Optimality Conditions and Duality Models for a Class of Nonsmooth Constrained Fractional Optimal Control Problems

AbstractBoth 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 finite-dimensional linear, fractional, and nonlinear programming