Singular Arcs in Optimal Control of Continuous-Time Bimodal Switched Linear Systems

This paper considers a singular problem in optimal control of continuous-time bimodal switched linear systems. A relaxed switched system with a continuous-valued switching signal is considered and the representations of singular control and singular arcs are 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.