Distributed Optimization for Control

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Topic Information

Dear Colleagues,

Distributed control and optimization have become a major concern in recent years due to an increase in industrial applications, such as multivehicle mobility, smart grid operations, and intelligent transportation management. Each agent of a networked system often only has access to its own private local features and only a local perspective of the network topology. Each agent must adopt an optimal strategy in a local sense to attain the overall maximum performance. The interaction of the agents can generate a capability to find the optimal solution that is beyond each agent’s competence. Distributed optimization for control would offer valuable mathematical tools for determining the best control strategies and choices for networked agents.

The current topical collection aims to attract high-quality contributions in distributed control and optimization over networks, decentralized algorithms, and their practical applications.

Topics of interest:

• Distributed control over networks;
• Distributed methods for optimization in networks;
• Distributed optimization algorithms for control;
• Game theory to distributed control;
• Robust distributed optimization;
• Stochastic distributed optimization;
• Computational algorithms for distributed optimization and control;
• New distributed optimization and control techniques in smart grids, transportation, social networks, etc.

Dr. Honglei Xu
Dr. Lingyun Wang
Topic Editors

Keywords

Participating Journals

Journal Name	Impact Factor	CiteScore	Launched Year	First Decision (median)	APC
Applied Sciences applsci	2.5	5.3	2011	18.4 Days	CHF 2400
Energies energies	3.0	6.2	2008	16.8 Days	CHF 2600
Mathematics mathematics	2.3	4.0	2013	18.3 Days	CHF 2600
Electronics electronics	2.6	5.3	2012	16.4 Days	CHF 2400
Designs designs	-	3.9	2017	21.7 Days	CHF 1600

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Published Papers (16 papers)

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15 pages, 479 KiB  

Open AccessArticle

A Class of Distributed Online Aggregative Optimization in Unknown Dynamic Environment

by Chengqian Yang, Shuang Wang, Shuang Zhang, Shiwei Lin and Bomin Huang

Mathematics 2024, 12(16), 2460; https://doi.org/10.3390/math12162460 - 8 Aug 2024

Viewed by 957

Abstract

This paper considers a class of distributed online aggregative optimization problems over an undirected and connected network. It takes into account an unknown dynamic environment and some aggregation functions, which is different from the problem formulation of the existing approach, making the aggregative [...] Read more.

This paper considers a class of distributed online aggregative optimization problems over an undirected and connected network. It takes into account an unknown dynamic environment and some aggregation functions, which is different from the problem formulation of the existing approach, making the aggregative optimization problem more challenging. A distributed online optimization algorithm is designed for the considered problem via the mirror descent algorithm and the distributed average tracking method. In particular, the dynamic environment and the gradient are estimated by the averaged tracking methods, and then an online optimization algorithm is designed via a dynamic mirror descent method. It is shown that the dynamic regret is bounded in the order of $\mathcal{O}\left(\sqrt{T}\right)$. Finally, the effectiveness of the designed algorithm is verified by some simulations of cooperative control of a multi-robot system. Full article

(This article belongs to the Topic Distributed Optimization for Control)

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22 pages, 992 KiB  

Open AccessArticle

Data-Driven Containment Control for a Class of Nonlinear Multi-Agent Systems: A Model Free Adaptive Control Approach

by Ye Ren, Honghai Ji, Deli Li, Yongqiang Xie, Shuangshuang Xiong and Li Wang

Appl. Sci. 2024, 14(13), 5527; https://doi.org/10.3390/app14135527 - 25 Jun 2024

Cited by 1 | Viewed by 1222

Abstract

This paper studies the containment control problem of heterogeneous multi-agent systems (MASs) with multiple leaders. The follower agent dynamics are assumed to be unknown and nonlinear. First, each follower is transformed into an incremental data description based on the dynamic linearization technique. Then, [...] Read more.

