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The Consensus Of Two Types Of Multi-Agent Systems With State-Dependent Switching Topology

Posted on:2017-12-04Degree:MasterType:Thesis
Country:ChinaCandidate:J J WangFull Text:PDF
GTID:2348330491461988Subject:Applied Mathematics
Abstract/Summary:PDF Full Text Request
In this paper, we mainly studies the consensus problem of homogeneous multi-agent systems based on the Hegselmann-Krause model state-dependent switching topology, and this only depends on the properties of the systems and the profound comprehension for the relative principles in the systems. It is necessary for us to research the inherent properties of the dynamical systems deeply, because undoubtedly, it can generalize the depth and breadth of engineering applied research in the future, which may bring spectacular prospects for the relative research.The main results of this paper are mainly provided in Chapter 2 and 3. The consensus results of homogeneous multi-agent systems with state-dependent switching topology are given in two cases, according to whether the switches happen in the thresholds.In Chapter 2, the consensus of the finite discrete multi-agent systems with one dimensional state space under countable infinity time scale is given when no switches happened in the thresholds, and we point out that the convergence results can be generalized to any higher dimensional state spaces.In Chapter 3, we also studies the finite discrete multi-agent systems with one dimensional state space, but the switches occur in the threshold in these systems. We can have a foresight that we may get a stronger result in the systems which are switched more easily; but the stability of the equilibrium point of the finite-time consensus has been studied, what we will see is that why we can only do the similar research in the systems in §3.1. The continuum of multi-agent is raised from the second part of Chapter 3, and the new topology and respective definition of convergence, and respective convergence and stability of equilibrium point was studied. Then the connections between the discrete systems in this chapter and the continuum of the multi-agent are discussed. The discrete systems are the special examples of continuum systems, and any continuum system can be approximated by discrete systems in any finite time scale.As for Chapter 4, a summary about Chapter 2 and 3 is presented in this chapter. The similarities and differences about the models and results in Chapter 2 and 3 and the logic of the thread of the thought of this paper are analyzed profoundly, what's more, the key point of the mathematical ideas and methods are pointed out, hence the limitations of the generalization of the models are induced. Furthermore, in mathematical sense, for the purpose of generalization of more abstract state spaces, the necessary properties in analysis and topology are pointed out, which may give some ideas in similar theoretical researches.
Keywords/Search Tags:Hegselmann-Krause Model, Endogenous Systems, Homogeneous Systems, Con- sensus Problem, Multi-agent Continuum, Banach Spaces
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