An optimal control problem formulation for a state dependent resource allocation strategy

In this paper, the problem of optimal resource allocation depending on the system evolution is faced. A preliminary analysis defines the global effort required in any subset of the system state space according to needed or desired goals. Then, in the definition of the cost function, the control action is weighted by a piecewise constant function of the state, whose different constant values are defined for each subset previously defined. The aim is to weight the control according to the distinct conditions, so getting different solutions in each state space region so to optimize the planned resources according to the global goal. A constructive algorithm to compute iteratively the final control law is outlined. The effectiveness of the proposed approach is tested on a typical model of human immunodeficiency virus (HIV) present in literature