Initialization-free Distributed Algorithms for Optimal Resource Allocation with Feasibility Constraints and its Application to Economic Dispatch of Power Systems

In this paper, the distributed resource allocation optimization problem is investigated. The allocation decisions are made to minimize the sum of all the agents' local objective functions while satisfying both the global network resource constraint and the local allocation feasibility constraints. Here the data corresponding to each agent in this separable optimization problem, such as the network resources, the local allocation feasibility constraint, and the local objective function, is only accessible to individual agent and cannot be shared with others, which renders new challenges in this distributed optimization problem. Based on either projection or differentiated projection, two classes of continuous-time algorithms are proposed to solve this distributed optimization problem in an initialization-free and scalable manner. Thus, no re-initialization is required even if the operation environment or network configuration is changed, making it possible to achieve a "plug-and-play" optimal operation of networked heterogeneous agents. The algorithm convergence is guaranteed for strictly convex objective functions, and the exponential convergence is proved for strongly convex functions without local constraints. Then the proposed algorithm is applied to the distributed economic dispatch problem in power grids, to demonstrate how it can achieve the global optimum in a scalable way, even when the generation cost, or system load, or network configuration, is changing.Comment: 13 pages, 7 figure

Stability Analysis of Constrained Optimization Dynamics via Passivity Techniques

In this paper, we present passivity based convergence analysis of continuous time primal-dual gradient method for convex optimization problems. We first show that a convex optimization problem with only affine equality constraints admit a Brayton Moser formulation. This observation leads to a new passivity property derived from a Krasovskii type storage function. Secondly, the inequality constraints are modeled as a state dependent switching system. Using hybrid methods, it is shown that each switching mode is passive and the passivity of the system is preserved under arbitrary switching. Finally, the two systems, (i) one derived from the Brayton Moser formulation and (ii) the state dependent switching system, are interconnected in a power conserving way. The resulting trajectories of the overall system are shown to converge asymptotically, to the optimal solution of the convex optimization problem. The proposed methodology is applied to an energy management problem in buildings and simulations are provided for corroboration

Primal-Dual Gradient Flow Algorithm for Distributed Support Vector Machines

In this paper, a primal-dual gradient flow algorithm for distributed support vector machines (DSVM) is proposed. A network of computing nodes, each carrying a subset of horizontally partitioned large dataset is considered. The nodes are represented as dynamical systems with Arrow-Hurwicz-Uzawa gradient flow dynamics, derived from the Lagrangian function of the DSVM problem. It is first proved that the nodes are passive dynamical systems. Then, by employing the Krasovskii type candidate Lyapunov functions, it is proved that the computing nodes asymptotically converge to the optimal primal-dual solution

Distributed Resource Allocation Over Random Networks Based on Stochastic Approximation

In this paper, a stochastic approximation (SA) based distributed algorithm is proposed to solve the resource allocation (RA) with uncertainties. In this problem, a group of agents cooperatively optimize a separable optimization problem with a linear network resource constraint and allocation feasibility constraints, where the global objective function is the sum of agents' local objective functions. Each agent can only get noisy observations of its local function's gradient and its local resource, which cannot be shared by other agents or transmitted to a center. Moreover, there are communication uncertainties such as time-varying topologies (described by random graphs) and additive channel noises. To solve the RA, we propose an SA-based distributed algorithm, and prove that agents can collaboratively achieve the optimal allocation with probability one by virtue of ordinary differential equation (ODE) method for SA. Finally, simulations related to the demand response management in power systems verify the effectiveness of the proposed algorithm.Comment: 9 pages,3 figures, submitted to Systems & Control Letter

Accelerated Distributed Primal-Dual Dynamics using Adaptive Synchronization

This paper proposes an adaptive primal-dual dynamics for distributed optimization in multi-agent systems. The proposed dynamics incorporates an adaptive synchronization law that reinforces the interconnection strength between the primal variables of the coupled agents, the given law accelerates the convergence of the proposed dynamics to the saddle-point solution. The resulting dynamics is represented as a feedback interconnected networked system that proves to be passive. The passivity properties of the proposed dynamics are exploited along with the LaSalle's invariance principle for hybrid systems, to establish asymptotic convergence and stability of the saddle-point solution. Further, the primal dynamics is analyzed for the rate of convergence and stronger convergence bounds are established, it is proved that the primal dynamics achieve accelerated convergence under the adaptive synchronization. The robustness of the proposed dynamics is quantified using L2-gain analysis and the correlation between the rate of convergence and robustness of the proposed dynamics is presented. The effectiveness of the proposed dynamics is demonstrated by applying it to solve distributed least squares and distributed support vector machines problems

A Novel Consensus-based Distributed Algorithm for Economic Dispatch Based on Local Estimation of Power Mismatch

