Optimal Consensus Research Articles

Robust Longitudinal Distributed Model Predictive Control of Connected and Automated Vehicles With Coupled Safety Constraints

This paper deals with robust cooperative control of connected and automated vehicles (CAVs) with special consideration of the coupled safety inter-vehicle distance constraints. To address the hard constraints caused by the vehicle physical limitations and the coupled safety constraints among adjacent vehicles explicitly, the distributed model predictive control (DMPC) problem for CAVs is formulated. By virtue of the Lagrangian multiplier method and the dual decomposition technique, the DMPC problem subject to coupled constraints is recast into a distributed dual variable consensus optimization problem comprised of a series of subsystems with local copies of the dual variables, which is then cooperatively solved in parallel based on the alternating direction method of multiplier (ADMM) under the distributed information exchange mechanism. In addition, the disturbance is dynamically mitigated by the feedback control, and its influence on the vehicle status is quantified by the associated robust positively invariant set. Robust cooperative control protocols are proposed to regulate the cooperative operations of CAVs, and the recursive feasibility and the closed-loop stability are theoretically proved. Numerical experiments are carried out to illustrate the effectiveness of the proposed method.

Push-LSVRG-UP: Distributed Stochastic Optimization Over Unbalanced Directed Networks With Uncoordinated Triggered Probabilities

Distributed stochastic optimization, arising in the crossing and integration of traditional stochastic optimization, distributed computing and storage, and network science, has advantages of high efficiency and a low per-iteration computational complexity in resolving large-scale optimization problems. This paper concentrates on resolving a large-scale convex finite-sum optimization problem in a multi-agent system over unbalanced directed networks. To tackle this problem in an efficient way, a distributed consensus optimization algorithm, adopting the push-sum technique and a distributed loopless stochastic variance-reduced gradient (LSVRG) method with uncoordinated triggered probabilities, is developed and named Push-LSVRG-UP. Each agent under this algorithmic framework performs only local computation and communicates only with its neighbors without leaking their private information. The convergence analysis of Push-LSVRG-UP is relied on analyzing the contraction relationships between four error terms associated with the multi-agent system. Theoretical results provide an explicit feasible range of the constant step-size, a linear convergence rate, and an iteration complexity of Push-LSVRG-UP when achieving the globally optimal solution. It is shown that Push-LSVRG-UP achieves the superior characteristics of accelerated linear convergence, fewer storage costs, and a lower per-iteration computational complexity than most existing works. Meanwhile, the introduction of an uncoordinated probabilistic triggered mechanism allows Push-LSVRG-UP to facilitate the independence and flexibility of agents in computing local batch gradients. In simulations, the practicability and improved performance of Push-LSVRG-UP are manifested via resolving two distributed learning problems based on real-world datasets.

A novel policy iteration algorithm for solving the optimal consensus control problem of a discrete-time multiagent system with unknown dynamics

A novel policy iteration algorithm for solving the optimal consensus control problem of a discrete-time multiagent system with unknown dynamics

Adaptive NN Optimal Consensus Fault-Tolerant Control for Stochastic Nonlinear Multiagent Systems.

This article investigates the problem of adaptive neural network (NN) optimal consensus tracking control for nonlinear multiagent systems (MASs) with stochastic disturbances and actuator bias faults. In control design, NN is adopted to approximate the unknown nonlinear dynamic, and a state identifier is constructed. The fault estimator is designed to solve the problem raised by time-varying actuator bias fault. By utilizing adaptive dynamic programming (ADP) in identifier-critic-actor construction, an adaptive NN optimal consensus fault-tolerant control algorithm is presented. It is proven that all signals of the controlled system are uniformly ultimately bounded (UUB) in probability, and all states of the follower agents can remain consensus with the leader's state. Finally, simulation results are given to illustrate the effectiveness of the developed optimal consensus control scheme and theorem.

Optimal consensus control models on the sphere

In this paper, we investigate the consensus models on the sphere with control signals, where both the first and second order systems are considered. We provide the existence of the optimal control-trajectory pair and derive the first order optimality condition taking the form of the Pontryagin Minimum Principle. Numeric simulations are also presented to show that the obtained optimal control can help to accelerate the process of reaching a consensus.

