Optimal Distributed Control for Leader-Follower Networks: A Scalable Design

Arabneydi, Jalal; Baharloo, Mohammad; Aghdam, Amir G.

doi:10.1109/ccece.2018.8447800

Cited by 11 publications

(16 citation statements)

References 14 publications

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“…where MT +1 = 0 dx×dx and MT +1 = 0 2dx×2dx . According to [14], [15], the optimal performance J * T is obtained under the following linear strategies:…”

Section: Resultsmentioning

confidence: 99%

“…In their previous work [15], the authors show that if the mean-field xt is available to the leader and followers, then the optimal solution is unique and linear. However, collecting and sharing the mean-field among all agents is not costefficient, in general, specially when the number of followers n is large.…”

Section: Main Challenges and Contributionsmentioning

confidence: 99%

“…Lemma 3 Let ∆J denote the discrepancy between the performance of the optimal strategies (10) and (11), and that of the proposed strategies (14) and (15). wherẽ…”

Section: Assumptionmentioning

confidence: 99%

“…Theorem 2 Let Assumptions 1, 2 and 3 hold. Then, the strategies proposed in (14) and (15) are ε(n)-optimal solutions for Problem 1 such that…”

Section: Assumptionmentioning

confidence: 99%

See 3 more Smart Citations

Near-Optimal Control Strategy in Leader-Follower Networks: A Case Study for Linear Quadratic Mean-Field Teams

Baharloo

Arabneydi

Aghdam

2018

2018 IEEE Conference on Decision and Control (CDC)

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In this paper, a decentralized stochastic control system consisting of one leader and many homogeneous followers is studied. The leader and followers are coupled in both dynamics and cost, where the dynamics are linear and the cost function is quadratic in the states and actions of the leader and followers. The objective of the leader and followers is to reach consensus while minimizing their communication and energy costs. The leader knows its local state and each follower knows its local state and the state of the leader. The number of required links to implement this decentralized information structure is equal to the number of followers, which is the minimum number of links for a communication graph to be connected. In the special case of leaderless, no link is required among followers, i.e., the communication graph is not even connected. We propose a near-optimal control strategy that converges to the optimal solution as the number of followers increases. One of the salient features of the proposed solution is that it provides a design scheme, where the convergence rate as well as the collective behavior of the followers can be designed by choosing appropriate cost functions. In addition, the computational complexity of the proposed solution does not depend on the number of followers. Furthermore, the proposed strategy can be computed in a distributed manner, where the leader solves one Riccati equation and each follower solves two Riccati equations to calculate their strategies. Two numerical examples are provided to demonstrate the effectiveness of the results in the control of multi-agent systems.

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“…where MT +1 = 0 dx×dx and MT +1 = 0 2dx×2dx . According to [14], [15], the optimal performance J * T is obtained under the following linear strategies:…”

Section: Resultsmentioning

confidence: 99%

Section: Main Challenges and Contributionsmentioning

confidence: 99%

“…Lemma 3 Let ∆J denote the discrepancy between the performance of the optimal strategies (10) and (11), and that of the proposed strategies (14) and (15). wherẽ…”

Section: Assumptionmentioning

confidence: 99%

“…Theorem 2 Let Assumptions 1, 2 and 3 hold. Then, the strategies proposed in (14) and (15) are ε(n)-optimal solutions for Problem 1 such that…”

Section: Assumptionmentioning

confidence: 99%

See 2 more Smart Citations

Near-Optimal Control Strategy in Leader-Follower Networks: A Case Study for Linear Quadratic Mean-Field Teams

Baharloo

Arabneydi

Aghdam

2018

2018 IEEE Conference on Decision and Control (CDC)

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“…In addition, we raise a practical question that when the solution of an infinite-population network constructs a meaningful approximation for the finitepopulation one. Inspired by existing techniques for meanfield teams [19], [20], [21], [22], [23], [24], we first compute the optimal solution of a finite-population network for the case where the empirical distribution of infected nodes is observable. Next, we derive an infinite-population Bellman equation that requires no observation of infected nodes, and identify a stability condition under which the solution of the infinite-population network constitutes a near-optimal solution for the finite-population one.…”

Section: Introductionmentioning

confidence: 99%

A Mean-Field Team Approach to Minimize the Spread of Infection in a Network

Arabneydi

Aghdam

2019

2019 American Control Conference (ACC)

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In this paper, a stochastic dynamic control strategy is presented to prevent the spread of an infection over a homogeneous network. The infectious process is persistent, i.e., it continues to contaminate the network once it is established. It is assumed that there is a finite set of network management options available such as degrees of nodes and promotional plans to minimize the number of infected nodes while taking the implementation cost into account. The network is modeled by an exchangeable controlled Markov chain, whose transition probability matrices depend on three parameters: the selected network management option, the state of the infectious process, and the empirical distribution of infected nodes (with not necessarily a linear dependence). Borrowing some techniques from mean-field team theory the optimal strategy is obtained for any finite number of nodes using dynamic programming decomposition and the convolution of some binomial probability mass functions. For infinite-population networks, the optimal solution is described by a Bellman equation. It is shown that the infinite-population strategy is a meaningful sub-optimal solution for finite-population networks if a certain condition holds. The theoretical results are verified by an example of rumor control in social networks.

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