This paper proposes a novel consensus-based distributed control algorithm for solving the economic dispatch problem of distributed generators. A legacy central controller can be eliminated in order to avoid a single point of failure, relieve computational burden, maintain data privacy, and support plug-and-play functionalities. The optimal economic dispatch is achieved by allowing the iterative coordination of local agents (consumers and distributed generators). As coordination information, the local estimation of power mismatch is shared among distributed generators through communication networks and does not contain any private information, ultimately contributing to a fair electricity market. Additionally, the proposed distributed algorithm is particularly designed for easy implementation and configuration of a large number of agents in which the distributed decision making can be implemented in a simple proportional-integral (PI) or integral (I) controller. In MATLAB/Simulink simulation, the accuracy of the proposed distributed algorithm is demonstrated in a 29-node system in comparison with the centralized algorithm. Scalability and a fast convergence rate are also demonstrated in a 1400-node case study. Further, the experimental test demonstrates the practical performance of the proposed distributed algorithm using the VOLTTRON platform and a cluster of low-cost credit-card-size single-board PCs.Comment: 16 Pages, 13 figures Figures order and references are corrected

Constrained hierarchical networked optimization for energy markets

In this paper, we propose a distributed control strategy for the design of an energy market. The method relies on a hierarchical structure of aggregators for the coordination of prosumers (agents which can produce and consume energy). The hierarchy reflects the voltage level separations of the electrical grid and allows aggregating prosumers in pools, while taking into account the grid operational constraints. To reach optimal coordination, the prosumers communicate their forecasted power profile to the upper level of the hierarchy. Each time the information crosses upwards a level of the hierarchy, it is first aggregated, both to strongly reduce the data flow and to preserve the privacy. In the first part of the paper, the decomposition algorithm, which is based on the alternating direction method of multipliers (ADMM), is presented. In the second part, we explore how the proposed algorithm scales with increasing number of prosumers and hierarchical levels, through extensive simulations based on randomly generated scenarios

State-of-the-Art Economic Load Dispatch of Power Systems Using Particle Swarm Optimization

Metaheuristic particle swarm optimization (PSO) algorithm has emerged as one of the most promising optimization techniques in solving highly constrained non-linear and non-convex optimization problems in different areas of electrical engineering. Economic operation of the power system is one of the most important areas of electrical engineering where PSO has been used efficiently in solving various issues of practical systems. In this paper, a comprehensive survey of research works in solving various aspects of economic load dispatch (ELD) problems of power system engineering using different types of PSO algorithms is presented. Five important areas of ELD problems have been identified, and the papers published in the general area of ELD using PSO have been classified into these five sections. These five areas are (i) single objective economic load dispatch, (ii) dynamic economic load dispatch, (iii) economic load dispatch with non-conventional sources, (iv) multi-objective environmental/economic dispatch, and (v) economic load dispatch of microgrids. At the end of each category, a table is provided which describes the main features of the papers in brief. The promising future works are given at the conclusion of the review

A Proximal Diffusion Strategy for Multi-Agent Optimization with Sparse Affine Constraints

This work develops a proximal primal-dual decentralized strategy for multi-agent optimization problems that involve multiple coupled affine constraints, where each constraint may involve only a subset of the agents. The constraints are generally sparse, meaning that only a small subset of the agents are involved in them. This scenario arises in many applications including decentralized control formulations, resource allocation problems, and smart grids. Traditional decentralized solutions tend to ignore the structure of the constraints and lead to degraded performance. We instead develop a decentralized solution that exploits the sparsity structure. Under constant step-size learning, the asymptotic convergence of the proposed algorithm is established in the presence of non-smooth terms, and it occurs at a linear rate in the smooth case. We also examine how the performance of the algorithm is influenced by the sparsity of the constraints. Simulations illustrate the superior performance of the proposed strategy.Comment: accepted for publication in IEEE TA

Applications of Deep Reinforcement Learning in Communications and Networking: A Survey

This paper presents a comprehensive literature review on applications of deep reinforcement learning in communications and networking. Modern networks, e.g., Internet of Things (IoT) and Unmanned Aerial Vehicle (UAV) networks, become more decentralized and autonomous. In such networks, network entities need to make decisions locally to maximize the network performance under uncertainty of network environment. Reinforcement learning has been efficiently used to enable the network entities to obtain the optimal policy including, e.g., decisions or actions, given their states when the state and action spaces are small. However, in complex and large-scale networks, the state and action spaces are usually large, and the reinforcement learning may not be able to find the optimal policy in reasonable time. Therefore, deep reinforcement learning, a combination of reinforcement learning with deep learning, has been developed to overcome the shortcomings. In this survey, we first give a tutorial of deep reinforcement learning from fundamental concepts to advanced models. Then, we review deep reinforcement learning approaches proposed to address emerging issues in communications and networking. The issues include dynamic network access, data rate control, wireless caching, data offloading, network security, and connectivity preservation which are all important to next generation networks such as 5G and beyond. Furthermore, we present applications of deep reinforcement learning for traffic routing, resource sharing, and data collection. Finally, we highlight important challenges, open issues, and future research directions of applying deep reinforcement learning.Comment: 37 pages, 13 figures, 6 tables, 174 reference paper