Semi-Autonomous Consensus: Network Measures and Adaptive Trees

Examining the effectiveness of control in networked systems is a thriving research area. Autonomous systems that can be intermittently influenced (controlled) by external agents find applications ranging from machine calibration to satellite control. We refer to this class of networks as semi-autonomous. If the semi-autonomous agents´ interaction dynamics are consensus-based, we dub this subclass as semi-autonomous consensus, which is the focus of the paper. Within such a subclass, we consider the dynamics of networked agents in the context of performance (friendly influence) and security (unfriendly influence). Our approach to appraise a semi-autonomous consensus network is to expose the network to fundamental test signals, namely white noise and an impulse, and use the resultant system response to quantify network performance and security. Traditionally, input-output properties are varied by altering the dynamics of the network agents. We instead adopt topological methods for this task, designing five protocols for tree graphs that rewire the network topology, leaving the network agents´ dynamics untouched. In pursuit of this objective, four adaptive protocols are introduced to either increase or decrease the mean tracking and variance damping measures, respectively. Finally, a proposed fifth hybrid protocol is shown to have a guaranteed performance for both measures using a game-theoretic formalism.