| For the effective operation of data communication networks, the flow and power controllers must ensure convergence to the optimal solution, transient performance (speed of convergence), robustness to disturbances and delays, and scalability to the network size. The purpose of this dissertation is to develop robust nonlinear controllers for broad classes of networks, including wired and wireless data networks, with considerations of power and interference.; In wired computer networks, we studied Internet's robustness with respect to additive disturbances (caused by e.g., modeling errors, unmodeled flows, and uncooperative users). This study is important because it shows us whether small disturbances can cause undesirable oscillation or network crash. Using recently developed input-to-state stability tools from nonlinear control theory, we established robustness of classes of protocols, and developed bounds for possible oscillations. Because these bounds depend on network parameters, our result also indicates strategies for network redesign. Furthermore, this study enabled us to show global asymptotic stability of Kelly's models for the Internet for sufficiently small delays in forward and return channels. When delay is large, we found global asymptotic stability could still be achieved by scaling down the controller gains.; Detection and rectification of uncooperative flows in the network is another important robustness issue since uncooperative users may change their congestion control schemes to gain more than their fair share, at the cost of cooperative users. In the dissertation, we designed a control-theoretic algorithm to force uncooperative users to comply with their fair share by adjusting the prices fed back to them. A significant advantage of our design is that it was implemented at the edge of the network (e.g. by Internet service providers) without costly network upgrades, and hence can be used with any congestion notification policy deployed by the current Internet. In this design, we applied singular perturbation techniques and achieved a separation of time-scales between the network congestion feedback loop and the price-adjustment loop, thus recovering the fair allocation of bandwidth upon a fast transient phase. The convergence of users' sending rates to their cooperative values was shown with the help of a Lyapunov function obtained from our passivity framework. (Abstract shortened by UMI.)... |
