This study presents a fixed-time convergent algorithm to achieve distributed least square (DLS) solutions of networked linear equations. Each agent in the network only knows a subset of the equations and can only exch...
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This study presents a fixed-time convergent algorithm to achieve distributed least square (DLS) solutions of networked linear equations. Each agent in the network only knows a subset of the equations and can only exchange messages with its nearest neighbors. Unlike finite-time counterparts, the settling time of the fixed-time distributed algorithm does not depend upon the initial states, and can be preassigned according to the requirements of the task. Numerical simulations verify the theoretical results.
We present a novel generalized constrained convex optimization model for multiagent systems that contains both the local, coupled equality, and inequality constraints, and a global resource allocation constraint. This...
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We present a novel generalized constrained convex optimization model for multiagent systems that contains both the local, coupled equality, and inequality constraints, and a global resource allocation constraint. This model unifies the traditional constrained optimization problem, the resource allocation problem, and the economic dispatch problem. Unlike the majority of literature where each local objective function is required to be convex, we only require a milder condition that the global objective function is convex. The gradient of the global Lagrangian is estimated locally by each agent using the dynamic average consensus protocol. Synchronously, modified primal-dual dynamics produce the optimal solution via the estimated gradient. The generalized Lagrange multiplier method is introduced to avoid the usual positive projections in the presence of inequality constraints. This leads to smooth dynamics and a continuous Lyapunov derivative, which enables the exponential stability analysis. Simulation examples support the proposed distributed methods.
This paper presents an overview on the recent advances in the research of security of cyber-physical systems. We place particular emphases on consensus problems for multi-agent systems in hostile environments and thei...
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This paper presents an overview on the recent advances in the research of security of cyber-physical systems. We place particular emphases on consensus problems for multi-agent systems in hostile environments and their analyses on the resiliency against two types of attacks. First, we discuss a class of data injection attacks by focusing on the approach based on mean subsequence reduced (MSR) algorithms and their variants. Agents equipped with such algorithms will ignore their neighbors taking extreme state values. Characterizations on the properties necessary for network topologies and moreover a number of extensions with enhanced resiliency will be established. As the second class of attacks, the effects of denial-of-service (DoS) attacks will be examined in the context of multi-agent consensus. By employing a DoS model based on the energy constraints of the attacker, we will observe that robustness against such attacks may depend on system properties such as dynamics of the individual agents and network structures. Applications of the algorithms will be further discussed for clock synchronization in wireless sensor networks and control of a group of mobile robots.
This article proposes a new control strategy for the voltage regulation of unbalanced low-voltage (LV) distribution grids with high penetration of distributed renewable energy sources (DRESs). The proposed method uses...
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This article proposes a new control strategy for the voltage regulation of unbalanced low-voltage (LV) distribution grids with high penetration of distributed renewable energy sources (DRESs). The proposed method uses the available reactive power of DRESs as the primary means for voltage regulation. Furthermore, its distinct feature is the use of a distributed control architecture prioritizing the response of DRESs to maintain the network voltages within permissible limits and minimize the network losses. The prioritization process is locally implemented by each DRES combining two types of information: (a) the sensitivity matrix that quantifies the impact of reactive power variations on the network voltages and (b) voltage measurements along the network. Time-domain and time-series simulations on the IEEE European LV test feeder are performed to evaluate the performance of the proposed method against existing decentralized, distributed and centralized, optimization-based methods.
All existing solutions to distributed consensus are organised around a Paxos-like structure wherein processes contend for exclusive leadership in one phase, and then either use their dominant position to propose a val...
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All existing solutions to distributed consensus are organised around a Paxos-like structure wherein processes contend for exclusive leadership in one phase, and then either use their dominant position to propose a value in the next phase or elect an alternate leader. This approach may be characterised as adversarial and phase-asymmetric, requiring distinct message schemas and process behaviours for each phase. In over three decades of research, no algorithm has diverged from this basic model, alluding to it perhaps being the only viable solution to consensus. This paper presents a new consensus algorithm named Spire, characterised by a phase-symmetric, cooperative structure. Processes do not contend for leadership;instead, they collude to iteratively establish a dominant value and may do so concurrently without conflicting. Each successive iteration is structured identically to the previous, employing the same messages and invoking the same behaviour. By these characteristics, Spire buckles the trend in protocol design, proving that at least two disjoint cardinal solutions to consensus exist. The resulting phase symmetry halves the number of distinct messages and behaviours, offering a clear intuition and an approachable foundation for learning consensus and building practical systems.
With the rising number of applications for sensor networks comes a need for more accurate cooperative fusion algorithms. In this paper, a distributed and optimal state estimator is presented for implementation through...
