Fractional Control Problems Research Articles

Duality for multiobjective fractional generalized control problems with [formula omitted]-convexity

The concept of efficiency is used to formulate duality for multiobjective fractional control problems. Wolfe and Mond–Weier-type duals are formulated. Using the generalized ( F , ρ ) -convexity on the functions involved, we establish the weak and strong duality theorems for multiobjective fractional generalized control problems.

Duality and sufficiency for fractional control problems with invexity

Duality and sufficiency for fractional control problems with invexity

Duality for multiobjective fractional control problems with generalized invexity

Wolfe and Mond-Weir type duals for multiobjective control problems are formulated. Under pseudo-invexity/quasi-invexity assumptions on the functions involved, weak and strong duality theorems are proved to relate efficient solutions of the primal and dual problems.

An existence theorem for a fractional control problem

Computational algorithms in mathematical programming have been much in use in the theory of optimal control (see, for example Refs. 1–2). In the present work, we use the algorithm devised by Dinkelback (Ref. 3) for a nonlinear fractional programming problem to prove an existence theorem for a control problem with the cost functional having a fractional form which subsumes the control problem considered by Lee and Marcus (Ref. 4) as a particular case.