Optimization Problem Of Multi-agent Systems Research Articles

Differentially private distributed online optimization via push-sum one-point bandit dual averaging

This paper focuses on the distributed online optimization problem in multi-agent systems considering privacy preservation. Each agent exchanges local information with neighboring agents on the strongly connected time-varying directed graphs. Since the process of information transmission is prone to information leakage, a distributed push-sum dual averaging algorithm based on the differential privacy mechanism is proposed to protect the privacy of the data. In addition, to handle situations where the gradient information of the node cost function is unknown, the one-point gradient estimation is designed to calculate the true gradient information and guide the update of the decision variables. With the appropriate choice of the stepsizes and the exploration parameters, the algorithm can effectively protect the privacy of agents while achieving sublinear regret with the convergence rate O(T34). Furthermore, this paper also explores the effect of one-point estimation parameters on the regret in the online setting and investigates the relation between the convergence effect of individual regret and differential privacy levels. Finally, several federated learning experiments were conducted to verify the efficacy of the algorithm.

Distributed dynamic event-triggered algorithm for optimization problem with time delay.

This paper focuses on studying the optimization problem of multi-agent systems (MAS) under undirected graph. To reduce the communication frequency among agents, a zero-gradient-sum (ZGS) algorithm based on dynamic event-triggered (DET) mechanism is investigated. The event-triggered condition of each agent only uses its own state information and the neighbor's state information at the previous triggering instants, without requiring continuous state information from the neighbor. In addition, the designed algorithm allows for the sampling period to be arbitrarily large. The Lyapunov method is utilized to derive the sufficient conditions that incorporate time delay and parameters. As the event is only checked at the periodic moment, zeno behavior can be directly excluded. Finally, numerical simulations demonstrate the effectiveness of the theoretical results.

Distributed optimization for multi-agent systems with communication delays and external disturbances under a directed network

This article studies the distributed optimization problem for multi-agent systems with communication delays and external disturbances in a directed network. Firstly, a distributed optimization algorithm is proposed based on the internal model principle in which the internal model term can effectively compensate for external environmental disturbances. Secondly, the relationship between the optimal solution and the equilibrium point of the system is discussed through the properties of the Laplacian matrix and graph theory. Some sufficient conditions are derived by using the Lyapunov–Razumikhin theory, which ensures all agents asymptotically reach the optimal value of the distributed optimization problem. Moreover, an aperiodic sampled-data control protocol is proposed, which can be well transformed into the proposed time-varying delay protocol and analyzed by using the Lyapunov–Razumikhin theory. Finally, an example is given to verify the effectiveness of the results.

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

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.

Distributed Optimization Algorithms for MASs With Network Attacks: From Continuous-Time to Event-Triggered Communication

In this paper, the distributed optimization problem for multi-agent systems under the existence of cyber attacks is researched. Each agent has a private local cost function which is assumed to be continuously differentiable and strongly convex with the Lipschitz continuous gradient. The global objective function is the sum of these local cost functions, and the communication topologies among agents are balanced and directed. Unlike most multi-agent systems in the existing literature, the cyber attacks in networks, which may result in the failure of information transmission, are considered. Two novel distributed optimization algorithms with the continuous-time communication are studied for such an optimization problem. In addition, in order to reduce computation and communication consumption efficiently, we further enhance these algorithms with an event-triggered communication mechanism. Under some assumptions and restrictions on attacks, sufficient yet efficient conditions for the convergence of the proposed algorithms are derived. Furthermore, the Zeno-behavior is shown to be excluded for the event-triggered distributed optimization algorithms. Finally, some numerical simulation examples are provided to illustrate and validate the efficiency of the proposed optimization algorithms.