Self-taught Multi-view Spectral Clustering

By integrating multiple views, i.e., multi-view learning (ML), we can discover the underlying data structures so that the performance of learning tasks can improve. As a basic and important branch of ML, multi-view clustering has achieved great success recently in pattern recognition and machine learning communities. Most existing multi-view spectral clustering methods heavily adopt the relax-and-discretize strategy to obtain discrete cluster labels (clustering results), i.e., using predefined similarity graphs to learn a consensus Laplacian embedding shared by all views for K-means clustering. However, the above clustering strategy may significantly affect clustering performance since there is information loss between independent steps. In this paper, we establish a novel Self-taught Multi-view Spectral Clustering (SMSC) framework to address the above issue. As the main contributions of this paper, we provide two versions of SMSC based on convex combination and centroid graph fusion schemes. Specifically, a self-taught mechanism is introduced in SMSC, which can effectively feedback the manifold structure induced by Laplacian embedding and the cluster information hidden in the discrete indicator matrix to learn an optimal consensus similarity graph for graph partitioning. The effectiveness of the proposed methods has been evaluated on real-world multi-view datasets, and experimental results show that our methods outperform other state-of-the-art baselines.

Consensus optimization approach for distributed Kalman filtering: Performance recovery of centralized filtering

This paper investigates the distributed Kalman filtering (DKF) from distributed optimization viewpoint. Motivated by the fact that Kalman filtering is a maximum a posteriori estimation (MAP) problem, which is a quadratic optimization problem, we reformulate DKF problem as a consensus optimization problem, resulting in that it can be solved by many existing distributed optimization algorithms. A new DKF algorithm employing the dual ascent method is proposed, and its stability is proved under mild assumptions. The performance of the proposed algorithm is evaluated through numerical experiments.

Optimal consensus control for partially unknown multi-agent systems with switching communication topology*

Since the local neighborhood tracking error system for switching multi-agent systems (MASs) is time-varying, the existing optimal consensus method for fixed MASs cannot be used in switching MASs. This paper proposes a new approach to solve the optimal consensus problems of linear switching MASs. Firstly, a new augment local neighborhood tracking error (ALNTE) system, which is based on the joint communication topology, is developed to construct the control object, and the open-loop estimation method is used to estimate the ALNTE for individuals. Secondly, based on the ALNTE system, the performance index is designed, and the value iteration method is used to solve the coupled Hamilton-Jacobi-Bellman equations and obtain the optimal control. Finally, theoretical analysis is given to prove the learning stability and control stability of the value iteration method, and a numerical simulation is used to verify the effectiveness of the proposed method.

Event-Triggered Optimal Consensus of Second-Order MASs With Disturbances and Cyber Attacks on Communications Edges

This paper investigates the distributed optimal consensus problem (DOCP) for second-order multi-agent systems (MASs) in the presence of system disturbances and cyber attacks on communication edges. In optimization, the global objective function is the sum of a class of local private objective functions, which are assumed to be strongly convex and continuously differentiable with Lipschitz continuous gradients. Unlike most optimization problems for MASs studied in the literature, in this study, the dynamics of agents are second-order and disturbed, considering cyber attacks among neighboring agents. In order to achieve DOC with low online resource consumption, novel distributed event-triggered controllers are designed for agents. Not only the communication and computation resources can be saved, but also the frequency of controller updates can be reduced. Moreover, the controllers can prevent the information of the states of second-order MASs from leaking to neighbors. Under restrictions on cyber attacks, sufficient conditions are derived, under which all controlled agents can achieve consensus on the optimal solution of the global objective function exponentially. Furthermore, the Zeno-behavior is excluded on triggering time sequences. Finally, three simulation examples are shown to illustrate the effectiveness of the designed controllers in saving online resources.

