Optimal Consensus Research Articles

Leveraging Blockchain for Multi-Operator Access Sharing Management in Internet of Vehicles

Wireless service providers (WSPs) are seeking cooperation to share both resources (spectrum, infrastructures) and costs. In particular, cooperation is critical for vehicle-to-everything (V2X) applications that value quality-of-service foremost. However, cooperation is inefficient without strong trust bases. Recently, blockchain arises as a promising solution to decentralized trust, owing to its transparency and immutability. Therefore, we propose a WSP cooperation framework based on blockchain, which keeps a shared ledger on resource utilization. In this paper, we first study the WSP selection problem of vehicles by evolutionary game. Then, we make the blockchain public to vehicles to maintain its decentralization and enhance its security by crowdsourcing idle computing resources from vehicles. To deal with the mobility of vehicles, as well as to improve the consensus efficiency, we propose delegated proof-of-work (DPoW) scheme, which introduces delegate nodes for participating in the blockchain consensus on behalf of the vehicles. The alternating direction method of multipliers (ADMM) optimization framework is further used to derive optimal consensus parameters including block size, computing resource demand of delegate nodes, and prices paid for vehicles. We conduct extensive simulations to show the effectiveness of the proposed methods.

Distributed Optimization of High-Order Nonlinear Systems: Saving Computation and Communication via Prefiltering

This brief investigates a distributed optimization problem for high-order strict-feedback nonlinear multiagent systems. A virtual system is built for each agent using a distributed proportional-integral (PI) optimization algorithm to estimate the global optimal solution online. The estimate is then input into a prefilter to generate an alternative estimate and its high-order derivatives. Based on these signals, a backstepping controller is used to make the actual system track the alternative estimate asymptotically, which thereby realizes exact global consensus optimization. Compared to the existing result, the proposed algorithm is fully distributed under undirected topologies with much weaker assumptions on local and global objective functions, lower computation and communication cost. Exact global optimal consensus can also be reached in the cases with directed topologies and intermittent communications. The effectiveness of the method is verified by simulations.

Optimal output consensus of second‐order uncertain nonlinear systems on weight‐unbalanced directed networks

AbstractThis article investigates the distributed optimal output consensus problem of second‐order uncertain nonlinear multiagent systems over weight‐unbalanced directed networks. Under the standard assumption that local cost functions are strongly convex with globally Lipschitz gradients, a novel distributed dynamic state feedback controller is developed such that the outputs of all the agents reach the optimal solution to minimize the global cost function which is the sum of all the local cost functions. The controller design is based on a two‐layer strategy, where a distributed optimal coordinator and a reference‐tracking controller are proposed to address the challenges arising from unbalanced directed networks and uncertain nonlinear functions respectively. A key feature of the proposed controller is that the nonlinear functions containing the uncertainties and disturbances are not required to be globally Lipschitz. Furthermore, by exploiting adaptive control technique, no prior knowledge of the uncertainties or disturbances is required either. Two simulation examples are finally provided to illustrate the effectiveness of the proposed control scheme.

Model-Free distributed optimal consensus control of nonlinear multi-agent systems: A graphical game approach

In this paper, the optimal consensus control problem of nonlinear multi-agent systems(MASs) with completely unknown dynamics is considered. The problem is formulated in a differential graphical game approach which can be solved by Hamilton-Jacobi (HJ) equations. The main difficulty in solving the HJ equations lies in the nonlinear coupling between equations. Based on the Adaptive Dynamic Programming (ADP) technique, an VI-PI mixed HDP algorithm is proposed to solve the HJ equations distributedly. With the PI step, a suitable iterative initial value can be obtained according to the initial policies. Then, VI steps are run to get the optimal solution with exponential convergence rate. Neural networks (NNs) are applied to approximate the value functions, which makes the data-driven end-to-end learning possible. A numerical simulation is conducted to show the effectiveness of the proposed algorithm.

Distributed optimization for a class of uncertain nonlinear multi‐agent systems with arbitrary relative degree subject to exogenous disturbances

AbstractThis paper studies the distributed optimization problem on the framework of a class of arbitrary relative degree uncertain nonlinear multi‐agent systems with the presence of exogenous disturbances. Based on the internal model principle and the pseudo gradient approach, a novel continuous‐time distributed optimization control protocol is proposed to make all the agents reach optimal consensus by utilizing local cost functions information and neighbors' states information. The main advantage of our algorithm is that it can run on systems with more complex dynamics, while the existing algorithms apply only to integral‐type systems or unity relative degree nonlinear systems. Moreover, the convergence of the algorithm is proved by Lyapunov function and graph theory analysis. Finally, the distributed protocol is physically implemented by circuits and tested on a group of Chua's circuit systems to show the effectiveness of the theoretical results.

