Analysis of Coordination in Multi-Agent Systems Through Partial Difference Equations. Part I: The Laplacian Control

Ferrari-Trecate, Giancarlo; Buffa, Annalisa; Gati, Mehdi

doi:10.3182/20050703-6-cz-1902.02086

Cited by 20 publications

(20 citation statements)

References 5 publications

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“…These results have been established in [15,16] through the joint use of tools in control theory and algebraic graph theory. A formal analysis of the PdE (4a) has been conducted in [11,14] showing a complete accordance with results available within the theory of the heat equation [17]; -in the case of a single leader (i.e. N ∂SF = {x L }) with fixed position (i.e.…”

Section: Multiple Stationary Leadersmentioning

confidence: 82%

“…This property has also been shown in [11,14] within the PdE framework, thus highlighting the profound links between model (4) and the heat equation with Dirichlet boundary conditions [17].…”

Section: Multiple Stationary Leadersmentioning

confidence: 88%

“…Then, the collective dynamics is represented by the modelṙ (4) is an example of a continuous-time Partial difference Equation (PdE) with non-homogeneous Dirichlet boundary conditions. We defer the reader to [13,11,14] for an introduction to PdEs.…”

Section: Multiple Stationary Leadersmentioning

confidence: 99%

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Laplacian Sheep: A Hybrid, Stop-Go Policy for Leader-Based Containment Control

Ferrari-Trecate

Egerstedt

Buffa

et al. 2006

Lecture Notes in Computer Science

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Abstract. The problem of driving a collection of mobile robots to a given target location is studied in the context of partial difference equations. In particular, we are interested in achieving this transfer while ensuring that the agents stay in the convex polytope spanned by dedicated leader-agents, whose dynamics will be given by a hybrid Stop-Go policy. The resulting system ensures containment through the enabling result that under a Laplacian, decentralized control strategy for the followers, these followers will converge to a location in the convex leader polytope, as long as the leaders are stationary and the interaction graph is connected. Simulation results testify to the viability of the proposed, hybrid control strategy.

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Section: Multiple Stationary Leadersmentioning

confidence: 82%

Section: Multiple Stationary Leadersmentioning

confidence: 88%

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Laplacian Sheep: A Hybrid, Stop-Go Policy for Leader-Based Containment Control

Ferrari-Trecate

Egerstedt

Buffa

et al. 2006

Lecture Notes in Computer Science

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“…Here B is an n × n matrix (typically the identity matrix), u is a vector of inputs whose i th component u i is the scalar input exerted by agent i. Theorem 2: Given the network dynamics in Equation (4). If…”

Section: Motion Probesmentioning

confidence: 99%

“…One recently discovered aspect of a Laplacian-based control strategy for networked systems is its connection to the heat equation through the introduction of so-called partial difference equations as discrete analogs of partial differential equations [1], [4]. This analogy enables the connection to traditional boundary-value problems.…”

Section: Introductionmentioning

confidence: 99%

Motion probes for fault detection and recovery in networked control systems

Franceschelli

Egerstedt

Giua

2008

2008 American Control Conference

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In this paper we address the problem of how to excite networked control systems in such a way that faulty, and possibly malicious, agents can be detected. In particular, we envision a scenario in which a subset of the agents in the network are executing a different control strategy than what has been prescribed and the problem under consideration consists of two subtasks, namely detection of the faulty agents, and isolation and mitigation of their impact on the remaining agents. We achieve this by proposing a collection of "motion probes" that leave certain aspects of the network invariant while ensuring that non-cooperative agents are identified and isolated. While we propose a useful tool to identify the faulty agents, the actual algorithms and policies that make use of the motion probes are left to future research.Published as: M. Franceschelli, M. Egerstedt, A. Giua, "Motion probes for fault detection and recovery in

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Partial differential equation‐based multiagent systems formation‐containment control with α‐leader input delay

Chen,

Wang,

Wang

et al. 2023

Asian Journal of Control

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This paper investigates the formation‐containment problem for a multiagent system, where the agents are classified into containment followers, formation leaders, anchor leader, and ‐leader. The ‐leader stabilizes formation leaders to desired formation deployment, while formation leaders adopt local state feedback distributed control law without desired formation position and the anchor leader fixes to its desired position. The containment followers adopted consensus distributed control law and converge to the convex hull spanned by the leader agents. Formation leaders' distributed control law parameters are proposed based on the discrete form of the desired partial differential equation (PDE) formation deployment, which is stabilized by the ‐leader agent and transited by communication topology. Based on its neighbor leader agent's delay state, ‐leader control law designed an integral‐type delay‐compensated control law by the backstepping method and the equivalence principle. In order to prove the rightness and existence of delay‐compensated control law, the well‐posedness of kernel functions are given by semigroup perturbation theory and solutions in the sense of distribution. Finally, a simulation example is given to verify the theoretical results.

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Analysis of Coordination in Multi-Agent Systems Through Partial Difference Equations. Part I: The Laplacian Control

Cited by 20 publications

References 5 publications

Laplacian Sheep: A Hybrid, Stop-Go Policy for Leader-Based Containment Control

Laplacian Sheep: A Hybrid, Stop-Go Policy for Leader-Based Containment Control

Motion probes for fault detection and recovery in networked control systems

Partial differential equation‐based multiagent systems formation‐containment control with α‐leader input delay

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