| The aim of this thesis is to investigate the complexity in a class of hybrid systems: networked control systems (NCSs), where sampling, quantization, time delay, packet dropout, network protocol and controller design are the main design issues. The study begins with limiting behavior of digital implementations of analog control systems. It is shown that as the sampling period tends to zero, internal stability and performance of an analog system can be recovered in the digital implementation via the bilinear transformation. Following this is a new network data transmission strategy that is proposed to reduce network traffic, thus avoiding large time delays and high percentage of packet dropout. The effectiveness of this transmission strategy is illustrated by simulations. Then the qualitative behavior of the nonsmooth dynamical systems arising from the aforementioned transmission strategy is investigated. Though it appears innocent, surprisingly, this type of nonsmooth system possesses bewildering dynamics. Local stability of fixed points, existence of periodic orbits, strange attractors and topological entropies are investigated in considerable detail first for scalar cases. Then it is proved that this type of system is not structurally stable. Following this is the analysis of the difficulties involved in studying these systems. Next the two-dimensional cases are studied with emphasis on their geometric structures. After that, a two-dimensional continuous-tune system, the counterpart of the above-mentioned discrete one is discussed, where special attention is paid to the demonstration of its rather complex dynamics. Because this study originates in the analysis of networked control systems, some control problems are discussed after the foregoing analysis. Finally several open problems are listed as our future research directions. |
