Continuous-Time Optimization Dynamics Mirroring ADMM Architecture and Passivity-Based Robustification Against Delays

Miyano, Tatsuya; Yamashita, Shunya; Hatanaka, Takeshi; Shibata, Kazuki; Jimbo, Takashi; Fujita, Masayuki

doi:10.1109/tcns.2020.2972590

Cited by 9 publications

(17 citation statements)

References 38 publications

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“…As a result, it leads to non-smooth dynamics, which is analyzed by the invariance principle for Carathéodory systems [10]. However, the discontinuous nature hinders the application of the invariance principle when delays are introduced into the systems, which results in the additional restrictive assumptions in [3], [4]. It is worth noting that a projection-free Lagrangian is adopted to solve local and couple inequalities in [11], which enables a smooth dynamics and the application of the LaSalle's invariance principle under delays.…”

Section: Introductionmentioning

confidence: 99%

Smooth Dynamics for Distributed Constrained Optimization With Heterogeneous Delays

Yamashita

Hatanaka

et al. 2020

IEEE Control Syst. Lett.

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This work investigates the distributed constrained optimization problem under inter-agent communication delays from the perspective of passivity. First, we propose a continuoustime algorithm for distributed constrained optimization with general convex objective functions. The asymptotic stability under general convexity is guaranteed by the phase lead compensation. The inequality constraints are handled by adopting a projectionfree generalized Lagrangian, whose primal-dual gradient dynamics preserves passivity and smoothness, enabling the application of the LaSalle's invariance principle in the presence of delays. Then, we incorporate the scattering transformation into the proposed algorithm to enhance the robustness against unknown and heterogeneous communication delays. Finally, a numerical example of a matching problem is provided to illustrate the results.

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Section: Introductionmentioning

confidence: 99%

Smooth Dynamics for Distributed Constrained Optimization With Heterogeneous Delays

Yamashita

Hatanaka

et al. 2020

IEEE Control Syst. Lett.

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“…A variation of the primal-dual dynamics is also studied in [4], wherein the authors employ the augmented Lagrangian instead of the Lagrangian. The authors of [5], [6] present continuous-time dynamics that mirrors another (distributed) optimization algorithm, namely the alternating direction method of multiplier (ADMM).…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we address delays in distributed optimization algorithms. To this end, we revisit the continuous-time ADMM presented in [6], where the algorithm is shown to take the same architecture as bilateral teleoperation [7] from the viewpoint of passivity. Based on this perspective, the authors also robustify the algorithm against delays by using the so-called scattering transformation that has been extensively studied in teleoperation [7].…”

Section: Introductionmentioning

confidence: 99%

“…The same is applied to [13]. Recently, the authors succeeded in eliminating the strict convexity assumption in the presence of delays, but the communication structure assumed therein is different from that in [6].…”

Section: Introductionmentioning

confidence: 99%

“…In this paper, we focus on constrained convex optimization investigated in [6]. We start with formulating the optimization problem in the ADMM form.…”

Section: Introductionmentioning

confidence: 99%

See 2 more Smart Citations

Robustification of Continuous-Time ADMM against Communication Delays under Non-Strict Convexity: A Passivity-Based Approach

Yamashita

Hatanaka

2020

SICE Journal of Control, Measurement, and System Integration

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In this paper, we address a class of distributed optimization problems with non-strictly convex cost functions in the presence of communication delays between an agent and a coordinator. To this end, we focus on a continuous-time optimization algorithm that mirrors the alternating direction method of multipliers. We first redesign the algorithm so that the dynamics ensures smoothness and a sub-block for primal optimization includes stable zeros. It is then revealed that the algorithm is composed of feedback interconnection of passive systems. We next robustify the algorithm against communication delays by applying the so-called scattering transformation. The smoothness of the dynamics allows one to use the invariance principle for delay systems, and accordingly, the state trajectories are shown to converge to an optimal solution even without the strict convexity assumption. Finally, the presented method is demonstrated via simulation of an environmental-monitoring problem.

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Passivity-based Analysis of the ADMM Algorithm for Constraint-Coupled Optimization

Notarnicola

Falsone

2022

Automatica

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Continuous-Time Optimization Dynamics Mirroring ADMM Architecture and Passivity-Based Robustification Against Delays

Cited by 9 publications

References 38 publications

Smooth Dynamics for Distributed Constrained Optimization With Heterogeneous Delays

Smooth Dynamics for Distributed Constrained Optimization With Heterogeneous Delays

Robustification of Continuous-Time ADMM against Communication Delays under Non-Strict Convexity: A Passivity-Based Approach

Passivity-based Analysis of the ADMM Algorithm for Constraint-Coupled Optimization

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