Distributed Lagrangian Methods for Network Resource Allocation

Motivated by a variety of applications in control engineering and information sciences, we study network resource allocation problems where the goal is to optimally allocate a fixed amount of resource over a network of nodes. In these problems, due to the large scale of the network and complicated inter-connections between nodes, any solution must be implemented in parallel and based only on local data resulting in a need for distributed algorithms. In this paper, we propose a novel distributed Lagrangian method, which requires only local computation and communication. Our focus is to understand the performance of this algorithm on the underlying network topology. Specifically, we obtain an upper bound on the rate of convergence of the algorithm as a function of the size and the topology of the underlying network. The effectiveness and applicability of the proposed method is demonstrated by its use in solving the important economic dispatch problem in power systems, specifically on the benchmark IEEE-14 and IEEE-118 bus systems

Distributed Delay-Tolerant Strategies for Equality-Constraint Sum-Preserving Resource Allocation

This paper proposes two nonlinear dynamics to solve constrained distributed optimization problem for resource allocation over a multi-agent network. In this setup, coupling constraint refers to resource-demand balance which is preserved at all-times. The proposed solutions can address various model nonlinearities, for example, due to quantization and/or saturation. Further, it allows to reach faster convergence or to robustify the solution against impulsive noise or uncertainties. We prove convergence over weakly connected networks using convex analysis and Lyapunov theory. Our findings show that convergence can be reached for general sign-preserving odd nonlinearity. We further propose delay-tolerant mechanisms to handle general bounded heterogeneous time-varying delays over the communication network of agents while preserving all-time feasibility. This work finds application in CPU scheduling and coverage control among others. This paper advances the state-of-the-art by addressing (i) possible nonlinearity on the agents/links, meanwhile handling (ii) resource-demand feasibility at all times, (iii) uniform-connectivity instead of all-time connectivity, and (iv) possible heterogeneous and time-varying delays. To our best knowledge, no existing work addresses contributions (i)-(iv) altogether. Simulations and comparative analysis are provided to corroborate our contributions

Distributed Energy Resource Management: All-Time Resource-Demand Feasibility, Delay-Tolerance, Nonlinearity, and Beyond

In this work, we propose distributed and networked energy management scenarios to optimize the production and reservation of energy among a set of distributed energy nodes. In other words, the idea is to optimally allocate the generated and reserved powers based on nodes' local cost gradient information while meeting the demand energy. One main concern is the all-time (or anytime) resource-demand feasibility, implying that at all iterations of the scheduling algorithm, the balance between the produced power and demand plus reserved power must hold. The other concern is to design algorithms to tolerate communication time-delays and changes in the network. Further, one can incorporate possible model nonlinearity in the algorithm to address both inherent (e.g., saturation and quantization) and purposefully-added (e.g., signum-based) nonlinearities in the model. The proposed optimal allocation algorithm addresses all the above concerns, while it benefits from possible features of the distributed (or networked) solutions such as no-single-node-of-failure and distributed information processing. We show both the all-time feasibility of the proposed scheme and its convergence under certain bound on the step-rate using Lyapunov-type proofs.Comment: IEEE LCSS 202