Optimal control of parallel buffers by using output feedback based on Practical Observers

Abstract

We address the optimal allocation of the capacity of a single server to buffers with different arrival flows and priority. The well-posedness is studied in a general setting with a state equation having a lower semicontinuous, nonlinear r.h.s. and a linear discounted cost function. The solution of the problem given by a discontinuous feedback control is presented by referring to a two-buffer system under the assumption of the perfect knowledge of the inflow rates. Such an assumption is relaxed by using an output feedback control scheme, for which a reduced-order practical observer is proposed to estimate the unknown inflow rates. Ultimate boundedness is proved for such a setup by using a different control law that takes into account the loss of observability at steady state. The effectiveness of the resulting approach is shown by means of simulations.