4. Controllability issues

The controllability of systems governed by ordinary differential equations is a classic question that can be formulated as follows: given an initial state y ₀ and a final state y _f , is there a control u and a time T such that, starting from y(0) = y ₀ , we have y(T; u) = y _f ? For stationary linear systems, the answer is given by an algebraic criterion based on the rank of the controllability matrix. For systems governed by partial differential equations, we can ask the same type of questions, but the answers are more complicated!