Optimal obstacle avoidance consensus formation control method for fixed-wing UAV with variable topology

Optimal obstacle avoidance consensus formation control method for fixed-wing UAV with variable topology

Optimal consensus model-free control for multi-agent systems subject to input delays and switching topologies

In this paper, the optimal consensus control problem of the discrete-time multi-agent systems with switching topologies and input delays is investigated by adopting the adaptive dynamic programming method. Through introducing a new state variable, the original input-delayed system can be transformed into a delay-free one. Then, a novel local performance index function is designed for each agent to eliminate the impact of switching topologies, which does not explicitly rely on the information of neighbors. Based on Bellman optimality principle, Lyapunov stability theorem and deep reinforcement learning method, the stability of the error system and the optimality of the value function are proved. In order to solve the consensus problem of the unknown systems, we propose a new value iteration algorithm based on the input and output data of the system, which can not only guarantee the achievement of consensus but also minimize the performance index function. Finally, two numerical simulations based on actor-critic neural networks are given, including the following two cases: periodic switching topologies and Markov switching topologies, to verify the effectiveness of the proposed optimal control scheme.

Optimal Leader-Following Consensus Control of Fractional-Order Multi-Agent Systems Based on the Actor-Critic Algorithm

Aimed at the optimal leader-following consensus problem of fractional-order multi-agent systems, an reinforcement learning strategy was designed based on the intermittent event trigger. With the periodic intermittent strategy as the basic mechanism, the event trigger and the actor-critic algorithm in reinforcement learning were organically integrated. According to the 1st-order approximation of the fractional differential, the reinforcement learning algorithm structure based on the periodic intermittent event trigger strategy was proposed. Finally, the feasibility and effectiveness of the algorithm was proved through numerical simulation experiments.

Optimal Consensus Control Models on the Sphere

Optimal Consensus Control Models on the Sphere

Event‐Triggered Adaptive Dynamic Programming Consensus Tracking Control for Discrete‐Time Multiagent Systems

This paper proposes a novel adaptive dynamic programming (ADP) approach to address the optimal consensus control problem for discrete‐time multiagent systems (MASs). Compared with the traditional optimal control algorithms for MASs, the proposed algorithm is designed on the basis of the event‐triggered scheme which can save the communication and computation resources. First, the consensus tracking problem is transferred into the input‐state stable (ISS) problem. Based on this, the event‐triggered condition for each agent is designed and the event‐triggered ADP is presented. Second, neural networks are introduced to simplify the application of the proposed algorithm. Third, the stability analysis of the MASs under the event‐triggered conditions is provided and the estimate errors of the neural networks’ weights are also proved to be ultimately uniformly bounded. Finally, the simulation results demonstrate the effectiveness of the event‐triggered ADP consensus control method.

Lightweight Direct Acyclic Graph Blockchain for Enhancing Resource-Constrained IoT Environment

Blockchain technology is regarded as the emergent security solution for many applications related to the Internet of Things (<i>IoT</i>). In concept, blockchain has a linear structure that grows with the number of transactions entered. This growth in size is the main obstacle to the blockchain, which makes it unsuitable for resource-constrained IoT environments. Moreover, conventional consensus algorithms such as PoW, PoS are very computationally heavy. This paper solves these problems by introducing a new lightweight blockchain structure and lightweight consensus algorithm. The Multi-Zone Direct Acyclic Graph (DAG) Blockchain (<i>Multizone-DAG-Blockchain</i>) framework is proposed for the fog-based IoT environment. In this context, fog computing technology is integrated with the IoT to offload IoT tasks to the fog nodes, thus preserving the energy consumption of the IoT devices. Both IoT and fog nodes are initially authenticated using a non-cloneable physical function- based validation mechanism (<i>DPUF-VM</i>) in which multiple authentication certificates are verified in the blockchain. Each transaction is stored in a hash function in the blockchain using the lightweight CubeHash algorithm and signed by the Four-Q- Curve algorithm. In the cloud, sensitive data is stored as ciphertext. Fog nodes provide data security to avoid the energy consumption and complexity of IoT nodes. The fog node first performs a redundancy analysis using the Jaccard Similarity (JS) measure and sensitivity analysis using the Neutrosophic Neural Intelligent Network (<i>N2IN</i>) algorithm. A lightweight proof-of-authentication (<i>PoAh</i>) algorithm is presented and executed by the optimal consensus node selected by the bi- objective spiral optimization (<i>BoSo</i>) algorithm for transaction validation. The proposed work is modeled in Network Simulator 3.26 (ns-3.26), and the performance is evaluated in terms of energy consumption, storage cost, response time, and throughput.

