Reach a nonlinear consensus for MAS via doubly stochastic quadratic operators

This technical note addresses the new nonlinear protocol class of doubly stochastic quadratic operators (DSQOs) for coordination of consensus problem in multi-agent systems (MAS). We derive the conditions for ensuring that every agent reaches consensus on a desired rate of the group’s decision where the group decision value in its agent’s initial statuses varies. Besides that, we investigate a non-linear protocol sub-class of extreme DSQO (EDSQO) to reach a consensus for MAS to a common value with nonlinear low-complexity rules and fast time convergence if the interactions for each agent are not selfish. In addition, to extend the results to reach a consensus and to avoid the selfish case we specify a general class of DSQO for reaching a consensus under any given case of initial states. The case that MAS reach a consensus by DSQO is if each member of the agent group has positive interactions of DSQO (PDSQO) with the others. The convergence of both EDSQO and PDSQO classes is found to be directed towards the centre point. Finally, experimental simulations are given to support the analysis from theoretical aspect

Consensus by High Gegree of DeGroot model for multi-agent systems

Nonlinear distributions by the high degree of DeGroot model has been studied in this for consensus problem of multi-agent systems (MAS). The idea behind the convergence of nonlinear distribution is that when the degree of nonlinear distribution is increasing the number of iterations is in turn decreasing. From these viewpoints, the efficient aspects of the proposed nonlinearity model by high degree are that the resulting process is of fast convergence and the consensus could not depend on the kind of transition matri

Consensus of fractional nonlinear dynamics stochastic operators for multiagent systems

In this paper, we consider nonlinear models of DeGroot, quadratic stochastic operators (QSO) and doubly stochastic quadratic operators (DSQO) with fractional degree for consensus problem in multi-agent systems (MAS).By the limit behaviour of nonlinear approach, we discuss the convergence of the solutions of the models considered. The findings from the results of the carried out investigation demonstrates an efficient approach to convergence for consensus problem in MAS. The main advantages of the proposed work are i) fast convergence to consensus ii) flexible and low complexity in computation iii) ability to achieve optimal consensus. The study is built on fractional representation of 1/n where n→∞. Further, the simulation results on the related protocols are also presented

The nonlinear limit control of EDSQOs on finite dimensional simplex

Consensus problems in multi agent systems (MAS) are theoretical aspect convergence of doubly stochastic quadratic operators. This work has presented the dynamic classifications of extreme doubly stochastic quadratic operators (EDSQOs) on finite-dimensional simplex (FDS) based on the limit behaviour of the trajectories. The limit behaviour of the trajectories of EDSQOs, on FDS is either in state of convergence, or fixed or periodic. This paper aimed at examining the behaviour of these states. The paper modelled the states and proves theoretically the characteristics of each state. The results indicate that convergence operators converge to the centre (1/m), and EDSQOs point are fixed with two or more points whereas periodic states exhibit sinusoidal behaviour. This work has contributed in understanding the limit of EDSQOs of the exterior initial points as fixed and periodic points developed spread attribute toward a fixed point

Linear and nonlinear stochastic distribution for consensus problem in multi-agent systems

This paper presents a linear and nonlinear stochastic distribution for the interactions in multi-agent systems (MAS). The interactions are considered for the agents to reach a consensus using hetero-homogeneous transition stochastic matrices. The states of the agents are presented as variables sharing information in the MAS dynamically. The paper studies the interaction among agents for the attainment of consensus by limit behavior from their initial states’ trajectories. The paper provides a linear distribution of DeGroot model compared with a nonlinear distribution of change stochastic quadratic operators (CSQOs), doubly stochastic quadratic operators (DSQOs) and extreme doubly stochastic quadratic operators (EDSQOs) for a consensus problem in MAS. The comparison study is considered for stochastic matrix (SM) and doubly stochastic matrix (DSM) cases of the hetero-homogeneous transition stochastic matrices. In the case of SM, the work’s results show that the DeGroot linear model converges to the same unknown limit while CSQOs, DSQOs and EDSQOs converge to the center. However, the results show that the linear of DeGroot and nonlinear distributions of CSQOs, DSQOs and EDSQOs converge to the center with DSM. Additionally, the case of DSM is observed to converge faster compared to that of SM in the case of nonlinear distribution of CSQOs, DSQOs and EDSQOs. In general, the novelty of this study is in showing that the nonlinear stochastic distribution reaches a consensus faster than all cases. In fact, the EDSQO is a very simple system compared to other nonlinear distributions

A study of positive exponential consensus on DeGroot model

A nonlinear consensus model is assigned to resolve the consensus problem of multi-agent systems (MAS). Other studies have constructed consensus systems based on low-complexity computation linear equations or complex nonlinear equations. Linear equations are less efficient in reaching a consensus due to their slow computation process, where nonlinear equations are more efficient. The three major challenges in designing nonlinear consensus equations are: building a system of nonlinear equations that have solution, easy to calculate, and less time consuming. This study aims to create a consensus system that is nonlinear and easy to calculate. According to our survey, the DeGroot model (DGM) of 1974 is a linear model and the first effect consensus model with a flexible computation process for finite nodes. We examine if raising the exponential level for the initial cases of agents allows the system to achieve a consensus and move the DGM to a nonlinear level. The results show that by raising the exponent, the DGM is able to reach a consensus. The consensus of the DGM reaches a certain positive value that depends on the initial states of the agents and the transition matrix, whereas the consensus of the proposed exponential DGM (EDGM) reaches zero with a flexible and unrestricted matrix. Moreover, EDGM is a nonlinear model and reaches the consensus faster than the DGM linear model. The results are supported by theoretical evidence and numerical analysis

