This paper is mainly devoted to the distributed second-order multi-agent optimization problem with unbalanced and directed networks, where the gradient of the private objective functions might be unbounded. To deal wi...
详细信息
This paper is mainly devoted to the distributed second-order multi-agent optimization problem with unbalanced and directed networks, where the gradient of the private objective functions might be unbounded. To deal with this problem, a new distributed algorithm is proposed based on the local neighbor information and the private objective functions. By a coordination transformation, the closed-loop system is divided into two simple first order subsystems. Under the assumption of the strong connectivity of networks, it is proved that all agents can collaboratively converge to some optimal solution of the team objective function. At last, we give two numerical examples to show the effectiveness of our proposed algorithm. (c) 2021 Elsevier Inc. All rights reserved.
This paper investigates a distributed optimization problem for heterogeneous linear multi-agent systems with uncertain parameters and external disturbances. For each agent, the optimal solution of the global objective...
详细信息
This paper investigates a distributed optimization problem for heterogeneous linear multi-agent systems with uncertain parameters and external disturbances. For each agent, the optimal solution of the global objective functions can be regarded as an unknown constant reference signal. From this angle, the problem is transformed into an output regulation problem for an exosystem whose states and outputs are to be estimated. To ensure the trackability of the estimated signal, a fundamental design condition for the exosystem observer to achieve robust output regulation is given in the context of internal model control. Exact global optimization is then realized by embedding an appropriate distributed optimization algorithm (i.e., the exosystem observer) in each agent to estimate the global optimal solution. The result for exosystem observer design is extended to yield an adaptive fault-tolerant control algorithm to deal with a class of practical actuator fault uncertainties. The exosystem observer-based output regulation method provides a general distributed robust optimization framework for uncertain systems with disturbances and actuator faults, which can directly apply to various consensus problems. Simulations are provided to illustrate the effectiveness of the method.
There has been an increasing necessity for scalable optimization methods, especially due to the explosion in the size of data sets and model complexity in modern machine learning applications. Scalable solvers often d...
详细信息
There has been an increasing necessity for scalable optimization methods, especially due to the explosion in the size of data sets and model complexity in modern machine learning applications. Scalable solvers often distribute the computation over a network of processing units. For simple algorithms, such as gradient descent, the dependence of the convergence time with the topology of this network is well known. However, for more involved algorithms, such as the alternating direction method of multipliers (ADMM), much less is known. At the heart of many distributed optimization algorithms, there exists a gossip subroutine which averages local information over the network, whose efficiency is crucial for the overall performance of the method. In this article, we review recent research in this area, and with the goal of isolating such a communication exchange behavior, we compare different algorithms when applied to a canonical distributed averaging consensus problem. We also show interesting connections between ADMM and the lifted Markov chains besides providing an explicit characterization of its convergence and optimal parameter tuning in terms of spectral properties of the network. Finally, we empirically study the connection between network topology and convergence rates for different algorithms on a real-world problem of sensor localization.
We study strongly convex distributed optimization problems where a set of agents are interested in solving a separable optimization problem collaboratively. In this article, we propose and study a two-time-scale decen...
详细信息
We study strongly convex distributed optimization problems where a set of agents are interested in solving a separable optimization problem collaboratively. In this article, we propose and study a two-time-scale decentralized gradient descent algorithm for a broad class of lossy sharing of information over time-varying graphs. One time-scale fades out the (lossy) incoming information from neighboring agents, and one time-scale regulates the local loss functions' gradients. We show that assuming a proper choice of step-size sequences, certain connectivity conditions, and bounded gradients along the trajectory of the dynamics, the agents' estimates converge to the optimal solution with the rate of O(T-1/2). We also provide novel tools to study distributed optimization with diminishing averaging weights over time-varying graphs.
作者:
Zeng, XianlinChen, JieHong, YiguangBeijing Inst Technol
Sch Automat Key Lab Intelligent Control & Decis Complex Syst Beijing 100081 Peoples R China Beijing Inst Technol
Minist Educ Key Lab Biomimet Robots & Syst Beijing Adv Innovat Ctr Intelligent Robots & Syst Beijing 100081 Peoples R China Tongji Univ
Shanghai Res Inst Intelligent Autonomous Syst Dept Control Sci & Engn Shanghai 200092 Peoples R China Chinese Acad Sci
Acad Math & Syst Sci Key Lab Syst & Control Beijing 100190 Peoples R China Univ Chinese Acad Sci
Sch Math Sci Beijing 100190 Peoples R China
This article proposes a distributed optimization design to compute continuous-time algebraic Riccati inequalities (ARIs), where the information of matrices is distributed among agents. We propose a design procedure to...
详细信息
This article proposes a distributed optimization design to compute continuous-time algebraic Riccati inequalities (ARIs), where the information of matrices is distributed among agents. We propose a design procedure to tackle the nonlinearity, the inequality, and the coupled information structure of ARI;then, we design a distributed algorithm based on an optimization approach and analyze its convergence properties. The proposed algorithm is able to verify whether ARI is feasible in a distributed way and converges to a solution if ARI is feasible for any initial condition.
