A transposition theorem with applications to constrained optimal control problems

The paper establishes a Gordan-type transposition theorem for systems comprised of nonhomogeneous nonautonomous linear differential equations and convex functional inequalities. It then utilizes this result for deriving saddle point optimality conditions for convex control problems with linear dynamics, and for constructing a dual problem for a class of generalized fractional optimal control problems. As byproducts of the results developed in this paper, duality formulations for optimal control problems with ordinary, minmax, and fractional performance criteria is also obtained.