Direct Integrability for State Feedback Optimal Control with Singular Solutions

The paper studies the problem of determining the optimal control when singular arcs are present in the solution. In the general classical approach, the expressions obtained depend on the state and the costate variables at the same time, so requiring a forward-backward integration for the computation of the control. In this paper, firstly sufficient conditions on the dynamics structure are discussed, in order to have both the control and the switching function depending on the state only, computable by a simple forward integration. Then, the possibility to extend this result by means of a preliminary dynamic extension is presented. The approach has been checked and validated making use of a classical SIR epidemic model.