This paper studies the containment control problem of heterogeneous multi-agent systems (MASs) with multiple leaders. The follower agent dynamics are assumed to be unknown and nonlinear. First, each follower is transformed into an incremental data description based on the dynamic linearization technique. Then, a distributed model-free adaptive containment control law is proposed such that all followers will be driven into the convex hull of the leaders. Furthermore, the algorithm is extended to the time-switching and dynamic leaders case. As a data-driven approach, the proposed controller design uses only the received input and output (I/O) data of these agents rather than agent mathematical models. Finally, to test the potential in real applications, three representative examples considering various environment factors, including external disturbances, are simulated to show the effectiveness and resilience of this method. Full article

(This article belongs to the Topic Distributed Optimization for Control)

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15 pages, 1538 KiB  

Open AccessArticle

Adaptive Neural Network Prescribed Time Control for Constrained Multi-Robotics Systems with Parametric Uncertainties

by Ruizhi Tang, Hai Lin, Zheng Liu, Xiaoyang Zhou and Yixiang Gu

Mathematics 2024, 12(12), 1880; https://doi.org/10.3390/math12121880 - 17 Jun 2024

Viewed by 1262

Abstract

This study designed an adaptive neural network (NN) control method for a category of multi-robotic systems with parametric uncertainties. In practical engineering applications, systems commonly face design challenges due to uncertainties in their parameters. Especially when a system’s parameters are completely unknown, the [...] Read more.

This study designed an adaptive neural network (NN) control method for a category of multi-robotic systems with parametric uncertainties. In practical engineering applications, systems commonly face design challenges due to uncertainties in their parameters. Especially when a system’s parameters are completely unknown, the unpredictability caused by parametric uncertainties may increase control complexity, and even cause system instability. To address these problems, an adaptive NN compensation mechanism is proposed. Moreover, using backstepping and barrier Lyapunov functions (BLFs), guarantee that state constraints can be ensured. With the aid of the transform function, systems’ convergence speeds were greatly improved. Under the implemented control strategy, the prescribed time control of multi-robotic systems with parametric uncertainties under the prescribed performance was achieved. Finally, the efficacy of the proposed control strategy was verified through the application of several cases. Full article

(This article belongs to the Topic Distributed Optimization for Control)

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15 pages, 1413 KiB  

Open AccessArticle

StructSim: Meta-Structure-Based Similarity Measure in Heterogeneous Information Networks

by Yuyan Zheng, Jianhua Qu and Jiajia Yang

Appl. Sci. 2024, 14(2), 935; https://doi.org/10.3390/app14020935 - 22 Jan 2024

Cited by 1 | Viewed by 1520

Abstract

Similarity measures in heterogeneous information networks (HINs) have become increasingly important in recent years. Most measures in such networks are based on the meta path, a relation sequence connecting object types. However, in real-world scenarios, there exist many complex semantic relationships, which cannot [...] Read more.

Similarity measures in heterogeneous information networks (HINs) have become increasingly important in recent years. Most measures in such networks are based on the meta path, a relation sequence connecting object types. However, in real-world scenarios, there exist many complex semantic relationships, which cannot be captured by the meta path. Therefore, a meta structure is proposed, which is a directed acyclic graph of object and relation types. In this paper, we explore the complex semantic meanings in HINs and propose a meta-structure-based similarity measure called StructSim. StructSim models the probability of subgraph expansion with bias from source node to target node. Different from existing methods, StructSim claims that the subgraph expansion is biased, i.e., the probability may be different when expanding from the same node to different nodes with the same type based on the meta structure. Moreover, StructSim defines the expansion bias by considering two types of node information, including out-neighbors of current expanded nodes and in-neighbors of next hop nodes to be expanded. To facilitate the implementation of StructSim, we further designed the node composition operator and expansion probability matrix with bias. Extensive experiments on DBLP and YAGO datasets demonstrate that StructSim is more effective than the state-of-the-art approaches. Full article

(This article belongs to the Topic Distributed Optimization for Control)

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17 pages, 4192 KiB  

Open AccessArticle

An Optimized Control System for the Independent Control of the Inputs of the Doherty Power Amplifier

by Pallav Kumar Sah, Matthew Poulton, Hung Luyen and Ifana Mahbub

Designs 2023, 7(6), 131; https://doi.org/10.3390/designs7060131 - 14 Nov 2023

Viewed by 2224

Abstract

This study presents a systematic design of an optimized drive signal control system for 2.5 GHz Doherty power amplifiers (DPAs). The designed system enables the analysis of the independent control of the amplitude and phase for the signals between the main and peak [...] Read more.

