The transversality conditions for infinite-horizon optimal control   problem with a free right endpoint and the stability of the adjoint variable   (in Russian)
  An infinite-horizon optimal control problem with a free right endpoint is considered. In this paper we proved that Lyapunov stability of the adjoint variable implying the vanishing of the adjoint variable at infinity along optimal solution. 
Dmitry Khlopin
math.OC cs.SY