Properties of singular solutions in optimal control problems under input dynamic extension

The paper addresses the problem of optimal control design in presence of singular solutions for single input dynamics. The dynamical extension for systems obtained adding an integrator on the input is addressed and analyzed. The possibility of computing the optimal control for dynamically extended systems from the solution of the initial ones is investigated, as well as the inverse procedure. These relationships are well evidenced for the singular solutions, showing the possibility of simplifying the optimal control computation. An example is introduced to better highlight the presented results.