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Optimization of a fractional Mayer problem - existence of solutions, maximum principle, gradient methods

Idczak D., Walczak S.

Opuscula Mathematica

2014

Vol. 34, no. 4

763--775

In the paper, we study a linear-quadratic optimal control problem of Mayer type given by a fractional control system. First, we prove a theorem on the existence of a solution to such a problem. Next, using the local implicit function theorem, we derive a formula for the gradient of a cost functional under constraints given by a control system and prove a maximum principle in the case of a control constraint set. The formula for the gradient is used to implement the gradient methods for the problem under consideration.

Optimal synthesis via superdifferentials of value function

Frankowska H.

Control and Cybernetics

2005

Vol. 34, no 3

787-803

We derive a differential inclusion governing the evolution of optimal trajectories to the Mayor problem. The value function is allowed to be discontinuous. This inclusion has convex compact right-hand sides.