Consensus of Nonlinear Multiagent Systems With Uncertainties Using Reinforcement Learning Based Sliding Mode Control

This paper investigates distributed control protocols design for uncertain nonlinear multi-agent systems with the goal of achieving the optimal consensus. The critical challenges encountered when designing the optimal distributed control protocols are mainly caused by the internal coupling of agents, uncertainty and nonlinear dynamics. Communication delay among agents makes overcoming these challenges even more difficult. To this end, a novel sliding mode control design method is developed based on the sliding mode control principle and the reinforcement learning technique. The remarkable highlights of the developed method in this paper include the design of distributed sliding mode controllers and the integrated framework of sliding mode control and reinforcement learning, which bring the outcome of successfully learning the composite distributed control protocols for multi-agent systems. Thus, all agents can successfully eliminate the negative impacts brought by system uncertainties and communication delay among agents, and finally follow the leader with a nearly optimal approach. The reachability of sliding mode surfaces and the optimal consensus are rigorously proven and analyzed. Finally, simulation results illustrate the effectiveness of the developed method.

The Main Vectors for the Development of Estonian National Policy in the Late XX - Early XXI Centuries

The practical foundations of the national policy of modern Estonia were laid in the conditions of the collapse of the USSR and the associated aggravation of interethnic relations. The contradictions of this period largely influenced the definition of the vector of further development of post-Soviet states, including in Estonia. In general, it can be assumed that the first five years of the recent history of Estonian statehood, the main stake in its national policy was made to stimulate the re-migration of most Russian-speaking residents. In the second half of the 1990s. in the official circles of Estonia, attention is gradually increasing to the need for a certain integration of national minorities into public life, which can be explained by the influence of the foreign policy conjuncture, namely to satisfy the recommendations of the European Union, which the Estonian state sought to join. It seems that the most acute issue for the Russian-speaking population of Estonia remains the language policy, which is closely linked by the government of this country with the task of forming Estonian identity among the non-Estonian population. It should be noted that this trend is a logical consequence of the new Estonia 2035 development strategy adopted by the Riigikogu on May 12, 2021, which declares the consolidation of society and extremely succinctly mentions the need to "pay attention to the availability of access to different layers of culture among Estonian communities and communities of national minorities." At the same time, the primacy of Estonian identity is affirmed, which is confirmed by various regulatory acts of the Estonian state in the field of education, language and youth policy. Sometimes you can find individual proposals for adjusting Estonia's policy in the field of finding the optimal interethnic consensus - in the spirit of, for example, the Leitzhart rental consonational model, which has been tested in practice in Switzerland, the Netherlands, Belgium or Northern Ireland. However, at present, such proposals lie rather in the theoretical plane.

A Cross-Layer Defense Method for Blockchain Empowered CBTC Systems Against Data Tampering Attacks

Due to the high integration of wireless communication and networking technologies, the communication-based train control (CBTC) systems are exposed to additional cyber-attack surfaces, allowing sophisticated attackers to combine cyber attack vectors with physical attack means to achieve malicious goals. Notably, the decentralized authentication features are missing in existing communication protocols which make the CBTC be easily compromised by data tampering attacks, and lead to serious operational accidents. With outstanding advantages in decentralized authentication, blockchain provides new effective solutions for decentralized identity authentication in CBTC. Consequently, it is critical to study the complex physical consequences of cyber breaches from a cross-layer defense perspective. In this paper, we propose a novel cross-layer defense method for cyber security in blockchain empowered CBTC against data tampering attacks. In the physical layer, the joint Kalman filter and <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$\chi ^{2} $ </tex-math></inline-formula> detector is proposed for the train state estimation and detection. In the cyber layer, an asymmetric encryption-based secure communication protocol with identity authentication and the blockchain-based distributed key management system with the adaptive consensus mechanism are designed for data communication security. Considering the unavailable direct observation of the CBTC cyber security states, a partially observable Markov (POMDP) decision model is constructed to derive the optimal adaptive consensus strategies for balancing cyber security and efficiency. Extensive simulation results show that the proposed blockchain empowered CBTC cross-layer defense method can effectively improve the cyber security protection capability and minimize the impact of data tampering attacks on the train operation.

