A state dependent approach to resource allocation strategies

In optimal control problems, once the model, the boundary conditions and the constraints are fixed, the result depends obviously on the choice of the cost index and, in particular, on the weights assumed for the variables considered. The weights take into account the different mutual influence of the elements included in the cost index; therefore different choices yield to different control strategies. In this paper the aim is to face the problem of optimal resource allocation depending on the system evolution; in the definition of the cost function, the control action is weighted by a piecewise constant function of the state, aiming at optimizing the planned resources according to the global goal. The switching instants are not known in advance and their identification is part of the problem. A constructive algorithm to compute iteratively the final control law is outlined. The effectiveness of the proposed approach is tested on a model of human immunodeficiency virus (HIV) recently proposed in literature.