# How to evaluate the convexity of an optimal control problem?

Can we consider an optimal control problem, a convex optimization problem like static optimization problems? If it is possible, under what conditions, will this problem be a convex problem? For example, in the general problem as follows, how can we check the convexity of the problem (if we arrive to a solution, is it optimal or not)?

$$\max_{u \in \mathcal{U}} Q(u) = \int_{0}^{T} F(x(t),u(t), t) dt + S(x(T),T) \\ \dot{x}(t)= f(x(t),u(t), t)$$

Moreover, is it possible to obtain an explicit form for $$Q(u)$$? When is $$Q(u)$$ a concave of $$u$$?