Turnpike theorem for terminal functionals in infinite horizon optimal control problems

An optimal control problem for continuous time systems described by a special class of multi-valued mappings and quasi-concave utility functions is considered. The objective is defined as an analogue of the terminal functional defined over an infinite time horizon. An upper bound of this functional over all solutions to the system is established. The turnpike property is proved which states that all optimal solutions converge to some unique optimal stationary point.