Distributed discrete‐time optimization algorithms with applications to resource allocation in epidemics control

Ramírez-Llanos, Eduardo; Martínez, Sònia

doi:10.1002/oca.2340

Cited by 21 publications

(15 citation statements)

References 30 publications

(31 reference statements)

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“…, the ASDPD is still distributed. Communications with two-hop or multi-hop neighbors are also used in [29]- [31]. However, it may make the communication graph denser.…”

Section: Remark 2 Because the Element Ijmentioning

confidence: 99%

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Asynchronous Distributed Power Control of Multimicrogrid Systems

Wang

Chen

Liu

et al. 2020

IEEE Trans. Control Netw. Syst.

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Asynchrony widely exists in microgrids (MGs), such as non-identical sampling rates and communication delays, which challenges the MG control. This paper addresses the asynchronous distributed power control problem of hybrid microgrids, considering different kinds of asynchrony, such as non-identical sampling rates and random time delays. To this end, we first formulate the economic dispatch problem of MGs and devise a synchronous algorithm. Then, we analyze the impact of asynchrony and propose an asynchronous iteration algorithm based on the synchronous version. By introducing a random clock at each iteration, different types of asynchrony are fitted into a unified framework, where the asynchronous algorithm is converted into a fixed-point iteration problem with a nonexpansive operator, leading to a convergence proof. We further provide an upper bound estimation of the time delay of the communication. Moreover, the real-time implementation of the proposed algorithm in both AC and DC MGs is introduced. By measuring the frequency/voltage, the controller is simplified by reducing one order and adapt to the fast varying load demand. Finally, simulations on a benchmark MG and experiments are utilized to verify the effectiveness and advantages of the proposed algorithm. Index Terms-Asynchronous control, distributed control, multi-agent system, multi-microgrid networks, time delay. I. INTRODUCTION Multi-Microgrid systems or Microgrids (MGs) are clusters of distributed generators (DGs), energy storage systems and loads, which are generally categorized into three types: AC, DC and hybrid AC/DC MGs [1], [2]. A hybrid AC/DC MG has the advantage of reducing processes of multiple inverse conversions in the involved individual AC or DC grid [3]. Recently, the distributed power control for MGs has attracted more and more attention due to its fast response speed, privacy

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“…, the ASDPD is still distributed. Communications with two-hop or multi-hop neighbors are also used in [29]- [31]. However, it may make the communication graph denser.…”

Section: Remark 2 Because the Element Ijmentioning

confidence: 99%

“…(31e) In the algorithm (31), only µ needs to be transmitted between neighbors. Moreover, the variablesz, z are not necessary, which simplifies the controller greatly.…”

Section: B Real-time Asdpdmentioning

confidence: 99%

Asynchronous Distributed Power Control of Multimicrogrid Systems

Wang

Chen

Liu

et al. 2020

IEEE Trans. Control Netw. Syst.

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“…Discrete-time algorithms to solve this problem do exist, see e.g. [18] in which the authors achieve convergence to a ball around the optimizer whose radius is a function of the step size. However, the analysis of discrete-time algorithms to solve P2 via a Newton-like method is outside the scope of this work.…”

Section: Formulation Of Continuous Time Dynamicsmentioning

confidence: 99%

Distributed approximate Newton algorithms and weight design for constrained optimization

2019

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Motivated by economic dispatch and linearly-constrained resource allocation problems, this paper proposes a class of novel distributed approx-Newton algorithms that approximate the standard Newton optimization method. We first develop the notion of an optimal edge weighting for the communication graph over which agents implement the second-order algorithm, and propose a convex approximation for the nonconvex weight design problem. We next build on the optimal weight design to develop a discrete distributed approx-Newton algorithm which converges linearly to the optimal solution for economic dispatch problems with unknown cost functions and relaxed local box constraints. For the full box-constrained problem, we develop a continuous distributed approx-Newton algorithm which is inspired by first-order saddle-point methods and rigorously prove its convergence to the primal and dual optimizers. A main property of each of these distributed algorithms is that they only require agents to exchange constant-size communication messages, which lends itself to scalable implementations. Simulations demonstrate that the distributed approx-Newton algorithms with our weight design have superior convergence properties compared to existing weighting strategies for first-order saddle-point and gradient descent methods.

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“…In the literature, such problems have often been addressed assuming limited changes in the network structures, that is, by studying how to re-arrange the network structure or distribute antidote in order to increase the population's resistance against a possible epidemic. Important results have been found by using geometric programming [19]; distributed algorithms have been recently proposed to address this problem [20], [21]. However, the ongoing health crisis has highlighted the importance of having control schemes, which take into account the dynamic evolution of the epidemic process, and can thus be updated online, as the outbreak evolves.…”

Section: Introductionmentioning

confidence: 99%

Optimal policy design to mitigate epidemics on networks using an SIS model

Cenedese¹,

Zino²,

Cucuzzella³

et al. 2021

Preprint

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Understanding how to effectively control an epidemic spreading on a network is a problem of paramount importance for the scientific community. The ongoing COVID-19 pandemic has highlighted the need for policies that mitigate the spread, without relying on pharmaceutical interventions, that is, without the medical assurance of the recovery process. These policies typically entail lockdowns and mobility restrictions, having thus nonnegligible socio-economic consequences for the population. In this paper, we focus on the problem of finding the optimum policies that "flatten the epidemic curve" while limiting the negative consequences for the society, and formulate it as a nonlinear control problem over a finite prediction horizon. We utilize the model predictive control theory to design a strategy to effectively control the disease, balancing safety and normalcy. An explicit formalization of the control scheme is provided for the susceptible-infected-susceptible epidemic model over a network. Its performance and flexibility are demonstrated by means of numerical simulations.

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Distributed discrete‐time optimization algorithms with applications to resource allocation in epidemics control

Cited by 21 publications

References 30 publications

Asynchronous Distributed Power Control of Multimicrogrid Systems

Asynchronous Distributed Power Control of Multimicrogrid Systems

Distributed approximate Newton algorithms and weight design for constrained optimization

Optimal policy design to mitigate epidemics on networks using an SIS model

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