Controllability of dynamical systems with constraints

The article is devoted to analysing the approximate controllability without constrains and constrained controllability with non-negative controls of a given type second order infinite dimensional system. The considered dynamical system is governed by evolution equation with three damping terms and three terms without derivatives. Following this aim spectral theory for linear unbounded operators is involved. At first, remind the representation of considered infinite dimensional dynamical system by the infinite series of finite dimensional systems. Next, two theorems on necessary and sufficient conditions of unconstrained and constrained approximate controllability of considered system are formulated and proved. Finally, proven theorems are applied to two particular dynamical systems, including one infinite dimensional.