Singular solution in optimal control for two input dynamics: The case of a SIRC epidemic model

The analysis of singular solutions in optimal control problems is addressed. The case of systems with two inputs is investigated characterising all the possible combination of singular arcs and constant boundary values. It is described the extension to a two input system of a previously proposed procedure for computing the control along the singular arcs in a state feedback form for one input dynamics. The procedure makes use of the possibility of computation in an analytical form of the costate as a function of the state. The example of a SIRC epidemic model is used to verify the effectiveness of the result.