllability of 1D distributed parameter dynamical systems is investigated. The constrained controllability conditions obtained represent an extension of the unconstrained controllability results given by Glothin (1974).