Network flow control under capacity constraints: A case study

In this paper, we demonstrate how tools from nonlinear system theory can play an important role in tackling "hard nonlinearities" and "unknown disturbances" in network flow control problems. Specifically, a nonlinear control law is presented for a communication network buffer management model under physical constraints. Explicit conditions are identified under which the problem of asymptotic regulation of a class of networks against unknown inter-node traffic is solvable, in the presence of control input and state saturation. The conditions include a Lipschitz-type condition and a "PE" condition. Under these conditions, we achieve either asymptotic or practical regulation for a single-node system. We also propose a decentralized, discontinuous control law to achieve (global) asymptotic regulation of large-scale networks. Our main result on controlling large-scale networks is based on an interesting extension of the well-known Young's inequality for the case with saturation nonlinearities. We present computer simulations to illustrate the effectiveness of the proposed flow control schemes.