Dynamic coverage is one of the fundamental problems in multi-agent systems (MASs), and is related to optimal placement of nodes to observe a physical space. In a typical coverage problem, a set of targets are required...
详细信息
Dynamic coverage is one of the fundamental problems in multi-agent systems (MASs), and is related to optimal placement of nodes to observe a physical space. In a typical coverage problem, a set of targets are required to be monitored. The problem becomes more challenging when the targets are allowed to move as well. Efficient coverage control by mobile agents in a specific area poses many challenges, such as optimal coverage of all targets, dynamic redeployment of agents as targets change their location, trajectory control of each agent during redeployment and determining the number of mobile agents to cover specific targets. In particular, for dynamic coverage problems, agents are deployed to provide coverage to the mobile targets and the agents dynamically redeploy themselves in such a way that they provide maximum coverage to targets not only when they are stationary but also when they are in motion. In many scenarios, such as disaster recovery or public event coverage, dynamic behavior of agents to reach to the next optimal position, plays an important role in determining the performance of the system. In this paper, we propose an augmented Lagrangian based algorithm, which provides a mechanism to control the trajectory of agents to reach the optimal position. By adjusting the gain parameters of the proposed algorithm, we achieve negligible overshoot in response to fast dynamics that is not possible by using conventional Lagrangian. Also, the proposed algorithm is close to the optimal trajectory. Thus, by using the proposed algorithm, we can improve the dynamic performance without compromising the optimal deployment of the agents. The numerical evaluation results show significant improvement in dynamic performance for an example scenario of an MAS.
This paper deals with the problem of distributed optimization of a multiagent system with network connectivity preservation. In order to realize cooperative interactions, a connected network is the prerequisite for hi...
详细信息
This paper deals with the problem of distributed optimization of a multiagent system with network connectivity preservation. In order to realize cooperative interactions, a connected network is the prerequisite for high-quality information exchange among agents. However, sensing or communication capability is range-limited, so it is impractical to simply make an assumption that network connectivity is preserved by default. To address this concern, a class of generalized potentials including discontinuities caused by unexpected obstacles or noises are designed. For a class of quadratic cost functions, based on the potentials, a new distributed protocol is proposed to formally guarantee the network connectivity over time and to realize the state agreement in finite time while the sum of local functions known to individual agents is optimized. Since the right-hand side of the proposed protocol is discontinuous, some nonsmooth analysis tools are applied to analyze system performance. In some practical scenarios, where initial states are unavailable, a distributed protocol is further developed to realize the consensus in a prescribed finite time while solving the distributed optimization problem and maintaining network connectivity. Illustrative examples are provided to demonstrate the effectiveness of the proposed protocols.
The distributed optimization algorithms using consensus control are proposed for solving multi-agent optimization problems. The multi-agent optimization problem has discrete and continuous decision variables to minimi...
详细信息
The distributed optimization algorithms using consensus control are proposed for solving multi-agent optimization problems. The multi-agent optimization problem has discrete and continuous decision variables to minimize the sum of local cost functions with local and global constraints. The problem is formulated as a mixed integer programming problem. In this study, we propose two distributed optimization algorithms to solve the problem. A feasible solution is obtained by solving the continuous optimization problem using an existing distributed optimization method with consensus control and solving the discrete optimization problem by fixing 0-1 variables. In the proposed method 1, all possible combinations of a binary variables are searched. Since all combinations are searched, the exact optimal solution can be obtained. However, it is difficult to apply to largescale problems. In the proposed method 2, we derive the solution of binary variables by using Lagrangian decomposition and coordination approach. The proposed method 2 can provide approximate solutions for more complex problems within a practical computation time. These methods are successfully implemented to obtain near-optimal solutions in a distributed environment for supply chain planning problems for multiple companies and multi-agent unit commitment problem. The number of information exchanges in the two proposed methods is evaluated. The information exchange for these methods can significantly reduce the data exchange compared with the conventional centralized optimization method. Computational experiments for the multi-agent unit commitment problems and supply chain planning problems for multiple companies demonstrate the effectiveness of the proposed methods.
This paper studies the distributed optimization problem for continuous-time multiagent systems with general linear dynamics. The objective is to cooperatively optimize a team performance function formed by a sum of co...
详细信息
This paper studies the distributed optimization problem for continuous-time multiagent systems with general linear dynamics. The objective is to cooperatively optimize a team performance function formed by a sum of convex local objective functions. Each agent utilizes only local interaction and the gradient of its own local objective function. To achieve the cooperative goal, a couple of fully distributed optimal algorithms are designed. First, an edge-based adaptive algorithm is developed for linear multiagent systems with a class of convex local objective functions. Then, a node-based adaptive algorithm is constructed to solve the distributed optimization problem for a class of agents satisfying the bounded-input bounded-state stable property. Sufficient conditions are given to ensure that all agents reach a consensus while minimizing the team performance function. Finally, numerical examples are provided to illustrate the theoretical results.
暂无评论