Multiplex PI-Control for Consensus in Networks of Heterogeneous Linear Agents

In this paper, we propose a multiplex proportional-integral approach, for solving consensus problems in networks of heterogeneous nodes dynamics affected by constant disturbances. The proportional and integral actions are deployed on two different layers across the network, each with its own topology. Sufficient conditions for convergence are derived that depend upon the structure of the network, the parameters characterizing the control layers and the node dynamics. The effectiveness of the theoretical results is illustrated using a power network model as a representative example.Comment: 13 pages, 6 Figures, Preprint submitted to Automatic

Node dynamics on graphs: dynamical heterogeneity in consensus, synchronisation and final value approximation for complex networks

Here we consider a range of Laplacian-based dynamics on graphs such as dynamical invariance and coarse-graining, and node-specific properties such as convergence, observability and consensus-value prediction. Firstly, using the intrinsic relationship between the external equitable partition (EEP) and the spectral properties of the graph Laplacian, we characterise convergence and observability properties of consensus dynamics on networks. In particular, we establish the relationship between the original consensus dynamics and the associated consensus of the quotient graph under varied initial conditions. We show that the EEP with respect to a node can reveal nodes in the graph with increased rate of asymptotic convergence to the consensus value as characterised by the second smallest eigenvalue of the quotient Laplacian. Secondly, we extend this characterisation of the relationship between the EEP and Laplacian based dynamics to study the synchronisation of coupled oscillator dynamics on networks. We show that the existence of a non-trivial EEP describes partial synchronisation dynamics for nodes within cells of the partition. Considering linearised stability analysis, the existence of a nontrivial EEP with respect to an individual node can imply an increased rate of asymptotic convergence to the synchronisation manifold, or a decreased rate of de-synchronisation, analogous to the linear consensus case. We show that high degree 'hub' nodes in large complex networks such as Erdős-Rényi, scale free and entangled graphs are more likely to exhibit such dynamical heterogeneity under both linear consensus and non-linear coupled oscillator dynamics. Finally, we consider a separate but related problem concerning the ability of a node to compute the final value for discrete consensus dynamics given only a finite number of its own state values. We develop an algorithm to compute an approximation to the consensus value by individual nodes that is ϵ close to the true consensus value, and show that in most cases this is possible for substantially less steps than required for true convergence of the system dynamics. Again considering a variety of complex networks we show that, on average, high degree nodes, and nodes belonging to graphs with fast asymptotic convergence, approximate the consensus value employing fewer steps.Open Acces

Evolutionary robotics and neuroscience

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Distributed H∞ Controller Design and Robustness Analysis for Vehicle Platooning Under Random Packet Drop

This paper presents the design of a robust distributed state-feedback controller in the discrete-time domain for homogeneous vehicle platoons with undirected topologies, whose dynamics are subjected to external disturbances and under random single packet drop scenario. A linear matrix inequality (LMI) approach is used for devising the control gains such that a bounded H∞ norm is guaranteed. Furthermore, a lower bound of the robustness measure, denoted as γ gain, is derived analytically for two platoon communication topologies, i.e., the bidirectional predecessor following (BPF) and the bidirectional predecessor leader following (BPLF). It is shown that the γ gain is highly affected by the communication topology and drastically reduces when the information of the leader is sent to all followers. Finally, numerical results demonstrate the ability of the proposed methodology to impose the platoon control objective for the BPF and BPLF topology under random single packet drop

Adaptive sliding mode observation in a network of dynamical systems

This paper considers the problem of reconstructing state information in all the nodes of a complex network of dynamical systems. The individual nodes comprise a known linear part and unknown but bounded uncertainties in certain channels of the system. A supervisory adaptive sliding mode observer configuration is proposed for estimating the states. A linear matrix inequality (LMI) approach is suggested to synthesise the gains of the sliding mode observer. Although deployed centrally to estimate all the states of the complex network, the design process depends only on the dynamics of an individual node of the network. The methodology is demonstrated by considering a network of Chua oscillators

Synchronising H∞ robust distributed controller for multi-robotic manipulators

In this paper the problem of synchronisation of multiple robotic manipulators using Hoo robust distributed control systems with respect to the parameter uncertainties and disturbance inputs acting on the manipulators is addressed. Robust synchronising controllers only use the information of outputs of the manipulators, and the corresponding parameters of these output-feedback controllers are designed by computing a series of linear matrix inequalities instead of solving the complex differential (e.g. Hamilton-Jacobi) (in)equalities. The proposed controller can guarantee H∞ robust performance with respect to the external disturbance inputs and parameters uncertainties, asymptotic stability and synchronisation in the networked manipulators. Using an illustrative example we compare the results extracted in this paper to other works existing in the literature

Robust fault estimation using relative information in linear multi-agent networks

Journal ArticleIn this technical note, a robust fault estimation method, based on sliding mode observers, is proposed for a collection of agents undertaking a shared task and exchanging only relative information over a communication network. Since the 'system of systems' formed by the agents is not observable with respect to relative sensing information, by appropriate transformations and scalings of the inputs and outputs of the actual system, a meaningful observable subsystem is created. For this new subsystem, after modal decomposition based on the associated Laplacian, decoupled sliding mode observers, depending only on the individual node level dynamics of the network, can be created exploiting an existing design philosophy. These collectively form a centralized fault estimation scheme for the original system. © 1963-2012 IEEE