Abstract: This article considers the theoretical study, simulation validation and performance analysis to make a deep overview on the topology control technology in wireless sensor networks. Topological structure automatically varies with the increasing, reduction and mobility of nodes, and topology control aims to self-organize construct global topology of connected network through the sensor nodes in order to ensure the connectivity and coverage of the network. In this article, the theoretical basis and numerical steps of four kinds of topology control algorithms are emphatically summarized. Then, two types of topological evolution algo-rithms are declaimed in detail to improve the network invulnerability, which contains an evolving model of scale-free networks and a construction of $k$ connected networks. That is, a mobile network topology model with local-area preference and a node scheduling optimization model based on $k$ connected networks are respectively proposed. Finally, we expound the prospect of topology control algorithm, introduction of mobile nodes, exploration of balanced control algorithms, application of complex network theory and combination with traditional algorithm and intelligent algorithm.

Key words: topology control, network invulnerability, scale-free networks, $k$ connected networks