Distributed Optimization Based on a Multiagent System in the Presence of Communication Delays
TL;DR: First, the relationship between optimal solutions and the equilibrium points of the multiagent system with time delay is revealed and sufficient conditions in form of linear matrix inequality are derived for ascertaining convergence to optimal solutions, in the cases of slow-varying delay and fast-variesing delay.
Abstract: In this paper, distributed optimization is addressed based on a continuous-time multiagent system in the presence of time-varying communication delays. First, the relationship between optimal solutions and the equilibrium points of the multiagent system with time delay is revealed. Next, delay-dependent and delay-independent sufficient conditions in form of linear matrix inequality are derived for ascertaining convergence to optimal solutions, in the cases of slow-varying delay and fast-varying delay. Furthermore, a set of conditions are also obtained for the delay-free case. In addition, a sampled-data communication scheme is presented based on the conditions for the fast varying delay systems. Simulation results are presented to substantiate the theoretical results. An application for distributed parameter estimation is also given.
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TL;DR: An overview of recent advances in event-triggered consensus of MASs is provided and some in-depth analysis is made on several event- Triggered schemes, including event-based sampling schemes, model-based event-Triggered scheme, sampled-data-basedevent-trIGgered schemes), and self- triggered sampling schemes.
Abstract: Event-triggered consensus of multiagent systems (MASs) has attracted tremendous attention from both theoretical and practical perspectives due to the fact that it enables all agents eventually to reach an agreement upon a common quantity of interest while significantly alleviating utilization of communication and computation resources. This paper aims to provide an overview of recent advances in event-triggered consensus of MASs. First, a basic framework of multiagent event-triggered operational mechanisms is established. Second, representative results and methodologies reported in the literature are reviewed and some in-depth analysis is made on several event-triggered schemes, including event-based sampling schemes, model-based event-triggered schemes, sampled-data-based event-triggered schemes, and self-triggered sampling schemes. Third, two examples are outlined to show applicability of event-triggered consensus in power sharing of microgrids and formation control of multirobot systems, respectively. Finally, some challenging issues on event-triggered consensus are proposed for future research.
770 citations
Cites background from "Distributed Optimization Based on a..."
...As a fundamental problem of cooperative control of MASs, consensus has attracted an interest of researchers due to their widespread applications in various areas, such as attitude alignment of satellites [3], formation of multiple robots [4]–[6], estimation over sensor networks [7]–[11], power management in power networks [12]–[14], distributed optimization [15]–[17], and so on....
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TL;DR: This survey paper aims to offer a detailed overview of existing distributed optimization algorithms and their applications in power systems, and focuses on the application of distributed optimization in the optimal coordination of distributed energy resources.
468 citations
TL;DR: Simulation results substantiate the efficacy of the proposed method for output-feedback path-following of under-actuated autonomous underwater vehicles and prove that all error signals in the closed-loop system are uniformly and ultimately bounded.
Abstract: This paper presents a design method for output-feedback path-following control of under-actuated autonomous underwater vehicles moving in a vertical plane without using surge, heave, and pitch velocities. Specifically, an extended state observer (ESO) is developed to recover the unmeasured velocities as well as to estimate total uncertainty induced by internal model uncertainty and external disturbance. At the kinematic level, a commanded guidance law is developed based on a vertical line-of-sight guidance scheme and the observed velocities. To optimize guidance signals, optimization-based reference governors are formulated as bound-constrained quadratic programming problems for computing optimal reference signals. Two globally convergent recurrent neural networks called projection neural networks are used to solve the optimization problems in real-time. Based on the optimal reference signals and ESO, a kinetic control law with disturbance rejection capability is constructed at the kinetic level. It is proved that all error signals in the closed-loop system are uniformly and ultimately bounded. Simulation results substantiate the efficacy of the proposed method for output-feedback path-following of under-actuated autonomous underwater vehicles.
281 citations
TL;DR: It is proved that all agents with any initial state can reach output consensus at an optimal solution to the given constrained optimization problem, provided that the graph describing the communication links among agents is undirected and connected.
Abstract: This technical note presents a continuous-time multi-agent system for distributed optimization with an additive objective function composed of individual objective functions subject to bound, equality, and inequality constraints. Each individual objective function is assumed to be convex in the region defined by its local bound constraints only without the need to be globally convex. All agents in the system communicate using a proportional-integral protocol with their output information instead of state information to reduce communication bandwidth. It is proved that all agents with any initial state can reach output consensus at an optimal solution to the given constrained optimization problem, provided that the graph describing the communication links among agents is undirected and connected. It is further proved that the system with only integral protocol is also convergent to the unique optimal solution if each individual objective function is strictly convex. Simulation results are presented to substantiate the theoretical results.