A Consensus Approach to Distributed Convex Optimization in Multi-Agent Systems

In this thesis we address the problem of distributed unconstrained convex optimization under separability assumptions, i.e., the framework where a network of agents, each endowed with local private convex cost and subject to communication constraints, wants to collaborate to compute the minimizer of the sum of the local costs. We propose a design methodology that combines average consensus algorithms and separation of time-scales ideas. This strategy is proven, under suitable hypotheses, to be globally convergent to the true minimizer. Intuitively, the procedure lets the agents distributedly compute and sequentially update an approximated Newton-Raphson direction by means of suitable average consensus ratios. We consider both a scalar and a multidimensional scenario of the Synchronous Newton-Raphson Consensus, proposing some alternative strategies which trade-off communication and computational requirements with convergence speed. We provide analytical proofs of convergence and we show with numerical simulations that the speed of convergence of this strategy is comparable with alternative optimization strategies such as the Alternating Direction Method of Multipliers, the Distributed Subgradient Method and Distributed Control Method. Moreover, we consider the convergence rates of the Synchronous Newton-Raphson Consensus and the Gradient Descent Consensus under the simplificative assumption of quadratic local cost functions. We derive sufficient conditions which guarantee the convergence of the algorithms. From these conditions we then obtain closed form expressions that can be used to tune the parameters for maximizing the rate of convergence. Despite these formulas have been derived under quadratic local cost functions assumptions, they can be used as rules-of-thumb for tuning the parameters of the algorithms. Finally, we propose an asynchronous version of the Newton-Raphson Consensus. Beside having low computational complexity, low communication requirements and being interpretable as a distributed Newton-Raphson algorithm, the technique has also the beneficial properties of requiring very little coordination and naturally supporting time-varying topologies. Again, we analytically prove that under some assumptions it shows either local or global convergence properties. Through numerical simulations we corroborate these results and we compare the performance of the Asynchronous Newton-Raphson Consensus with other distributed optimization methods

Decentralized Stochastic Optimization and Gossip Algorithms with Compressed Communication

We consider decentralized stochastic optimization with the objective function (e.g. data samples for machine learning task) being distributed over $n$ machines that can only communicate to their neighbors on a fixed communication graph. To reduce the communication bottleneck, the nodes compress (e.g. quantize or sparsify) their model updates. We cover both unbiased and biased compression operators with quality denoted by $\omega \leq 1$ ($\omega=1$ meaning no compression). We (i) propose a novel gossip-based stochastic gradient descent algorithm, CHOCO-SGD, that converges at rate $\mathcal{O}\left(1/(nT) + 1/(T \delta^2 \omega)^2\right)$ for strongly convex objectives, where $T$ denotes the number of iterations and $\delta$ the eigengap of the connectivity matrix. Despite compression quality and network connectivity affecting the higher order terms, the first term in the rate, $\mathcal{O}(1/(nT))$, is the same as for the centralized baseline with exact communication. We (ii) present a novel gossip algorithm, CHOCO-GOSSIP, for the average consensus problem that converges in time $\mathcal{O}(1/(\delta^2\omega) \log (1/\epsilon))$ for accuracy $\epsilon > 0$. This is (up to our knowledge) the first gossip algorithm that supports arbitrary compressed messages for $\omega > 0$ and still exhibits linear convergence. We (iii) show in experiments that both of our algorithms do outperform the respective state-of-the-art baselines and CHOCO-SGD can reduce communication by at least two orders of magnitudes

Wide-Area Time-Synchronized Closed-Loop Control of Power Systems And Decentralized Active Distribution Networks

The rapidly expanding power system grid infrastructure and the need to reduce the occurrence of major blackouts and prevention or hardening of systems against cyber-attacks, have led to increased interest in the improved resilience of the electrical grid. Distributed and decentralized control have been widely applied to computer science research. However, for power system applications, the real-time application of decentralized and distributed control algorithms introduce several challenges. In this dissertation, new algorithms and methods for decentralized control, protection and energy management of Wide Area Monitoring, Protection and Control (WAMPAC) and the Active Distribution Network (ADN) are developed to improve the resiliency of the power system. To evaluate the findings of this dissertation, a laboratory-scale integrated Wide WAMPAC and ADN control platform was designed and implemented. The developed platform consists of phasor measurement units (PMU), intelligent electronic devices (IED) and programmable logic controllers (PLC). On top of the designed hardware control platform, a multi-agent cyber-physical interoperability viii framework was developed for real-time verification of the developed decentralized and distributed algorithms using local wireless and Internet-based cloud communication. A novel real-time multiagent system interoperability testbed was developed to enable utility independent private microgrids standardized interoperability framework and define behavioral models for expandability and plug-and-play operation. The state-of-theart power system multiagent framework is improved by providing specific attributes and a deliberative behavior modeling capability. The proposed multi-agent framework is validated in a laboratory based testbed involving developed intelligent electronic device prototypes and actual microgrid setups. Experimental results are demonstrated for both decentralized and distributed control approaches. A new adaptive real-time protection and remedial action scheme (RAS) method using agent-based distributed communication was developed for autonomous hybrid AC/DC microgrids to increase resiliency and continuous operability after fault conditions. Unlike the conventional consecutive time delay-based overcurrent protection schemes, the developed technique defines a selectivity mechanism considering the RAS of the microgrid after fault instant based on feeder characteristics and the location of the IEDs. The experimental results showed a significant improvement in terms of resiliency of microgrids through protection using agent-based distributed communication