This study presents a systematic design of an optimized drive signal control system for 2.5 GHz Doherty power amplifiers (DPAs). The designed system enables the analysis of the independent control of the amplitude and phase for the signals between the main and peak amplifiers of the DPA. The independent control of the signal is achieved by incorporating a variable attenuator (VA) and a variable phase shifter (VPS) in each of the two parallel paths of the DPA. This integration allows for driving varying power levels with an arbitrary phase difference between the individual parallel PAs for reduced control complexity and power consumption. The specific VA (Qorvo QPC6614) and VPS (Qorvo QPC2108) components are used for the test system to provide an amplitude attenuation range from 0.5 dB to 31.5 dB and a phase range from $0^{\circ }$ to ${360}^{\circ }$ at the intended operating frequency of 2.5 GHz, offering the benefit of characterizing the behavior of PAs for an extensive range of drive signals to optimize the output performance, such as PAE or the ACLR. For experimental validation, the designed drive signal control system is integrated with GaN PAs (Qorvo QPD0005—DUT) with a $P_{1dB}$ of 37.7 dBm. Each PA is preceded by a drive amplifier with a gain of 17.8 dB to boost the power fed into the PA. In this manuscript, we analyzed and compared the PAE of the DPA and parallel-connected PA for diverse input signals generated using a designed optimized control system. Full article

(This article belongs to the Topic Distributed Optimization for Control)

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16 pages, 3903 KiB  

Open AccessArticle

CCA-YOLO: An Improved Glove Defect Detection Algorithm Based on YOLOv5

by Huilong Jin, Ruiyan Du, Liyong Qiao, Lingru Cao, Jian Yao and Shuang Zhang

Appl. Sci. 2023, 13(18), 10173; https://doi.org/10.3390/app131810173 - 10 Sep 2023

Cited by 5 | Viewed by 2155

Abstract

Aiming to address the issue of low efficiency and a high false-detection rate in artificial defect detection in nitrile medical gloves, CCA-YOLO was proposed on the basis of YOLOv5 to realize the detection of tear and scratch defects. CCA-YOLO added a small-target detection [...] Read more.

Aiming to address the issue of low efficiency and a high false-detection rate in artificial defect detection in nitrile medical gloves, CCA-YOLO was proposed on the basis of YOLOv5 to realize the detection of tear and scratch defects. CCA-YOLO added a small-target detection layer to the YOLOv5 network backbone and further proposed an innovative channel coordinate attention mechanism. According to the different characteristics of tears and scratches, focal and efficient IoU loss and α-IoU loss functions were introduced to further improve the positioning accuracy. The data enhancement method was used to generate a dataset of nitrile gloves, which was divided into datasets for horizontal angular tear detection, vertical angular tear detection, and scratch detection. The problem of class imbalance with few defect samples was solved. Our experiments show that CCA-YOLO can effectively identify tear and scratch defects in nitrile medical gloves in the self-made datasets. Compared with YOLOv5, the mean average precision (mAP) of the three models for horizontal angular tear detection, vertical angular tear detection, and scratch detection can reach 99.3%, 99.8%, and 99.6%, showing increments of 4.2%, 5.3%, and 12.4%, respectively, thereby meeting the performance requirements of glove defect detection. Full article

(This article belongs to the Topic Distributed Optimization for Control)

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30 pages, 3705 KiB  

Open AccessReview

A Survey of Information Dissemination Model, Datasets, and Insight

by Yanchao Liu, Pengzhou Zhang, Lei Shi and Junpeng Gong

Mathematics 2023, 11(17), 3707; https://doi.org/10.3390/math11173707 - 28 Aug 2023

Cited by 8 | Viewed by 6982

Abstract

Information dissemination refers to how information spreads among users on social networks. With the widespread application of mobile communication and internet technologies, people increasingly rely on information on the internet, and the mode of information dissemination is constantly changing. Researchers have performed various [...] Read more.

Information dissemination refers to how information spreads among users on social networks. With the widespread application of mobile communication and internet technologies, people increasingly rely on information on the internet, and the mode of information dissemination is constantly changing. Researchers have performed various studies from mathematical modeling and cascade prediction perspectives to explore the previous problem. However, lacking a comprehensive review of the latest information dissemination models hinders scientific development. As a result, it is essential to review the latest models or methods. In this paper, we review information dissemination models from the past three years and conduct a detailed analysis, such as explanatory and predictive models. Moreover, we provide public datasets, evaluation metrics, and interface tools for researchers focusing more on algorithm design and modeling. Finally, we discuss the model application and future research directions. This paper aims to understand better the research progress and development trends for beginners and guide future research endeavors. We believe this article will attract more researchers’ interest and attention to the information dissemination field on social networks. Full article

