Synchronization of autonomous agents by an optimal networked controller

Mosebach, Andrej; Lunze, Jan

doi:10.1109/ecc.2014.6862471

Cited by 19 publications

(16 citation statements)

References 9 publications

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“…This type of cost function is applied in a variety of science and engineering applications such as medical treatments or biological systems4142, consensus or synchronization of distributed agents434445, networked systems46, social interactions47 and many more…”

Section: Resultsmentioning

confidence: 99%

Energy scaling of targeted optimal control of complex networks

2017

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Recently it has been shown that the control energy required to control a dynamical complex network is prohibitively large when there are only a few control inputs. Most methods to reduce the control energy have focused on where, in the network, to place additional control inputs. Here, in contrast, we show that by controlling the states of a subset of the nodes of a network, rather than the state of every node, while holding the number of control signals constant, the required energy to control a portion of the network can be reduced substantially. The energy requirements exponentially decay with the number of target nodes, suggesting that large networks can be controlled by a relatively small number of inputs as long as the target set is appropriately sized. We validate our conclusions in model and real networks to arrive at an energy scaling law to better design control objectives regardless of system size, energy restrictions, state restrictions, input node choices and target node choices.

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Section: Resultsmentioning

confidence: 99%

Energy scaling of targeted optimal control of complex networks

2017

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“…When applying the decomposition methods detailed below, this leads to tractable synthesis algorithms with a complexity in the order of a single subsystem. In contrast, [9] consider gradientbased optimization on the level of the entire interconnected subsystem, whereas [1] require conditions of the complexity of the maximum vertex degree plus one.…”

Section: Theorem 1 (Analysis Of Interconnected Lpv Systems [4])mentioning

confidence: 94%

“…Structural constraints on the multipliers decompose the problem [4], introducing some conservatism. The results encompass, e. g., Linear Quadratic (LQ)-type results [1], [9] by using convex optimization for analysis.…”

Section: Interconnected Lpv System Analysismentioning

confidence: 99%

Control of heterogeneous LPV subsystems interconnected through arbitrary and switching directed topologies

Hoffmann

Werner

2015

2015 54th IEEE Conference on Decision and Control (CDC)

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This paper introduces a novel technique for the synthesis of distributed Linear Parameter-Varying (LPV) controllers for heterogeneous LPV systems interconnected through arbitrary, time-varying, directed interaction topologies. A distributed system is constructed from interconnected subsystems for which a novel manipulation of interconnection channels is proposed that renders any interconnection representable as a virtual normal interconnection matrix. This guarantees the existence of a unitary diagonalizing transformation. The synthesis problem can then be essentially solved by Linear Fractional Transformation (LFT)-LPV gain-scheduling synthesis methods, in which the possibly varying eigenvalues of the virtual interconnection matrix act as the scheduling variables of the transformed problem and the computational complexity is in the order of a single subsystem. The method is benchmarked against an existing one and shows superior performance in both a numerical example and the leader-follower formation control problem of LPV quadrocopter models.

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“…The distributed linear quadratic problem is then to find a distributed diffusive control law that, for given initial states of the agents, minimizes the cost functional, while achieving consensus for the controlled network. This problem is non-convex and difficult to solve, and it is unclear whether a solution exists in general [1]. Therefore, in this paper, instead of addressing the version formulated above, we will study a suboptimal version of the distributed optimal control problem.…”

Section: Introductionmentioning

confidence: 99%

A Suboptimality Approach to Distributed Linear Quadratic Optimal Control

Jiao

Trentelman

Camlibel

2020

IEEE Trans. Automat. Contr.

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This paper is concerned with the distributed linear quadratic optimal control problem. In particular, we consider a suboptimal version of the distributed optimal control problem for undirected multi-agent networks. Given a multi-agent system with identical agent dynamics and an associated global quadratic cost functional, our objective is to design suboptimal distributed control laws that guarantee the controlled network to reach consensus and the associated cost to be smaller than an a priori given upper bound. We first analyze the suboptimality for a given linear system and then apply the results to linear multi-agent systems. Two design methods are then provided to compute such suboptimal distributed controllers, involving the solution of a single Riccati inequality of dimension equal to the dimension of the agent dynamics, and the smallest nonzero and the largest eigenvalue of the graph Laplacian. Furthermore, we relax the requirement of exact knowledge of the smallest nonzero and largest eigenvalue of the graph Laplacian by using only lower and upper bounds on these eigenvalues. Finally, a simulation example is provided to illustrate our design method.

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Synchronization of autonomous agents by an optimal networked controller

Cited by 19 publications

References 9 publications

Energy scaling of targeted optimal control of complex networks

Energy scaling of targeted optimal control of complex networks

Control of heterogeneous LPV subsystems interconnected through arbitrary and switching directed topologies

A Suboptimality Approach to Distributed Linear Quadratic Optimal Control

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