Sample-based Dynamic Event-triggered Algorithm for Optimization Problem of Multi-agent Systems

Sample-based Dynamic Event-triggered Algorithm for Optimization Problem of Multi-agent Systems

A distributed prescribed-time optimization analysis for multi-agent systems

This paper considers the distributed prescribed-time optimization problem of multi-agent systems (MASs). Considering the strongly convex function of time-invariant for each agent, the two-stage distributed prescribed-time optimization algorithm is designed based on the idea of zero-gradient-sum. Meanwhile, in order to save system resources, the event-triggered control mechanism is introduced into the algorithm in this paper. In the first stage, the distributed prescribed-time event-triggered algorithm is proposed to minimize the local objective functions of each agent at the prescribed-time interval. In the second stage, the algorithm is driven to optimize the global cost function while maintaining the gradient sum of all local cost functions to zero. The criteria for achieving the consensus and optimization of MASs are obtained by using Lyapunov stability theory and optimization theory. Moreover, it is proved in detail that using the two triggering functions will not result in Zeno behavior. The numerical example is given to demonstrate the correctness of the theoretical analysis and the effectiveness of the control algorithms.

Differentially private distributed optimization for multi-agent systems via the augmented Lagrangian algorithm

This paper is concerned with the private distributed optimization problem for multi-agent systems, where all agents cooperatively minimize the sum of individual convex objective functions with the additional requirement that the functions remain differential privacy. Based on the augmented Lagrangian algorithm, an effective distributed algorithm is presented to ensure the privacy by perturbing primal estimates with additive Laplace noises. The proposed algorithm is more likely to have a faster convergence rate compared to the primal-based algorithms, and has less computational burden contrast with the ADMM-based private algorithms. By means of an important factorization of weighted Laplacian matrix, it is proven that the error between optimal solution and ergodic average estimates is bounded, which is related to the privacy level. Within this framework, trade-offs between privacy level and convergence accuracy are analyzed. Finally the effectiveness of the proposed algorithm is illustrated by numerical examples.

Finite-time Distributed ConvexOptimization with Zero-Gradient-Sum Algorithms

This article considers the distributed finite-time optimization problem of multi-agent systems within the Zero-Gradient-Sum (ZGS) framework. We employ a distributed algorithm to drive the estimate of each agent to converge to the optimal solution of the global objective function, the sum of the local objectives. In a general case with non-quadratic local functions, we can obtain a finite-time convergence. Furthermore, when all the local cost functions are quadratic, the proposed algorithm can achieve a fixed-time result such that the upper bound of settling time can be estimated regardless of the initial conditions. Considering that the communication network may be affected by some external disturbances, we also extend to consider the case with switching topologies. Finally, the algorithms are demonstrated via an example simulation.

Random Gradient-Free Optimization for Multiagent Systems With Communication Noises Under a Time-Varying Weight Balanced Digraph

In this paper, we focus on a constrained convex optimization problem of multiagent systems under a time-varying topology. In such topology, it is not only B-strongly connected, but the communication noises are also existent. Each agent has access to its local cost function, which is a nonsmooth function. A gradient-free random protocol is come up with minimizing a sum of cost functions of all agents, which are projected to local constraint sets. First, considering the stochastic disturbances in the communication channels among agents, the upper bounds of disagreement estimate of agents’ states are obtained. Second, a sufficient condition on choosing step sizes and smoothing parameters is derived to guarantee that all agents almost surely converge to the stationary optimal point. At last, a numerical example and a comparison are provided to illustrate the feasibility of the random gradient-free algorithm.

Distributed Optimization With Nonconvex Velocity Constraints, Nonuniform Position Constraints, and Nonuniform Stepsizes

This note is devoted to the distributed optimization problem of multi-agent systems with nonconvex velocity constraints, nonuniform position constraints and nonuniform stepsizes. Two distributed constrained algorithms with nonconvex velocity constraints and nonuniform stepsizes are proposed in the absence and the presence of nonuniform position constraints by introducing a switching mechanism to guarantee all agents' position states to remain in a bounded region. The algorithm gains need not to be predesigned and can be selected by each agent using its own and neighbours' information. By a model transformation, the original nonlinear time-varying system is converted into a linear time-varying one with a nonlinear error term. Based on the properties of stochastic matrices, it is shown that the optimization problem can be solved as long as the communication topologies are jointly strongly connected and balanced. Numerical examples are given to show the obtained theoretical results.