(This article belongs to the Topic Distributed Optimization for Control)

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16 pages, 803 KiB  

Open AccessArticle

Distributed Finite-Time and Fixed-Time Nash Equilibrium Seeking for Non-Cooperative Game with Input Saturation

by Dong Wang, Zhenzhen Gao and Long Sheng

Mathematics 2023, 11(10), 2295; https://doi.org/10.3390/math11102295 - 15 May 2023

Cited by 7 | Viewed by 1605

Abstract

In this paper, a modified distributed Nash equilibrium seeking problem with input saturation has been investigated. The payoff function of each player is related to the communication topology, which is closer to the actual scenes. The sigmoid function is utilized to limit the [...] Read more.

In this paper, a modified distributed Nash equilibrium seeking problem with input saturation has been investigated. The payoff function of each player is related to the communication topology, which is closer to the actual scenes. The sigmoid function is utilized to limit the range of the input. Through the network communication between players and the gradient of the players’ payoff functions, the finite-time and fixed-time distributed Nash equilibrium seeking protocols with input saturation are given. Using the Lyapunov stability analysis, it is determined that the action of each player converges to the Nash equilibrium if all the players update their action according to the proposed algorithms. The numerical simulations are also provided to testify the algorithms. Full article

(This article belongs to the Topic Distributed Optimization for Control)

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22 pages, 1470 KiB  

Open AccessArticle

Minimization of the Compliance under a Nonlocal p-Laplacian Constraint

by Fuensanta Andrés, Damián Castaño and Julio Muñoz

Mathematics 2023, 11(7), 1679; https://doi.org/10.3390/math11071679 - 31 Mar 2023

Cited by 3 | Viewed by 1501

Abstract

This work is an extension of the paper by Cea and Malanowski to the nonlocal and nonlinear framework. The addressed topic is the study of an optimal control problem driven by a nonlocal p-Laplacian equation that includes a coefficient playing the role [...] Read more.

This work is an extension of the paper by Cea and Malanowski to the nonlocal and nonlinear framework. The addressed topic is the study of an optimal control problem driven by a nonlocal p-Laplacian equation that includes a coefficient playing the role of control in the optimization problem. The cost functional is the compliance, and the constraint on the states are of the Dirichlet homogeneous type. The goal of the present work is a numerical scheme for the nonlocal optimal control problem and its use to approximate solutions in the local setting. The main contributions of the paper are a maximum principle and a uniqueness result. These findings and the monotonicity properties of the p-Laplacian operator have been crucial to building an effective numerical scheme, which, at the same time, has provided the existence of optimal designs. Several numerical simulations complete the work. Full article

(This article belongs to the Topic Distributed Optimization for Control)

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14 pages, 13247 KiB  

Open AccessArticle

Optimally Initialized Model Reference Adaptive Controller of Wearable Lower Limb Rehabilitation Exoskeleton

by Mohammad Soleimani Amiri, Rizauddin Ramli and Ahmad Barari

Mathematics 2023, 11(7), 1564; https://doi.org/10.3390/math11071564 - 23 Mar 2023

Cited by 3 | Viewed by 1890

Abstract

A wearable lower-limb rehabilitation exoskeleton functions to fulfill the recovery process of limb functionality and assist physiotherapists. This paper presents an optimized adaptive control system for a wearable lower-limb rehabilitation exoskeleton. The tuning of the controller gains is defined as an optimization problem [...] Read more.

A wearable lower-limb rehabilitation exoskeleton functions to fulfill the recovery process of limb functionality and assist physiotherapists. This paper presents an optimized adaptive control system for a wearable lower-limb rehabilitation exoskeleton. The tuning of the controller gains is defined as an optimization problem for a closed-loop control system of the wearable lower-limb rehabilitation robot by genetic algorithm and particle swarm optimization. We presented a novel initialized model reference adaptive controller (IMRAC) for real-time joint trajectory tracking, in which controller gains are adjusted by the gradient-based method. An experimental test of a 4-degree of freedom lower-limb rehabilitation exoskeleton was carried out to observe the closed-loop performance of IMRAC for bipedal human walking. The statistical comparison between IMRAC and MRAC shows an efficient performance and robustness of our proposed method for the joint trajectory tracking of the lower-limb rehabilitation exoskeleton in real time. Full article

