Steering a Leader-Follower Team Via Linear Consensus

Pasqualetti, Fabio; Martini, Simone; Bicchi, Antonio

doi:10.1007/978-3-540-78929-1_54

Cited by 13 publications

(9 citation statements)

References 4 publications

(6 reference statements)

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“…These errors were analyzed for leader-follower systems with given leader sets based on the eigenvalues of the graph Laplacian in [106,112], where it was observed that the errors depend on the given leader set. Hence, an efficient, analytical approach to selecting leaders in order to minimize errors in the follower nodes' intermediate states would enable the leader nodes to steer the followers to the desired state while improving performance prior to convergence.…”

Section: Smooth Convergencementioning

confidence: 99%

Submodularity in Dynamics and Control of Networked Systems

Clark

Alomair

Bushnell

et al. 2016

Communications and Control Engineering

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Submodularity in Dynamics and Control of Networked Systems Andrew ClarkCo-Chairs of the Supervisory Committee:Radha Poovendran Electrical Engineering Linda Bushnell Electrical EngineeringControlling a networked dynamical system to reach a desired state is a fundamental challenge in applications including transportation, energy, social, and biological systems. One scalable approach to controlling such systems is to directly control the states of a subset of leader nodes, while relying on local interactions to steer the remaining nodes towards their desired states. The choice of leader nodes is known to affect system metrics including robustness to noise, rate of convergence to a desired state, and controllability of the system.Selecting an optimal subset of leader nodes, however, is inherently a combinatorial problem, making optimal leader node selection intractable in general.This thesis presents a submodular optimization framework to selecting leader nodes for control of networked systems. We investigate the problem of selecting a subset of leader nodes in order to minimize node state errors due to noise in the communication links between nodes. We prove that the error due to link noise is a supermodular function of the set of leader nodes, leading to the first polynomial-time algorithms for minimizing error due to link noise with provable optimality bounds. We develop our approach for networks with static topologies, as well as dynamic topologies due to random link failures, switching between predefined topologies, and arbitrary mobility.We study selecting leader nodes in order to minimize convergence error, defined as the error in the intermediate node states prior to reaching their desired values. We derive upper bounds for a class of convergence error metrics based on the hitting time of random walk on the network, which we prove to be a supermodular function of the set of input nodes.We present polynomial-time algorithms for minimizing convergence error with provable optimality bounds, for static as well as dynamic networks.Efficient algorithms have recently been proposed for selecting leader nodes to satisfy controllability, defined as the ability to drive the non-input nodes from any initial state to any desired state in finite time. These algorithms, however, do not incorporate performance criteria including robustness to noise and convergence rate. We study the problem of leader selection for joint performance and controllability, and prove that controllability can be formulated as a matroid constraint on the set of leader nodes. We propose efficient algorithms with provable optimality gap for selecting leader nodes for joint performance and controllability, and characterize the submodular structure of the largest controllable subgraph of a network.We also investigate selecting input nodes for guaranteeing synchronization in networked systems. Using the widely-studied Kuramoto model of nonlinear phase-coupled oscillators, we develop novel threshold-based conditions for a set of input nodes to ...

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Section: Smooth Convergencementioning

confidence: 99%

Submodularity in Dynamics and Control of Networked Systems

Clark

Alomair

Bushnell

et al. 2016

Communications and Control Engineering

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“…Using the metric (17), minimizing the convergence error is achieved by selecting leaders according to the optimization problem minimize ft (S 1 , . .…”

Section: Leader Selection Under Unknown Topology Distributionmentioning

confidence: 99%

“…The intermediate behavior of agents under linear weighted averaging algorithms was studied in [15], in which upper and lower bounds on the errors in the follower agents' intermediate states were derived for static networks without leaders. These errors were analyzed for leaderfollower systems with given leader sets based on the eigenvalues of the graph Laplacian in [16] and [17], where it was observed that the errors depend on the given leader set. Hence, an efficient, analytical approach to selecting leaders in order to minimize errors in the follower agents' intermediate states would enable the leader agents to steer the followers to the desired state while improving performance prior to convergence.…”

Section: Introductionmentioning

confidence: 99%

Minimizing Convergence Error in Multi-Agent Systems Via Leader Selection: A Supermodular Optimization Approach

Clark

Alomair

Bushnell

et al. 2014

IEEE Trans. Automat. Contr.

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In a leader-follower multi-agent system (MAS), the leader agents act as control inputs and influence the states of the remaining follower agents. The rate at which the follower agents converge to their desired states, as well as the errors in the follower agent states prior to convergence, are determined by the choice of leader agents. In this paper, we study leader selection in order to minimize convergence errors experienced by the follower agents, which we define as a norm of the distance between the follower agents' intermediate states and the convex hull of the leader agent states. By introducing a novel connection to random walks on the network graph, we show that the convergence error has an inherent supermodular structure as a function of the leader set. Supermodularity enables development of efficient discrete optimization algorithms that directly approximate the optimal leader set, provide provable performance guarantees, and do not rely on continuous relaxations. We formulate two leader selection problems within the supermodular optimization framework, namely, the problem of selecting a fixed number of leader agents in order to minimize the convergence error, as well as the problem of selecting the minimum-size set of leader agents to achieve a given bound on the convergence error. We introduce algorithms for approximating the optimal solution to both problems in static networks, dynamic networks with known topology distributions, and dynamic networks with unknown and unpredictable

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“…These approaches can be roughly classified as leader-follower approaches and leaderless approaches. In leaderfollower approach (Pasqualetti et al 2008;Sugar and Kumar 1998), the leader pursues the group objective and followers are supposed to follow their leader. The approach compromises over autonomy and does not consider cases where followers' objectives may be in conflict with each other or with the group objective.…”

Section: Related Workmentioning

confidence: 99%

Agent based coordination protocol for system of cyber-physical systems

et al. 2021

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Nowadays, society and business rely heavily on Information and Communication Technology (ICT) systems, which are progressing faster than ever. To stay on pace with them, focus is shifted towards integration of individual ICT systems into complex systems, which offers more functionality than simply the sum of individual systems. In this regard, Cyber-Physical Systems (CPSs) have gained significant importance and System-of-Systems (SoS) approach has been suggested for modeling complex CPSs to achieve a higher level goal, by dynamically building a large system with existing autonomous, and heterogeneous constituent systems (CSs). An important challenge in a system of Cyber-Physical Systems (SoCPSs) is to develop seamless collaboration between autonomous constituent-CPSs (CCPSs) to coordinate their operations. In this paper, we propose an agent based coordination mechanism to coordinate resource allocation and demand in SoCPSs. The approach models each CCPS as an agent and describes how multiple autonomous CCPSs, i.e., Virtual Power Plant (VPP), Commercial Greenhouse Growers (CGGs), communicate and collaborate with each other asynchronously through negotiation and how potential conflicts between CCPSs with conflicting goals are resolved. The efficacy of the proposed mechanism is validated through simulation of different real-world acyclic SoCPSs topologies. The results show that proposed approach is able to balance the individual requirements of multiple connected CPSs while achieving SoCPSs’ mission.

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Steering a Leader-Follower Team Via Linear Consensus

Cited by 13 publications

References 4 publications

Submodularity in Dynamics and Control of Networked Systems

Submodularity in Dynamics and Control of Networked Systems

Minimizing Convergence Error in Multi-Agent Systems Via Leader Selection: A Supermodular Optimization Approach

Agent based coordination protocol for system of cyber-physical systems

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