Opinion Dynamics and Minimum Adjustment-Driven Consensus Model for Multi-Criteria Large-Scale Group Decision Making Under a Novel Social Trust Propagation Mechanism

Compared with group decision making (GDM), it is more difficult to reach a consensus in large-scale group decision making (LSGDM) owing to the large number of decision makers (DMs). Moreover, studies on LSGDM under social trust networks are obviously fewer than those on GDM, and rarely utilize opinion dynamics to analyze the interaction of DMs. Therefore, in the context of multi-criteria large-scale group decision making (MCLSGDM), an MCLSGDM consensus decision framework and a bounded confidence-based consensus optimization model are proposed. First, a trust propagation method considering the relative importance of the trust degrees (TDs) is proposed. Then, a two-stage process of obtaining DMs’ opinions based on opinion dynamics is developed to analyze the interaction of DMs before clustering. Furthermore, a new method for determining the heterogeneous weights of DMs and subgroups is discussed. Finally, to consider the adjustment willingness of DMs, this study proposes a two-stage optimization consensus model based on bounded confidence. In addition, a numerical example is used to further elaborate the above methods and models, and highlight their rationality and superiority through a series of simulation experiments and comparative analysis.

On the Primal Feasibility in Dual Decomposition Methods Under Additive and Bounded Errors

With the unprecedented growth of signal processing and machine learning application domains, there has been a tremendous expansion of interest in distributed optimization methods to cope with the underlying large-scale problems. Nonetheless, inevitable system-specific challenges such as limited computational power, limited communication, latency requirements, measurement errors, and noises in wireless channels impose restrictions on the exactness of the underlying algorithms. Such restrictions have appealed to the exploration of algorithms' convergence behaviors under inexact settings. Despite the extensive research conducted in the area, it seems that the analysis of convergences of dual decomposition methods concerning primal optimality violations, together with dual optimality violations is less investigated. Here, we provide a systematic exposition of the convergence of <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">feasible points</i> in dual decomposition methods under inexact settings, for an important class of global consensus optimization problems. Convergences and the rate of convergences of the algorithms are mathematically substantiated, not only from a dual-domain standpoint but also from a primal-domain standpoint. Analytical results show that the algorithms converge to a neighborhood of optimality, the size of which depends on the level of underlying distortions.

Coordinated planning transmission tasks in heterogeneous space networks: A semi-distributed approach

This paper studies the coordinated planning of transmission tasks in the heterogeneous space networks to enable efficient sharing of ground stations cross satellite systems. Specifically, we first formulate the coordinated planning problem into a mixed integer liner programming (MILP) problem based on time expanded graph. Then, the problem is transferred and reformulated into a consensus optimization framework which can be solved by satellite systems parallelly. With alternating direction method of multipliers (ADMM), a semi-distributed coordinated transmission task planning algorithm is proposed, in which each satellite system plans its own tasks based on local information and limited communication with the coordination center. Simulation results demonstrate that compared with the centralized and fully-distributed methods, the proposed semi-distributed coordinated method can strike a better balance among task complete rate, complexity, and the amount of information required to be exchanged.

A Decentralized Primal-Dual Framework for Non-Convex Smooth Consensus Optimization

In this work, we introduce ADAPD, A DecentrAlized Primal-Dual algorithmic framework for solving non-convex and smooth consensus optimization problems over a network of distributed agents. The proposed framework relies on a novel problem formulation that elicits ADMM-type updates, where each agent first inexactly solves a local strongly convex subproblem with any method of its choice and then performs a neighbor communication to update a set of dual variables. We present two variants that allow for a single gradient step for the primal updates or multiple communications for the dual updates, to exploit the tradeoff between the per-iteration cost and the number of iterations. When multiple communications are performed, ADAPD can achieve theoretically optimal communication complexity results for non-convex and smooth consensus problems. Numerical experiments on several applications, including a deep-learning one, demonstrate the superiority of ADAPD over several popularly used decentralized methods.

