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distributed optimisation algorithm based on iterative learning control

INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE 2025年第4期56卷 827-840页

作者： Dong, Xiaochun Zhang, Ruikun Chen, Xiaoxue Lin, Xue Qingdao Univ Sci & Technol Sch Math & Phys Qingdao 266061 Peoples R China

In this paper, we study the distributed optimisation problem in an iterative environment, where the global objective function consists of agents' local objective functions, and each agent with the local objective function performs repeated tasks in finite time. The objective is to minimise the global objective function by the local communication of agents in the repeated running system. To solve this problem, we propose a distributed optimisation algorithm based on iterative learning methods that combines the terminal iterative learning strategy with the subgradient strategy. When the initial states of all agents are the same in each iteration, by the proposed algorithm, it is proved that all agents' states asymptotically converge to the optimal solution. Moreover, considering that the initial states of agents in each iteration may not be accurately measured, we further study the distributed optimisation problem under different initial states. We find that all agents' states asymptotically converge to the neighbourhood of the optimal solution. Finally, the effectiveness of the algorithm is verified by the numerical simulations.

关键词： distributed optimisation terminal iterative learning control multi-agent systems

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Adaptive event-triggered distributed optimisation for second-order nonlinear multi-agent systems with external disturbance

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INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE 2025年

作者： Tang, Run Zhu, Wei Pu, Huizhu Chongqing Univ Posts & Telecommun Key Lab Intelligent Anal & Decis Complex Syst Chongqing 400065 Peoples R China

In this paper, an unconstrained distributed optimisation problem for a class of second-order uncertain nonlinear systems subject to external disturbances is considered. In order to achieve optimal consensus and save communication resources, a novel distributed adaptive event-triggered control algorithm is proposed. Each agent updates its own state only at event-triggering instants without the requirement for global topology information. To effectively counteract the external disturbances and guide the states of all agents toward an optimal consensus point, the controller is designed based on gradient descent and the internal model principle. Furthermore, with Lyapunov stability theory, the designed controller can be proved to achieve asymptotic stability without time-varying parameters and the Zeno-behaviour is effectively excluded. Finally, a simulation example is provided to illustrate the validness of the designed control strategies.

关键词： Multi-agent systems distributed optimisation event-triggered control adaptive control nonlinear systems

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distributed optimisation problem with communication delay and external disturbance

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INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE 2017年第16期48卷 3530-3541页

作者： Ngoc-Tu Tran Xiao, Jiang-Wen Wang, Yan-Wu Yang, Wu Huazhong Univ Sci & Technol Sch Automat Wuhan Hubei Peoples R China Huazhong Univ Sci & Technol Key Lab Image Proc & Intelligent Control Minist Educ Wuhan Hubei Peoples R China China Three Gorges Univ Hubei Prov Collaborat Innovat Ctr New Energy Micr Wuhan Hubei Peoples R China

This paper investigates the distributed optimisation problem for the multi-agent systems (MASs) with the simultaneous presence of external disturbance and the communication delay. To solve this problem, a two-step design scheme is introduced. In the first step, based on the internal model principle, the internal model term is constructed to compensate the disturbance asymptotically. In the second step, a distributed optimisation algorithm is designed to solve the distributed optimisation problem based on the MASs with the simultaneous presence of disturbance and communication delay. Moreover, in the proposed algorithm, each agent interacts with its neighbours through the connected topology and the delay occurs during the information exchange. By utilising Lyapunov-Krasovskii functional, the delay-dependent conditions are derived for both slowly and fast time-varying delay, respectively, to ensure the convergence of the algorithm to the optimal solution of the optimisation problem. Several numerical simulation examples are provided to illustrate the effectiveness of the theoretical results.

关键词： Multi-agent systems distributed optimisation internal model principle external disturbance time-delay systems Lyapunov-Krasovskii functional

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distributed optimisation method for multi-resource constrained scheduling in coal supply chains

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INTERNATIONAL JOURNAL OF PRODUCTION RESEARCH 2013年第9期51卷 2740-2759页

作者： Thomas, Anu Singh, Gaurav Krishnamoorthy, Mohan Venkateswaran, Jayendran Indian Inst Technol IITB Monash Res Acad Bombay 400076 Maharashtra India CSIRO Math Informat & Stat Clayton Vic 3168 Australia Indian Inst Technol Bombay 400076 Maharashtra India

We consider an integrated planning and scheduling problem motivated by the coal supply chains in Australia. The problem considers production planning of several independent mines. The mines need trains to complete delivery of coal by the arrival of ships at the terminal. The trains, on the other hand, are in limited supply and therefore the mines need to share this common resource. For this problem, we present a mixed integer programming formulation which minimises total weighted earliness, tardiness and operational costs. We also present a distributed algorithm based on the Lagrangian relaxation, which incorporates the volume and Wedelin algorithms. The strength of our distributed algorithm is demonstrated by an extensive computational experiment on several randomly generated instances.