236 citations
TL;DR: The results in this paper can be applicable in an unknown environment such as drone rendezvous within a required time for military purpose while optimizing local objectives and an upper bound of settling time for consensus can be estimated without dependence on initial states of agents.
Abstract: This paper deals with the problem of distributed optimization for multiagent systems by using an edge-based fixed-time consensus approach. In the case of time-invariant cost functions, a new distributed protocol is proposed to achieve the state agreement in a fixed time while the sum of local convex functions known to individual agents is minimized. In the case of time-varying cost functions, based on the new distributed protocol in the case of time-invariant cost functions, a distributed protocol is provided by taking the Hessian matrix into account. In both cases, stability conditions are derived to ensure that the distributed optimization problem is solved under both fixed and switching communication topologies. A distinctive feature of the results in this paper is that an upper bound of settling time for consensus can be estimated without dependence on initial states of agents, and thus can be made arbitrarily small through adjusting system parameters. Therefore, the results in this paper can be applicable in an unknown environment such as drone rendezvous within a required time for military purpose while optimizing local objectives. Case studies of a power output agreement for battery packages are provided to demonstrate the effectiveness of the theoretical results.
193 citations
Cites background from "Distributed Optimization Based on a..."
...Another promising direction would be combining a neurodynamic strategy [45], [46] or taking time-delay into account [47] when using the fixed-time consensus approach to achieve distributed optimization....
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References
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Book•
23 May 2011TL;DR: It is argued that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas.
Abstract: Many problems of recent interest in statistics and machine learning can be posed in the framework of convex optimization. Due to the explosion in size and complexity of modern datasets, it is increasingly important to be able to solve problems with a very large number of features or training examples. As a result, both the decentralized collection or storage of these datasets as well as accompanying distributed solution methods are either necessary or at least highly desirable. In this review, we argue that the alternating direction method of multipliers is well suited to distributed convex optimization, and in particular to large-scale problems arising in statistics, machine learning, and related areas. The method was developed in the 1970s, with roots in the 1950s, and is equivalent or closely related to many other algorithms, such as dual decomposition, the method of multipliers, Douglas–Rachford splitting, Spingarn's method of partial inverses, Dykstra's alternating projections, Bregman iterative algorithms for l1 problems, proximal methods, and others. After briefly surveying the theory and history of the algorithm, we discuss applications to a wide variety of statistical and machine learning problems of recent interest, including the lasso, sparse logistic regression, basis pursuit, covariance selection, support vector machines, and many others. We also discuss general distributed optimization, extensions to the nonconvex setting, and efficient implementation, including some details on distributed MPI and Hadoop MapReduce implementations.
17,433 citations
"Distributed Optimization Based on a..." refers background in this paper
...The parameter vector to be estimated is θ = [1, 2, 3]T....
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TL;DR: A distinctive feature of this work is to address consensus problems for networks with directed information flow by establishing a direct connection between the algebraic connectivity of the network and the performance of a linear consensus protocol.
Abstract: In this paper, we discuss consensus problems for networks of dynamic agents with fixed and switching topologies. We analyze three cases: 1) directed networks with fixed topology; 2) directed networks with switching topology; and 3) undirected networks with communication time-delays and fixed topology. We introduce two consensus protocols for networks with and without time-delays and provide a convergence analysis in all three cases. We establish a direct connection between the algebraic connectivity (or Fiedler eigenvalue) of the network and the performance (or negotiation speed) of a linear consensus protocol. This required the generalization of the notion of algebraic connectivity of undirected graphs to digraphs. It turns out that balanced digraphs play a key role in addressing average-consensus problems. We introduce disagreement functions for convergence analysis of consensus protocols. A disagreement function is a Lyapunov function for the disagreement network dynamics. We proposed a simple disagreement function that is a common Lyapunov function for the disagreement dynamics of a directed network with switching topology. A distinctive feature of this work is to address consensus problems for networks with directed information flow. We provide analytical tools that rely on algebraic graph theory, matrix theory, and control theory. Simulations are provided that demonstrate the effectiveness of our theoretical results.
11,658 citations
"Distributed Optimization Based on a..." refers background in this paper
...Lemma 1 [33]: Let L ∈ Rn×n be the Laplace matrix of weighted directed graph G, the following properties hold....