(This article belongs to the Topic Distributed Optimization for Control)

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18 pages, 300 KiB  

Open AccessArticle

The Effect of Dead-Time and Damping Ratio on the Relative Performance of MPC and PID on Second Order Systems

by Yusuf Abubakar Sha’aban

Appl. Sci. 2023, 13(2), 1138; https://doi.org/10.3390/app13021138 - 14 Jan 2023

Cited by 2 | Viewed by 1943

Abstract

Most industrial processes are regulated using PID control. However, many such processes often operate far from optimally because PID may not be the most suitable control method. Moreover, second-order models represent a large class of all controlled systems. This work studies the performance [...] Read more.

Most industrial processes are regulated using PID control. However, many such processes often operate far from optimally because PID may not be the most suitable control method. Moreover, second-order models represent a large class of all controlled systems. This work studies the performance of some commonly used industrial PID controllers relative to MPC to understand when it is more suitable to use Model predictive control. MPC is used for this comparison because it has been the most successful industrial controller after PID. It can be concluded from the studies that improved performance can be achieved with MPC, even for modest dead time and when the damping ratio is relatively low. These improvements are prominent for dead-time dominant systems, whose dead-time to time-constant ratio is at least three. Full article

(This article belongs to the Topic Distributed Optimization for Control)

19 pages, 1537 KiB  

Open AccessArticle

Fixed-Time Distributed Optimization for Multi-Agent Systems with Input Delays and External Disturbances

by Xuening Xu, Zhiyong Yu and Haijun Jiang

Mathematics 2022, 10(24), 4689; https://doi.org/10.3390/math10244689 - 10 Dec 2022

Cited by 3 | Viewed by 1774

Abstract

This study concentrates on a fixed-time distributed optimization problem for multi-agent systems (MASs) with input delay and external disturbances. First, by adopting the Artstein model reduction technique, the time-delay system is first transformed into a delay-free one, and external disturbances are then effectively [...] Read more.

This study concentrates on a fixed-time distributed optimization problem for multi-agent systems (MASs) with input delay and external disturbances. First, by adopting the Artstein model reduction technique, the time-delay system is first transformed into a delay-free one, and external disturbances are then effectively eliminated by using an integral sliding mode control strategy. Second, a new centralized optimization mechanism is developed that allows all agents to reach the same state in a fixed time and then converge to the optimal value of the global objective function. Meanwhile, the optimization problem is extended to switching topologies. Moreover, as the gradient information of the global objective function is difficult to obtain in advance, we construct a decentralized optimization protocol that enables all agents to acquire the same state in a certain amount of time while also optimizing the global optimization problem. Finally, two numerical simulations are presented to validate the effectiveness and reliability of the developed control strategy. Full article

(This article belongs to the Topic Distributed Optimization for Control)

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16 pages, 3479 KiB  

Open AccessArticle

State-Space Modeling and Analysis for an Inverter-Based Intelligent Microgrid under Parametric Uncertainty

by Yiwei Feng and Zong Ma

Appl. Sci. 2022, 12(23), 12418; https://doi.org/10.3390/app122312418 - 4 Dec 2022

Viewed by 2467

Abstract

In this paper, a multivariable linear integral feedback regulation controller for a microgrid was proposed. Considering that the nominal structure model of the inverter could not effectively and in a timely manner deal with the impact of filter parameter uncertainty, there were changes [...] Read more.

In this paper, a multivariable linear integral feedback regulation controller for a microgrid was proposed. Considering that the nominal structure model of the inverter could not effectively and in a timely manner deal with the impact of filter parameter uncertainty, there were changes in output power quality among different generation environments. To solve the constraints imposed by uncertain factors on the system, we formulated the following scheme. First, based on the analysis of the asymptotic stability and power characteristics of the nominal model, we added the microgrid filter parameter uncertainty to this model. Secondly, under the action of the bounded range, the performance characteristics of the optimal cost were analyzed, adjusted, and optimized. The controller adjusted parameters to ensure the stable operation of the microgrid system, and to achieve the voltage stability regulation and output power balance. Finally, we built a test system to verify the feasibility and effectiveness of the proposed linear integral controller in MATLAB/Simulink. Full article

(This article belongs to the Topic Distributed Optimization for Control)

