I'm solving a simple optimal problem. My objective function is:
$$J(u) = \int_{t1}^{t2}(u_{1} + u_{2})dt$$
and other equations depend on $u_{1}$ and $u_{2}$ linearly. So when I formed Hamiltonian and differentiated it by $u_{1}$ (and second by $u_{2}$) it turned out it depends only on costate variables $\Psi_{i}$, so I can't solve $\partial H/\partial u$ in terms of u.
What does it imply? Is there something wrong? How do I proceed if I can't express u in terms of the solved co-state variables?