The aim of this book is to provide a practical working tool for students in\ud Engineering, Mathematics, and Physics, or in any other field where rigorous\ud Calculus is needed. The emphasis is thus on problems that enhance students’ skill in\ud solving standard exercises with a careful attitude, encouraging them to devote an\ud attentive eye to what may or may not be done in manipulating formulae or deriving\ud correct conclusions, while maintaining, whenever possible, a fresh approach, that is,\ud seeking guiding ideas.\ud Every chapter starts with a summary of the main results that should be kept\ud in mind and used for the exercises of that chapter; this is followed by a selection of\ud guided exercises. The theoretical preamble is meant to recapitulate the main definitions\ud and results and should also offer a bird’s-eye view on the topic treated in the\ud chapter. Hence, the student can quickly review the main theoretical facts and then,\ud most importantly, “learn by examples,” becoming acquainted with the specific\ud techniques by seeing them applied directly to the problems. Each exercise ends with\ud a short comment which underlines the main issues of that specific exercise, the\ud leading ideas, and the main techniques. A selection of problems closes each\ud chapter, the answers to which are all listed in Solutions. The reader is urged to try to\ud solve some of these problems, which are similar, but not always trivially analogous,\ud to those that have been presented in detail

No abstract

No abstract

No 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.