Dynamic extension for direct integrability of singular solutions in optimal control problems

The paper addresses the problem of optimal control design in presence of singular solutions. For this case, a procedure for avoiding the integration of the costate dynamics is proposed, giving the conditions under which the costate can be directly computed, under controllability condition for the dynamics, and presenting an approach for extending this property by a dynamic extension. The procedure is here described for a single input systems and for the case in which the first step of the iterative procedure is sufficient to get the solution. An example is used to show the feasibility of the approach