Structural Stability Investigation of Bang‐Singular‐Bang Optimal Controls

The paper is devoted to parametric optimal control problems with a scalar, partially singular optimal control function. In contrast to the case of pure bang‐bang behavior, the investigation of structural stability properties for partially singular controls so far has been rarely addressed in literature. The central result of the paper deals with the case of one first order singular arc under regular concatenation to bang‐arcs. Conditions will be provided which ensure the Lipschitz stability of bang‐singular junction times positions with respect to small parameter changes. Three examples illustrate the main theorem.