Bayesian Imputation with Optimal Look-Ahead-Bias and Variance Tradeoff

Missing time-series data is a prevalent problem in finance. Imputation methods for time-series data are usually applied to the full panel data with the purpose of training a model for a downstream out-of-sample task. For example, the imputation of missing returns may be applied prior to estimating a portfolio optimization model. However, this practice can result in a look-ahead-bias in the future performance of the downstream task. There is an inherent trade-off between the look-ahead-bias of using the full data set for imputation and the larger variance in the imputation from using only the training data. By connecting layers of information revealed in time, we propose a Bayesian consensus posterior that fuses an arbitrary number of posteriors to optimally control the variance and look-ahead-bias trade-off in the imputation. We derive tractable two-step optimization procedures for finding the optimal consensus posterior, with Kullback-Leibler divergence and Wasserstein distance as the measure of dissimilarity between posterior distributions. We demonstrate in simulations and an empirical study the benefit of our imputation mechanism for portfolio optimization with missing returns.

Optimal Design for an On-Wall Mounted Loudspeaker

The increased number of Internet services and the exposure of the personal information to the public network, create a problem with the privacy of the personal data. This problem is extremely impactful in the healthcare systems where the sensitive medical data circulate in the network. The emerging Blockchain technologies offer properties and tools for better personal data access management. The integration of the Blockchain technologies into the healthcare systems can provide better data privacy. However, beside the attractive properties, the current Blockchain technologies cannot achieve sufficient scalability to serve a global public healthcare system and cannot provide compatibility with the GDPR and HIPAA regulations. To overcome these limitations, this paper introduces new deducted Blockchain-based public healthcare system, the BloHeS, with main focus on several functional entities, such as optimal consensus mechanism, better storage organization, improved network organization and compatibility with GDPR and HIPAA regulations. It also defines a procedure for patient-centric data access management, protocols for Island management and new block structure.

A Hessian Inversion-Free Exact Second Order Method for Distributed Consensus Optimization

We consider a standard distributed consensus optimization problem where a set of agents connected over an undirected network minimize the sum of their individual (local) strongly convex costs. Alternating Direction Method of Multipliers (ADMM) and Proximal Method of Multipliers (PMM) have been proved to be effective frameworks for design of exact distributed second order methods (involving calculation of local cost Hessians). However, existing methods involve explicit calculation of local Hessian inverses at each iteration that may be very costly when the dimension of the optimization variable is large. In this article, we develop a novel method, termed Inexact Newton method for Distributed Optimization (INDO), that alleviates the need for Hessian inverse calculation. INDO follows the PMM framework but, unlike existing work, approximates the Newton direction through a generic fixed point method (e.g., Jacobi Overrelaxation) that does not involve Hessian inverses. We prove exact global linear convergence of INDO and provide analytical studies on how the degree of inexactness in the Newton direction calculation affects the overall method's convergence factor. Numerical experiments on several real data sets demonstrate that INDO's speed is on par (or better) as state of the art methods iteration-wise, hence having a comparable communication cost. At the same time, for sufficiently large optimization problem dimensions <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> (even at <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"><tex-math notation="LaTeX">$n$</tex-math></inline-formula> on the order of couple of hundreds), INDO achieves savings in computational cost by at least an order of magnitude.

Robust Decentralized Learning Using ADMM With Unreliable Agents

Many signal processing and machine learning problems can be formulated as consensus optimization problems which can be solved efficiently via a cooperative multi-agent system. However, the agents in the system can be unreliable due to a variety of reasons: noise, faults and attacks. Providing erroneous updates leads the optimization process in a wrong direction, and degrades the performance of distributed machine learning algorithms. This paper considers the problem of decentralized learning using ADMM in the presence of unreliable agents. First, we rigorously analyze the effect of erroneous updates (in ADMM learning iterations) on the convergence behavior of multi-agent system. We show that the algorithm linearly converges to a neighborhood of the optimal solution under certain conditions and characterize the neighborhood size analytically. Next, we provide guidelines for network design to achieve a faster convergence to the neighborhood. We also provide conditions on the erroneous updates for exact convergence to the optimal solution. Finally, to mitigate the influence of unreliable agents, we propose ROAD, a robust variant of ADMM, and show its resilience to unreliable agents with an exact convergence to the optimum.

