Ricerc@Sapienza

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 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