Time-optimality of bang-bang controls for chained systems

In our previous work (Sarychev and Nijmeier 1996) we provided a complete description of the set of (abnormal, singular and bang-bang) Pontryagin extremals for time-optimal problem with constrained controls for so-called chained systems, which are important for their own sake as well as for their applications. The study of optimality for singular and abnormal extremals is easy (see ibid.), but the optimality of bang-bang extremals is a delicate issue. In the present paper we address this issue of optimality for time-optimal control problems for 2-chained systems in R-n with control values constrained by the unit square. We provide particular study of optimality of the bang-bang extremal controls for chained systems in dimensions n = 3 and n = 4. Copyright (C) 2003 IFAC.