Distributed Kalman Filters With Random Sensor Activation and Noisy Channels

This paper studies distributed Kalman filtering problems for sensor networks with random sensor activation and noisy channels. Each sensor measures the target state with a random activation and receives state estimates of its neighbor nodes. Communication noises are considered in communication links between sensors and their neighbor nodes. Considering cross-covariance matrices between sensors, an optimal distributed Kalman filter (ODKF) with a given recursive structure is proposed for each sensor, which depends on the knowledge whether a sensor itself is activated to measure the target state or not and whose filter gains and covariance matrices depend on random activation rate of the sensor. In the ODKF algorithm, optimal Kalman filter gain for each sensor and different optimal consensus filter gains for state estimates of its neighbor nodes are designed in the linear unbiased minimum variance (LUMV) sense. To reduce computational cost, a suboptimal distributed Kalman filter (SDKF) is also presented by considering a locally minimum upper bound of the filtering error covariance matrix, where the calculation of cross-covariance matrices among sensor nodes is avoided. The stability and steady-state property of the proposed ODKF and SDKF algorithms are explored. Finally, the proposed methods are also extended to the nonlinear scenarios. Simulation examples show the effectiveness of the proposed algorithms.

Optimal consensus for uncertain high‐order multi‐agent systems by output feedback

AbstractThe distributed optimal output consensus problem for high‐order multi‐agent systems has been studied recently. In this article, we further focus on the same problem for high‐order multi‐agent systems subject to parametric uncertainties and aim at distributed robust controllers by measurement output feedback. We first develop a dynamic compensator to estimate the expected optimal consensus point and convert the problem into several decentralized robust tracking problems. Then, by combining the integral control technique and dirty derivative observer technique, we constructively propose a distributed output feedback integral controller to solve this problem under a mild graph connectivity condition.

A numerical study of 21-cm signal suppression and noise increase in direction-dependent calibration of LOFAR data

ABSTRACT We investigate systematic effects in direction-dependent gain calibration in the context of the Low-Frequency Array (LOFAR) 21-cm Epoch of Reionization (EoR) experiment. The LOFAR EoR Key Science Project aims to detect the 21-cm signal of neutral hydrogen on interferometric baselines of 50–250 λ. We show that suppression of faint signals can effectively be avoided by calibrating these short baselines using only the longer baselines. However, this approach causes an excess variance on the short baselines due to small gain errors induced by overfitting during calibration. We apply a regularized expectation–maximization algorithm with consensus optimization (sagecal-co) to real data with simulated signals to show that overfitting can be largely mitigated by penalising spectrally non-smooth gain solutions during calibration. This reduces the excess power with about a factor of 4 in the simulations. Our results agree with earlier theoretical analysis of this bias-variance trade off and support the gain-calibration approach to the LOFAR 21-cm signal data.

Distributed decision-coupled constrained optimization via Proximal-Tracking

In this paper we deal with decision-coupled problems involving multiple agents over a network. Each agent has its own local objective function and local constraints, and all agents aim at finding the value of a common decision vector that minimizes the sum of all agents’ cost functions and satisfies all local constraints. To this purpose, we introduce a Proximal-Tracking distributed optimization algorithm that integrates dynamic average consensus within the proximal minimization method. Convergence to an optimal consensus solution is guaranteed for any value of a constant penalty parameter, under a convexity assumption only, without requiring differentiability, Lipschitz continuity, or smoothness of the local objective functions. Numerical simulations show the effectiveness of the proposed scheme.

Adaptive neural inverse optimal tracking control for uncertain multi-agent systems

An adaptive neural inverse optimal consensus control method is presented for a class of multi-agent systems (MASs) with uncertain dynamics and time-varying disturbance. The auxiliary system is constructed for every agent, and then, based on backstepping technique, neural networks are utilized to approximate the unknown function and develop the distributed controllers. Additionally, there is only one unknown parameter need to be learned for each agent. It is proved that the proposed control scheme can ensure that all states of MASs are bounded and each agent is Input-to-state stabilizable (ISS). In the meantime, the inverse optimal controller also minimizes a meaningful cost function given in advance, which contains system input and disturbance. That is, the control scheme also reduces the cost of input. Simulation experiments illustrate the feasibility of the proposed method.