Optimal control problems involving optimal economic growth with infinite horizon (Q1805282)

The author considers the optimal control problem \[ \max \int_0^\infty h(t,x(t),u(t)) dt \] subject to \(\dot{x} = f(t,x,u)\), \(x(t)\in V(t)\), \(u(t)\in F(t,x(t))\), \(x(0) = x_0\). For the convex case, he proves existence of an optimal solution as well as, for a special case of the problem, upper semicontinuity of the solution set with respect to a certain weak topology in \((x,u)\)-space. For the nonconvex case, he proves existence of a solution of the corresponding relaxed problem as well as equality of the optimal values of the original and the relaxed problem.