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With the rising number of applications for sensor networks comes a need for more accurate cooperative fusion algorithms. In this paper, a distributed and optimal state estimator is presented for implementation through a dynamically switching, yet strongly connected, directed communication network to cooperatively estimate the state of a dynamic system. The Kalman-Consensus filter approach is used to incorporate a consensus protocol of neighboring state estimates into the traditional Kalman filter. It has been known that the main difficulty associated with implementing such an optimal solution is its fully coupled covariance matrix. Presented is a distributed computation of the covariance matrix at every node achieved by taking advantage of its independence from state estimates. Reductions to the distributed covariance computations are achieved through shared processing made available by the strongly connected digraph. Should the digraph change over time, a distributed topology estimation algorithm is included to facilitate the implementation of the proposed Kalman-Consensus filters. Together, these advances render a distributed and optimal solution to the consensus-based cooperative Kalman filter design problem. Convergence and stability of the proposed algorithms are analyzed and analytically concluded with performance verified through simulation of an illustrative example.
In this article, we propose a novel distributed alternating direction method of multipliers (ADMM) algorithm with synergetic communication and computation, called SCCD-ADMM, to reduce the total communication and compu...
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In this article, we propose a novel distributed alternating direction method of multipliers (ADMM) algorithm with synergetic communication and computation, called SCCD-ADMM, to reduce the total communication and computation cost of the system. Explicitly, in the proposed algorithm, each node interacts with only part of its neighboring nodes, the number of which is progressively determined according to a heuristic searching procedure, which takes into account both the predicted convergence rate and the communication and computation costs at each iteration, resulting in a trade-off between communication and computation. Then the node chooses its neighboring nodes according to an importance sampling distribution derived theoretically to minimize the variance with the latest information it locally stores. Finally, the node updates its local information with a new update rule which adapts to the number of communication nodes. We prove the convergence of the proposed algorithm and provide an upper bound of the convergence variance brought by randomness. Extensive simulations validate the excellent performances of the proposed algorithm in terms of convergence rate and variance, the overall communication and computation cost, the impact of network topology as well as the time for evaluation, in comparison with the traditional counterparts.
In this work, we study the generalized Nash equilibrium (GNE, see Definition 1) seeking problem for monotone generalized noncooperative games with set constraints and shared affine inequality constraints. A novel proj...
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In this work, we study the generalized Nash equilibrium (GNE, see Definition 1) seeking problem for monotone generalized noncooperative games with set constraints and shared affine inequality constraints. A novel projected gradient-based regularized penalized dynamical system is proposed to solve this issue. The idea is to use a differentiable penalty function with a time-varying penalty parameter to deal with the inequality constraints. A time-varying regularization term is used to deal with the ill-poseness caused by the monotonicity assumption and the time-varying penalty term. The proposed dynamical system extends the regularized dynamical system in the literature to the projected gradient-based regularized penalized dynamical system, which can be used to solve generalized noncooperative games with set constraints and coupled constraints. Furthermore, we propose a distributed algorithm by using leader-following consensus, where the players have access to neighboring information only. For both cases, the asymptotic convergence to the least-norm variational equilibrium of the game is proven. Numerical examples show the effectiveness and efficiency of the proposed algorithms.
A distributed optimization problem (DOP) with affine equality and convex inequality constraints is studied in this article. First, the consensus constraint of the considered DOP is relaxed and a related approximate DO...
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A distributed optimization problem (DOP) with affine equality and convex inequality constraints is studied in this article. First, the consensus constraint of the considered DOP is relaxed and a related approximate DOP (ADOP) is presented. It is proved that the optimal solutions of the ADOP (i.e., the near-optimal solutions of the original DOP) are able to approach the optimal solutions of the original DOP. A continuous-time algorithm is proposed for the ADOP and it is demonstrated that the state solution of the presented algorithm converges to the critical point set of the ADOP with general locally Lipschitz continuous objective functions. This means the presented algorithm is efficient for distributed nonconvex optimization problems. Particularly, when the objective functions are convex ones, the state solution of the presented algorithm is further proved to converge to a near-optimal solution of the original DOP. One illustrative example and an application on load sharing problems are shown to validate the effectiveness of the proposed algorithm.
This article proposes the first distributed algorithm that solves the weight-balancing problem using only finite rate and simplex communications among nodes, compliant with the directed nature of the graph edges. It i...
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This article proposes the first distributed algorithm that solves the weight-balancing problem using only finite rate and simplex communications among nodes, compliant with the directed nature of the graph edges. It is proved that the algorithm converges to a weight-balanced solution at sublinear rate. The analysis builds upon a new metric inspired by positional system representations, which characterizes the dynamics of information exchange over the network, and on a novel step-size rule. Building on this result, a novel distributed algorithm is proposed that solves the average consensus problem over digraphs, using, at each timeslot, finite rate simplex communications between adjacent nodes-some bits for the weight-balancing problem and others for the average consensus. Convergence of the proposed quantized consensus algorithm to the average of the node's unquantized initial values is established, both almost surely and in the moment generating function of the error;and a sublinear convergence rate is proved for sufficiently large step-sizes. Numerical results validate our theoretical findings.
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