ABSTRACT
In this chapter, we provide a brief background on dynamical systems, mainly covering the topics that will be important in a discussion of protocol and algorithm development for networking such as congestion control, admission control, scheduling, and neural network (NN) applications in closed-loop control of networks. It is quite common for noncontrol engineers working in wireless networking systems and control applications to have little understanding of feedback control and dynamical systems. Many of the phenomena they observe are not attributable to properties of NN but to the properties of feedback control systems. Control applications of dynamical systems are a complex area with several facets. An incomplete understanding of any one of these can lead to incorrect conclusions being drawn, with inaccurate attributions of causes — many are convinced that often the exploratory, regulatory, and behavioral phenomena observed in NN control systems are completely because of the NN; in fact, most are due to the rather remarkable nature of feedback itself. Included in this chapter are discrete-time systems, computer simulation, norms, and stability.