FedHybrid: A Hybrid Federated Optimization Method for Heterogeneous Clients

We consider a distributed consensus optimization problem over a server-client (federated) network, where all clients are connected to a central server. Current distributed algorithms fail to capture the heterogeneity in clients' local computation capacities. Motivated by the method of multipliers in centralized optimization, we derive a Newton-type primal-dual method with a distributed implementation utilizing the server-client topology. Then we propose <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">FedHybrid</i> as a hybrid primal-dual method that allows heterogeneous clients to perform different types of updates. Specifically, those clients with higher computational capabilities and/or cheaper costs to perform computation can implement Newton-type updates locally, while other clients can adopt much simpler gradient-type updates. Theoretically, we propose a novel merit function by combining the dual optimality gap and the primal tracking error. We prove that FedHybrid converges linearly to the exact optimal point for strongly convex functions, regardless of clients' choices of gradient-type or Newton-type updates. Finally, we show numerical studies to demonstrate the efficacy of our method in practice. To the best of our knowledge, this is the first hybrid method allowing heterogeneous local updates for distributed consensus optimization with provable convergence and rate guarantees.

Nonconvex Distributed Optimization via Lasalle and Singular Perturbations

In this letter we address nonconvex distributed consensus optimization, a popular framework for distributed big-data analytics and learning. We consider the Gradient Tracking algorithm and, by resorting to an elegant system theoretical analysis, we show that agent estimates asymptotically reach consensus to a stationary point. We take advantage of suitable coordinates to write the Gradient Tracking as the interconnection of a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">fast</i> dynamics and a <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">slow</i> one. To use a singular perturbation analysis, we separately study two auxiliary subsystems called <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">boundary layer</i> and <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">reduced</i> systems, respectively. We provide a Lyapunov function for the boundary layer system and use Lasalle-based arguments to show that trajectories of the reduced system converge to the set of stationary points. Finally, a customized version of a Lasalle’s Invariance Principle for singularly perturbed systems is proved to show the convergence properties of the Gradient Tracking.

Adaptive constrained output feedback optimal consensus tracking for uncertain nonlinear multi-agent systems and its application

This paper addresses the output feedback optimal consensus tracking control problem for a class of nonlinear multi-agent systems (MASs) with unknown internal dynamics and input saturation. Firstly, an adaptive observer is designed to reconstruct the unmeasurable states using neural networks (NNs) based on the augmented dynamic model. Subsequently, a novel distributed feedforward controller is proposed using the backstepping method, where an auxiliary state is introduced to deal with the input saturation problem. Unlike the traditional recursive design technique, the procedures we take can reduce the consensus tracking control problem into the optimal regulation issue, which is then solved by the adaptive dynamic programming (ADP) method. Therefore, the designed consensus control protocol consists of a distributed feedforward controller and a distributed optimal feedback controller. Moreover, the stability of the MASs is guaranteed by the Lyapunov theory. Numerical simulation on multi-missile guidance problem demonstrates the effectiveness of the proposed control scheme.

Local minimum adjustment for the consensus model with distribution linguistic preference relations considering preference reliability

Preference reliability analysis for preference relations reflected by the ordinal consistency and the cardinal consistency was intensively studied. The ordinal consistency is a minimum condition to guarantee that the decision maker’s pairwise comparison preferences between any triple alternatives are transitive. These issues for group decision-making with distribution linguistic preference relations have not been well addressed. This paper aims to provide a consensus model with distribution linguistic preference relations that controls both the cardinal consistency and the ordinal consistency. To do so, a new ordinal consistency for the distribution linguistic preference relations is defined, which is based on the transformation from the distribution linguistic preference relations to its expectation-based matrixes and then to its numerical scale matrixes. Two mixed integer linear programming models are respectively designed to eliminate the ordinal inconsistencies, and to simultaneously control the ordinal and cardinal consistencies so as to ensure the rationality of individual preference relations. Then, a consensus optimization model is developed in which only the individuals with consensus levels lower than the given threshold are allowed to modify their preferences. Preference reliability is also analyzed in the proposed consensus model. Finally, some classical examples are given to illustrate the proposed models. Comparative analysis validates the feasibility and effectiveness of the proposed approaches.