Network Identification and Control for Heterogeneous Multi-Agent Systems

QC 20241112

Abstract

In the last few decades, the study of identifying the network topology of multi-agent systems has attracted increasing attention, where the communication topology is not always accessible to controller design or analysis of multi-agent systems. One challenging objective is to generally identify the unknown network structure from the measurements of multi-agent systems and decide where and how to stimulate it to achieve the desired response. In this thesis, we investigate the problem of topology identification for multi-agent systems with unknown topology and the problem of simultaneous topology identification and synchronization of the multi-agent systems. 

In the first part of the thesis, we address the topology identification problem for complex dynamical networks with both unknown constant and switching topology. We propose a finite-time identification scheme that ensures accurate topology estimation by leveraging a finite-time adaptive controller tracking reference signals and providing sufficient excitation. Accurate topology estimation is achieved once a relaxed excitation condition holds. This scheme removes the assumption of linear independence conditions or persistent excitation conditions during the identification process and guarantees the success of accurate topology identification. In addition, we provide a new scheme that achieves topology identification and synchronization in finite time, which provides a solution to combine topology identification and other control tasks.  We adjust this scheme to solve the finite-time topology identification problem for the directed general topological matrix and its extensions for the cases of a symmetric matrix and a Laplacian matrix, thereby broadening its applicability to a wider range of complex networks. With a partial priori knowledge of network structure, adjusted algorithms improve efficiency and reduce computational complexity.  Moreover, we extend the scheme to handle the networks with unknown switching topology, which identifies both the switching instant and graph sequences.

In the second part of the thesis, we propose a novel approach for simultaneous topology identification and synchronization for dynamical directed networks to overcome the conflicting goals of topology identification and synchronization. A new perspective which relies on the edge-agreement framework is presented for the study of the topology identification problem and a new adaptive-control-based topology-identification algorithm based on the concept of $\delta$-persistency of excitation is employed to achieve simultaneous topology identification and synchronization. By the edge-agreement representation, strong stability results for the identification errors in terms of uniform semi-global practical asymptotic stability are provided. In addition, We also extend this adaptive controller-based approach to simultaneous estimation of topology and synchronization in complex dynamical networks with time-varying topology. Our approach transforms the problem of time-varying topology estimation into a problem of estimating the time-varying weights of a complete graph, based on the edge-agreement framework. Two auxiliary networks are introduced to bound the weight estimation errors: one that satisfies the persistent excitation condition to facilitate topology estimation, while the other, a uniform-$\delta$ persistently exciting network, ensures the boundedness of both weight estimation and synchronization errors, assuming bounded time-varying weights and their derivatives.

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