A Connection Between Dynamic Region-Following Formation Control and Distributed Average Tracking

This paper studies the inherent connection between dynamic region-following formation control (DRFFC) and distributed average tracking (DAT). We propose a fixed-gain DAT algorithm with robustness to initialization errors for linear multiagent systems, which is capable of achieving DAT with a zero tracking error for a large class of reference signals. In the case that the fixed gain cannot be chosen properly, we present an adaptive control gain design, under which each agent simply chooses its own gain and the restriction on knowing the upper bounds on the reference signals and their inputs is removed. We show that the proposed DAT algorithms can be employed to solve the DRFFC problem. This is an attempt on the applications of DAT algorithms to achieve distributed control; existing works most use DAT as distributed estimation algorithms. For single-integrator, double-integrator, higher-order linear dynamics, we derive the corresponding DRFFC algorithms from the DAT algorithm. Compared with existing DRFFC algorithms, the DAT-based DRFFC algorithms do not require the desired region to have a regular shape and is capable of generating a much richer formation behavior. Numerical examples are also included to show the validity of the derived results.