Differential flatness and boundary control for bandwidth allocation in Internet routes

The problem of feedback control of bandwidth allocation for Internet links is analysed in this article. It is shown that the procedure for numerical solution of a fluid flow partial differential equation (PDE) which describes the bandwidth allocation on a link results into a set of ordinary differential equations (ODEs) and into an associated state-space equations model. For the local subsystems, into which the flow PDE is decomposed, it becomes possible to apply boundary-based feedback control. The solution of the control problem proceeds by showing that the state-space model of the flow PDE stands for a differentially flat system. Next, for each subsystem which is related to an ODE, a virtual control input is computed, which can invert the subsystem’s dynamics and can eliminate the subsystem’s tracking error. From the last row of the state-space description, the control input (boundary condition) that is actually applied to the data-flow PDE is found. This control input contains recursively all virtual control inputs which were computed for the individual ODE subsystems associated with the previous rows of the state-space equation. Thus, by tracing the rows of the state-space model backwards, at each iteration of the control algorithm, one can finally obtain the control input that should be applied to the data flow PDE of the communication network so as to assure that all its state variables will converge to the desirable set points.