Singular arcs in optimal control of bimodal switched linear systems and approximate switching signals

This paper considers a singular problem in optimal control of bimodal switched linear systems. A relaxed switched system with a continuous-valued switching signal is considered and the representation of singular control and singular arcs is derived. The similarity in the structure between the singular control and a stabilizing switching law is revealed and an approximation of the singular control by a well-defined switching signal is addressed. The results are demonstrated by numerical simulations.