Consensus Seeking In Discrete-Time Multi-Agent Systems Under Independent Position And Velocity Topologies Of Xidian University

Consensus is well accepted as being a fundamental paradigm for coordination of multi-agent systems, which possess broad technological applications in different fields such as military, aviation, industry and even the daily life. The consensus problem for agents which are governed by double-integrator dynamics has also spurred great interest very recently partly due to its ability to model a broader class of complicated dynamical agents. However, almost all of the existing works concerning double-integrator agents are formulated based on the assumption that the position and velocity interactions among agents are modeled by the same digraph. In real applications, in order to optimize the coordination behavior or reduce the computational complexity, the setting that the position and velocity interaction topologies are modeled by different digraphs is necessary.With mainly this inspiration, this paper aims to use the iterative learning control theory to work on the design and analysis of multiple double-integrator agents with discrete-time dynamics consensus and formation control with the position and velocity interactions among agents being modeled by totally independent graphs. Which is more challenging and more practical. The main contents of this dissertation are summarized as follows:1. We consider the consensus problem of discrete-time double-integrator multi-agent systems in a very general framework where the position and velocity interactions among agents are modeled by independent graphs. Distributed algorithms are proposed and by using the tools from algebraic graph theory, matrix analysis and the contraction mapping principle, it is finally shown that the proposed algorithms are feasible in achieving the desired consensus behavior provided that there exists control gain matrices satisfy corresponding conditions. Then, the obtained conclusion is extended to achieve the formation control and we got the corresponding conclusion. Experimental results are used to validated the effectiveness of this method.2. Based on the above analysis, the obtained conclusion is extended to the case with a virtual leader under switching independent position and velocity interactions. And we get the sufficient condition to guarantee the multi-agent system consensus in the finite time interval. Through transfer the formation problem to the consensus problem which have been solved, deduction and sufficient conditions are given to obtain the desired relative formations of agents. It is shown that the derived results can effectively work, although not all the followers can get information from the leader. Such results is also illustrated via numerical simulations.