关键词： distributed optimisation integrated scheduling coal logistics resource constrained scheduling Wedelin algorithm

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distributed optimisation based on multi-agent system for resource allocation with communication time-delay

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IET CONTROL THEORY AND APPLICATIONS 2020年第4期14卷 549-557页

作者： Li, Kaixuan Liu, Qingshan Zeng, Zhigang Huazhong Univ Sci & Technol Sch Artificial Intelligence & Automat Wuhan 430074 Peoples R China Minist Educ Key Lab Image Proc & Intelligent Control Wuhan 430074 Peoples R China Southeast Univ Sch Math Nanjing 210096 Peoples R China Jiangsu Prov Key Lab Networked Collect Intelligen Nanjing 210096 Peoples R China

In this study, the distributed optimisation for solving resource allocation problem with both local bound and equality constraints is studied. A continuous-time multi-agent system with communication time-delay is proposed for the resource allocation. First, to reduce communication cost, a new modified multi-agent system is proposed inspired by previous work. Next, based on the system, the communication time-delay is considered to reduce the communication cost and match real situation. Then, by choosing proper parameters, sufficient conditions are derived for convergence to the optimal solution of the distributed optimisation. Moreover, delay-free case is also considered, which proves that the system is convergent based on directed communication graph by choosing proper parameters. Finally, simulation results demonstrate the characteristics of the system.

关键词： directed graphs delays continuous time systems resource allocation optimisation multi-agent systems modified multiagent system communication time-delay communication cost distributed optimisation delay-free case directed communication graph resource allocation local bound constraints local equality constraints continuous-time multiagent system sufficient conditions convergence

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distributed optimisation for Energy Management in Building Networks 12

Distributed Optimisation for Energy Management in Building N...

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UKACC 12th International Conference on Control (CONTROL)

作者： Edwards, Alec Calliess, Jan-Peter Margellos, Kostas Univ Oxford Dept Engn Sci Oxford England Univ Oxford Oxford Man Inst Quantitat Finance Oxford England

ISBN: (纸本)9781538628645

We formulate and solve an energy management problem for a cooperative network of buildings sharing some resource and communicating over a time varying network, each of which desires to maintain its privacy. As the network is time-varying, we are able to accommodate communication constraints or failure between agents. We begin by introducing validated bilinear modelling techniques for individual buildings, and continue by showing how the energy management problem involving a network of buildings can be addressed using a distributed optimisation algorithm recently proposed in the literature, with individual buildings treated as agents. To facilitate these assumptions, we linearise the bilinear models generated, and introduce linear local and coupling constraints to model a shared thermal energy storage device. We formulate a linear objective function to minimise based on the cost of energy used by the agent not taken from the storage. Finally, we demonstrate the efficacy of the distributed algorithm as applied to the energy management problem using an extensive simulation based study.

关键词： distributed optimisation building control energy management dual decomposition

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distributed optimisation of a logistic system and its suppliers using ant colonies

Distributed optimisation of a logistic system and its suppli...

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6th Portuguese Conference on Automatic Control

作者： Silva, C. A. Sousa, J. M. C. Runkler, T. A. Da Costa, J. M. G. Sa Univ Tecn Lisboa IDMEC GCAR Dept Mech EngnInst Super Tecn P-1049001 Lisbon Portugal Siemens AG Corp Technol D-81730 Munich Germany

This paper introduces a new multi-agent approach for collaborative management of logistic and supply systems based on the ant colony optimisation (ACO) meta-heuristic. The logistic system and its suppliers can be modelled as partners of a supply chain. The management methodology is defined as a set of distributed scheduling problems that exchange information during the optimisation process. Each problem is solved by an ant colony agent that uses the pheromone matrix as the communication platform. A simulation example shows that the proposed coordination mechanism improves the supply-chain performance compared to a traditional management approach, where both problems are considered separately.