Distributed optimal consensus algorithms in multi-agent systems

This paper investigates the distributed optimal consensus problem by designing the multi-agent communication systems, where each agent has local access to its own strongly convex utility function. Here, we design two distributed consensus-based optimization algorithms to tackle the optimization problem of multi-agent systems. One is the second-order optimization consensus algorithm, and another is the third-order algorithm. Moreover, the two algorithms can ensure that all agents achieve consensus at a common state which minimizes the sum of the objective function under the assumption that interaction graph is strongly connected and detailed balanced. For each of the proposed algorithms, it can be found that the equilibrium point of the algorithm is the optimal point and it is proved to be asymptotically stable under given conditions. Finally, the performance of the proposed algorithms are verified by two simulations based on an IEEE 14-bus test system and an IEEE 57-bus test system.

Distributed constrained optimization for multi-agent networks with nonsmooth objective functions

This paper investigates the distributed constrained optimization problem in multi-agent systems, where agents cooperatively minimize an objective function being the sum of each agent’s objective function while meeting equality and inequality constraints. By virtue of nonsmooth analysis and graph theory, a novel distributed continuous-time algorithm is proposed to solve such a kind of optimization problems. Different from existing continuous-time results relying on the differentiability or strict (strong) convexity of local objective functions, the proposed approach considers more general local objective functions which are only convex and not necessarily smooth. In addition, the proposed approach considers more general local constraints, not just box constraints considered in most existing studies. The optimality of the proposed algorithm is ensured under certain initial condition. Based on set-valued LaSalle invariance principle, the convergence of the proposed scheme is rigorously proved. Finally, simulation examples are applied to validate the effectiveness of the proposed algorithm.

Distributed optimization of multi-agent systems with delayed sampled-data

Abstract In this paper, we study the distributed optimization problem of multi-agent systems with delayed sampled-data, where the interconnected topology is directed, weighted-balanced and strongly connected, and also local cost functions are strongly convex with globally Lipschitz gradients. Based on synchronous and asynchronous sampled-data, we construct two respective algorithms. Our main results, sufficient conditions for the convergence to an optimal solution, are obtained under assumption that all design parameters are chosen properly. We also present one example to validate our theoretical results.

Distributed event-triggered scheme for a convex optimization problem in multi-agent systems

Abstract In this paper, a distributed event-triggered algorithm was proposed to solve a convex quadratic optimization problem of multi-agent systems under undirected and connected topologies. The event-triggered condition of each agent just requires its own state value and the state values of its neighbors at the triggering time, and hence the continuous communication and calculation are not required. Moreover, the minimum event-triggered interval is bounded by the sampling time and the Zeno behavior is therefore naturally avoided. The result is also extended to the networks with undirected and switching topologies. Numerical simulations show the effectiveness of the proposed approach.

Sampled-data based distributed convex optimization with event-triggered communication

This paper studies the distributed convex optimization problem for multi-agent systems over undirected and connected networks. Motivated by practical considerations, we propose a new distributed optimization algorithm with event-triggered communication. The proposed event detection is decentralized, sampled-data and not requires periodic communications among agents to calculate the threshold. Based on Lyapunov approaches, we show that the proposed algorithm is asymptotically converge to the unknown optimizer if the design parameters are chosen properly. We also give an upper bound on the convergence rate. Finally, we illustrate the effectiveness of the proposed algorithm by a numerical simulation.

A game theoretic approach for the distributed control of multi-agent systems under directed and time-varying topology

This paper presents a new game theory based method to control multi-agent systems under directed and time varying interaction topology. First, the sensing/communication matrix is introduced to cope with information sharing among agents, and to provide the minimal information requirement which ensures the system level objective is desirable. Second, different from traditional methods of controlling multi-agent systems, non-cooperative games are investigated to enforce agents to make rational decisions. And a new game model, termed stochastic weakly acyclic game, is developed to capture the optimal solution to the distributed optimization problem for multi-agent systems with directed topology. It is worth noting that the system level objective can be achieved at the points of the corresponding equilibriums of the new game model. The proposed method is illustrated with an example in smart grid where multiple distributed generators are controlled to reach the fair power utilization profile in the game formulation to ensure the aggregated power output are optimal.

Dynamic optimization for multi-agent systems with external disturbances

This paper studies the dynamic optimization problem for multi-agent systems in the presence of external disturbances. Different from the existing distributed optimization results, we formulate an optimization problem of continuous-time multi-agent systems with time-varying disturbance generated by an exosystem. Based on internal model and Lyapunov-based method, a distributed design is proposed to achieve the optimization. Finally, an example is given to illustrate the proposed optimization design.