Abstract :
Both parametric and nonparametric necessary and sufficient optimality conditions
are established for a class of nonsmooth constrained optimal control problems
with fractional objective functions and linear dynamics. Moreover, using the
forms and contents of these optimality principles, four parametric and eight
parameter-free duality models are constructed and weak, strong, and strict converse
duality theorems are proved. These optimality and duality results contain, as
special cases, similar results for fractional optimal control problems containing
square roots of positive semidefinite quadratic forms in their objective and constraint
functions. The optimality and duality criteria presented in this paper
generalize a number of existing results for optimal control problems and subsume a
fairly large number of cognate results obtained previously in the areas of finitedimensional
linear, fractional, and nonlinear programming