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16 pages, 828 KiB  

Open AccessArticle

SIMONE: A Dynamic Monitoring Simulator for the Evacuation of Navy Ships

by Heitor Martinez-Grueira, Rafael Asorey-Cacheda, Antonio-Javier Garcia-Sanchez and Joan Garcia-Haro

Appl. Sci. 2022, 12(22), 11786; https://doi.org/10.3390/app122211786 - 19 Nov 2022

Viewed by 1819

Abstract

In this paper, the automation of the evacuation process of a military ship is studied in real time. For this purpose, a scenario is reconfigured to produce a failure or damage. Then, an optimal network of alternative escape routes is computed. The resulting [...] Read more.

In this paper, the automation of the evacuation process of a military ship is studied in real time. For this purpose, a scenario is reconfigured to produce a failure or damage. Then, an optimal network of alternative escape routes is computed. The resulting escape route map can be indicated by lighting the appropriate corridors on the ship. Through these corridors, the members of the embarked population and the entire process is monitored so that the crew can reach their lifeboats in the shortest possible time. To undertake this automated process, the dynamic ship evacuation monitoring system (SIMONE, from its acronym in Spanish: Sistema de Monitorización Dinámica de Evacuación de Buques) has been developed. This system integrates a communication gateway with the integrated platform control system (IPCS) and integrated lighting system that will be installed in new Spanish naval constructions. Full article

(This article belongs to the Topic Distributed Optimization for Control)

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17 pages, 389 KiB  

Open AccessArticle

Distributed Optimization Algorithm for Composite Optimization Problems with Non-Smooth Function

by Yawei Shi, Liang Ran, Jialong Tang and Xiangzhao Wu

Mathematics 2022, 10(17), 3135; https://doi.org/10.3390/math10173135 - 1 Sep 2022

Cited by 1 | Viewed by 1854

Abstract

This paper mainly studies the distributed optimization problems in a class of undirected networks. The objective function of the problem consists of a smooth convex function and a non-smooth convex function. Each agent in the network needs to optimize the sum of the [...] Read more.

This paper mainly studies the distributed optimization problems in a class of undirected networks. The objective function of the problem consists of a smooth convex function and a non-smooth convex function. Each agent in the network needs to optimize the sum of the two objective functions. For this kind of problem, based on the operator splitting method, this paper uses the proximal operator to deal with the non-smooth term and further designs a distributed algorithm that allows the use of uncoordinated step-sizes. At the same time, by introducing the random-block coordinate mechanism, this paper develops an asynchronous iterative version of the synchronous algorithm. Finally, the convergence of the algorithms is proven, and the effectiveness is verified through numerical simulations. Full article

(This article belongs to the Topic Distributed Optimization for Control)

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24 pages, 10567 KiB  

Open AccessArticle

Mobile Sensor Networks for Finite-Time Distributed H_∞ Consensus Filtering of 3D Nonlinear Distributed Parameter Systems with Randomly Occurring Sensor Saturation

by Xueming Qian and Baotong Cui

Mathematics 2022, 10(17), 3134; https://doi.org/10.3390/math10173134 - 1 Sep 2022

Cited by 2 | Viewed by 1396

Abstract

This paper is concerned with designing a distributed bounded $H_{\infty }$ consensus filter to estimate an array of three-dimensional (3D) nonlinear distributed parameter systems subject to bounded perturbation. An optimization framework based on mobile sensing is proposed to improve the performance of distributed [...] Read more.

This paper is concerned with designing a distributed bounded $H_{\infty }$ consensus filter to estimate an array of three-dimensional (3D) nonlinear distributed parameter systems subject to bounded perturbation. An optimization framework based on mobile sensing is proposed to improve the performance of distributed filters. The measurement output is obtained from a mobile sensor network, where a phenomenon of randomly occurring sensor saturation is taken into account to reflect the reality in a mobile networked environment. A sufficient condition is established by utilizing operator-dependent Lyapunov functional for the filtering error system to be finite-time bounded. Note that the velocity law of each mobile sensor is included in this condition. The effect from the exogenous perturbation to the estimation accuracy is guaranteed at a given level by means of $H_{\infty }$ consensus performance constraint. Finally, simulation examples are presented to demonstrate the applicability of the theoretical results. Full article

(This article belongs to the Topic Distributed Optimization for Control)

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