A unified control method for consensus with various quantizers

Abstract

This paper studies the distributed consensus problem for networked general linear systems in the presence of different quantizers. The distinct features of this work are three-fold. First, both uniform and logarithmic quantization effects are analyzed. A unified control method (involving a distributed controller, a distributed event-detector, time-varying gains and constant parameters) is developed based on the relative quantized state information, which is applicable to practical scenarios where uniform and logarithmic quantization phenomena appear separately or alternately. Second, the updates of the relative information involved in the controller and the communication between adjacent agents are executed only at certain discrete event instants, significantly reducing the information update burden and data transmission load. Moreover, an internal variable, which is adjustable in accordance with the update law, is introduced in the event-detector to enhance the dynamic characteristics of the triggering performance with a lower triggering frequency. Simultaneously, the undesired Zeno behavior can be ruled out. Third, time-varying coupling gain (regulated by an adaptive rule) and triggering gain (relevant to the coupling gain) instead of constant ones are designed for the controller and the event-detector, respectively. Besides, other constant parameters can be easily tuned. These settings enable the developed control method to feature more flexibility and to be implemented in a fully distributed manner, requiring no global information. Finally, simulation examples are presented to illustrate the applicability of the theoretical results.