Optimal pricing control in distribution networks with time-varying   supply and demand
  This paper studies the problem of optimal flow control in dynamic inventory systems. A dynamic optimal distribution problem, including time-varying supply and demand, capacity constraints on the transportation lines, and convex flow cost functions of Legendre-type, is formalized and solved. The time-varying optimal flow is characterized in terms of the time-varying dual variables of a corresponding network optimization problem. A dynamic feedback controller is proposed that regulates the flows asymptotically to the optimal flows and achieves in addition a balancing of all storage levels. 
Mathias B\"urger and Claudio De Persis and Frank Allg\"ower
math.OC cs.SY