关键词： ant colonies supply-chain system distributed optimisation

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Consensus-based distributed optimisation of multi-agent networks via a two level subgradient-proximal algorithm

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INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE 2015年第7期46卷 1307-1318页

作者： Hu, Bin Guan, Zhi-Hong Liao, Rui-Quan Zhang, Ding-Xue Zheng, Gui-Lin Huazhong Univ Sci & Technol Coll Automat Wuhan 430074 Peoples R China Yangtze Univ Petr Engn Coll Jinzhou 434023 Peoples R China Wuhan Univ Dept Automat Wuhan 430072 Peoples R China

This paper presents a consensus-based stochastic subgradient algorithm for multi-agent networks to minimise multiple convex but not necessarily differential objective functions, subject to an intersection set of multiple closed convex constraint sets. Compared with the existing results an alternative subgradient algorithm is first introduced based on two level subgradient iterations, where the first level is to minimise the component functions, and the second to enforce the iterates not oscillate from the constraint set wildly. In addition, a distributed consensus-based type of the proposed subgradient algorithm is constructed within the framework of multi-agent networks for the case when the iteration index of local objective functions and local constraint sets is not homologous. Detailed convergence analysis of the proposed algorithms is established using matrix theories and super-martingale convergence theorem. In addition, a pre-step convergence factor is obtained in this study to characterise the distance between the iterations and the optimal set, while some existing literatures only present a convergence work. Simulation results are given to demonstrate the effectiveness of the developed theoretical results.

关键词： Markov chain average consensus multi-agent networks subgradient distributed optimisation

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Generalised gossip-based subgradient method for distributed optimisation

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INTERNATIONAL JOURNAL OF CONTROL 2019年第6期92卷 1209-1225页

作者： Jiang, Zhanhong Mukherjee, Kushal Sarkar, Soumik Iowa State Univ Dept Mech Engn Ames IA USA IBM Res New Delhi India Iowa State Univ Lab Mech 207 Dept Mech Engn Ames IA 50011 USA

This paper presents a generalised time-synchronous gossip-based algorithm for solving distributed optimisation problems associated with multi-agent networked systems. The proposed algorithm presents a generalisation such that the optimisation process can operate in the entire spectrum from 'complete consensus' to 'complete disagreement'. A user-defined control parameter theta is identified for controlling such tradeoff as well as the temporal convergence properties. We formulate the algorithm based upon generalised time-synchronous gossip algorithm and subgradient method and provide analytical results for first and second moment convergence analysis. The proposed algorithm also provides a convergence rate estimate of in the number of iterations m when the step size is constant. We consider the effect of noise in networked systems from the perspectives of modelling uncertainty and measurement noise in subgradient estimation process and communication among agents, respectively. A numerical case study based on a multi-agent building energy system is used to validate the proposed algorithm.

关键词： Generalised gossip distributed optimisation multi-agent systems

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Sampling-data-based distributed optimisation of second-order multi-agent systems with PI strategy

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INTERNATIONAL JOURNAL OF SYSTEMS SCIENCE 2023年第6期54卷 1299-1312页

作者： Cui, Qiuyan Liu, Kaien Ji, Zhijian Song, Wenjie Qingdao Univ Sch Math & Stat Qingdao Peoples R China Qingdao Univ Coll Automat Qingdao Peoples R China Qingdao Univ Sch Math & Stat Qingdao 266071 Shandong Peoples R China

This paper investigates the optimisation problem of second-order multi-agent systems. distributed optimisation algorithms are proposed based on sampling data. Two kinds of sampling techniques, namely, aperiodic sampling and dynamic event-triggered sampling, are utilised. Moreover, the proportional integral (PI) strategy is utilised in the proposed algorithms. Compared with the existing distributed optimisation algorithm based on periodic sampling, the proposed algorithm dependent on aperiodic sampling is more general. Compared with the existing steady event-triggered algorithm, the distributed optimisation algorithm based on dynamic event-triggered sampling has the merit of lower energy consumption. Under the assumption that the global cost function is strongly convex about global minimum point, it is proved that the proposed algorithms solve the optimisation problem. Lyapunov stability theory is applied to give sufficient criteria guaranteeing convergence to optimal point. Finally, the effectiveness of the proposed algorithms is illustrated by numerical simulation.

关键词： distributed optimisation second-order multi-agent systems aperiodic sampling dynamic event-triggered sampling PI strategy

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