Sampled-data Setting

Abstract

This chapter considers distributed multi-agent coordination in a sampled-data setting. We first study a distributed sampled-data coordinated tracking algorithm where a group of followers with single-integrator dynamics interacting with their neighbors at discrete-time instants intercepts a dynamic leader who is a neighbor of only a subset of the followers. We propose a proportional-derivative-like discrete-time algorithm and study the condition on the interaction graph, the sampling period, and the control gain to ensure stability under directed fixed interaction and give the quantitative bound of the tracking errors. We then study convergence of two distributed sampled-data coordination algorithms with respectively, absolute damping and relative damping for double-integrator dynamics under undirected/directed fixed interaction. We show necessary and sufficient conditions on the interaction graph, the sampling period, and the control gain such that coordination is achieved using these two algorithms by using matrix theory, bilinear transformation, and Cauchy theorem. We finally study convergence of the two distributed sampled-data coordination algorithms with respectively, absolute damping and relative damping for double-integrator dynamics under directed switching interaction. We derive sufficient conditions on the interaction graph, the sampling period, and the control gain to guarantee coordination by using the property of infinity products of row-stochastic matrices. Simulation results are presented to show the effectiveness of the theoretical results.