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...be found about multiagent systems in the presence of time delays (see [33]–[35]), where the impact of time delays on consensusability is extensively investigated....
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05 Mar 2007
TL;DR: A theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees is provided.
Abstract: This paper provides a theoretical framework for analysis of consensus algorithms for multi-agent networked systems with an emphasis on the role of directed information flow, robustness to changes in network topology due to link/node failures, time-delays, and performance guarantees. An overview of basic concepts of information consensus in networks and methods of convergence and performance analysis for the algorithms are provided. Our analysis framework is based on tools from matrix theory, algebraic graph theory, and control theory. We discuss the connections between consensus problems in networked dynamic systems and diverse applications including synchronization of coupled oscillators, flocking, formation control, fast consensus in small-world networks, Markov processes and gossip-based algorithms, load balancing in networks, rendezvous in space, distributed sensor fusion in sensor networks, and belief propagation. We establish direct connections between spectral and structural properties of complex networks and the speed of information diffusion of consensus algorithms. A brief introduction is provided on networked systems with nonlocal information flow that are considerably faster than distributed systems with lattice-type nearest neighbor interactions. Simulation results are presented that demonstrate the role of small-world effects on the speed of consensus algorithms and cooperative control of multivehicle formations
9,715 citations
"Distributed Optimization Based on a..." refers background in this paper
...Consensus is a popular research topic on multiagent systems (see [28]–[32] and references therein)....
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Book•
03 Mar 1993
TL;DR: The book is a solid reference for professionals as well as a useful text for students in the fields of operations research, management science, industrial engineering, applied mathematics, and also in engineering disciplines that deal with analytical optimization techniques.
Abstract: COMPREHENSIVE COVERAGE OF NONLINEAR PROGRAMMING THEORY AND ALGORITHMS, THOROUGHLY REVISED AND EXPANDED"Nonlinear Programming: Theory and Algorithms"--now in an extensively updated Third Edition--addresses the problem of optimizing an objective function in the presence of equality and inequality constraints. Many realistic problems cannot be adequately represented as a linear program owing to the nature of the nonlinearity of the objective function and/or the nonlinearity of any constraints. The "Third Edition" begins with a general introduction to nonlinear programming with illustrative examples and guidelines for model construction.Concentration on the three major parts of nonlinear programming is provided: Convex analysis with discussion of topological properties of convex sets, separation and support of convex sets, polyhedral sets, extreme points and extreme directions of polyhedral sets, and linear programmingOptimality conditions and duality with coverage of the nature, interpretation, and value of the classical Fritz John (FJ) and the Karush-Kuhn-Tucker (KKT) optimality conditions; the interrelationships between various proposed constraint qualifications; and Lagrangian duality and saddle point optimality conditionsAlgorithms and their convergence, with a presentation of algorithms for solving both unconstrained and constrained nonlinear programming problemsImportant features of the "Third Edition" include: New topics such as second interior point methods, nonconvex optimization, nondifferentiable optimization, and moreUpdated discussion and new applications in each chapterDetailed numerical examples and graphical illustrationsEssential coverage of modeling and formulating nonlinear programsSimple numerical problemsAdvanced theoretical exercisesThe book is a solid reference for professionals as well as a useful text for students in the fields of operations research, management science, industrial engineering, applied mathematics, and also in engineering disciplines that deal with analytical optimization techniques. The logical and self-contained format uniquely covers nonlinear programming techniques with a great depth of information and an abundance of valuable examples and illustrations that showcase the most current advances in nonlinear problems.
6,259 citations
"Distributed Optimization Based on a..." refers background in this paper
...In this section, some basic definitions and concepts on convex functions [36] and algebraic graph theory [37] are briefly introduced....
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TL;DR: The authors' convergence rate results explicitly characterize the tradeoff between a desired accuracy of the generated approximate optimal solutions and the number of iterations needed to achieve the accuracy.
Abstract: We study a distributed computation model for optimizing a sum of convex objective functions corresponding to multiple agents. For solving this (not necessarily smooth) optimization problem, we consider a subgradient method that is distributed among the agents. The method involves every agent minimizing his/her own objective function while exchanging information locally with other agents in the network over a time-varying topology. We provide convergence results and convergence rate estimates for the subgradient method. Our convergence rate results explicitly characterize the tradeoff between a desired accuracy of the generated approximate optimal solutions and the number of iterations needed to achieve the accuracy.
3,238 citations
"Distributed Optimization Based on a..." refers methods in this paper
...In [7], a discrete-time model using the local subgradient and convex mixture of local information with time-varying communication topology is presented for...
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