Suboptimal switched controls in context of singular arcs

In this paper suboptimal control in the case of hybrid systems is addressed. After a brief recall of necessary conditions on the optimal hybrid trajectory, it is shown that many hybrid optimal problems cannot have an hybrid solution. Nevertheless, we show in context of switched systems that there is some possibility to take advantage of the study of a convex embedding problem for which a solution exists. Indeed the presence of singular arcs in this solution explains why the original switched system has no solution and how suboptimal chattering solutions can be found.