Distributed Optimization of Clique-Wise Coupled Problems via Three-Operator Splitting

In this study, we explore distributed optimization problems with clique-wise coupling through the lens of operator splitting. This framework of clique-wise coupling extends beyond conventional pairwise coupled problems, encompassing consensus optimization and formation control, and is applicable to a wide array of examples. We first introduce a matrix, called the clique-wise duplication (CD) matrix, which enables decoupled reformulations for operator splitting methods and distributed computation. Leveraging this matrix, we propose a new distributed optimization algorithm via Davis-Yin splitting (DYS), a versatile three-operator splitting method. We then delve into the properties of this method and demonstrate how existing consensus optimization methods (NIDS, Exact Diffusion, and Diffusion) can be derived from our proposed method. Furthermore, being inspired by this observation, we derive a Diffusion-like method, the clique-based projected gradient descent (CPGD), and present Nesterov's acceleration and in-depth convergence analysis for various step sizes. The paper concludes with numerical examples that underscore the efficacy of our proposed method.Comment: 16page

Distributed Dynamic Pricing for Car-sharing Systems with Stochastic Demand Shift

2022 IEEE 25th International Conference on Intelligent Transportation Systems (ITSC), 08-12 October 2022This study investigated one-way car-sharing systems under dynamic pricing. Despite their convenience, one-way car-sharing systems have the limitation that vehicles can be unevenly parked according to the demand of customers. To distribute car parking, we consider introducing dynamic pricing in which customers can shift their demand (i.e., change origins and destinations by walking) according to usage prices. A model of this system is developed with consideration of stochastic processes representing human behavior in the demand shift. Furthermore, we develop a common, distributed dynamic pricing policy to minimize the unevenness of the vehicles according to the network topology representing the layout of stations. Numerical examples using a realistic traffic simulator demonstrate the effectiveness of the developed method

Cooperative reference frame estimation for multi-agent systems via formation control

In this study, we propose a distributed method for multi-agent systems to estimate a global reference frame by constructing a common reference frame for all agents with only local measurements. Our method is a combination of formation control and similarity evaluation of feature point matching. Here, we design a distributed controller to achieve a prescribed configuration and a distributed estimator to construct a common reference frame, which calculates the similarity between the measured relative positions and the prescribed configuration. Then, we quantify the error range between the common reference frame and the global reference frame and show that the constructed common reference frame is the best. The proposed method requires only the information on the relative positions of neighbor robots through local measurements and does not require inter-robot communication or relative posture observation. Finally, we conducted simulations with 12 agents and an experiment with 8 two-wheeled robots to verify the effectiveness of the proposed method

Distributed Optimization of Clique-wise Coupled Problems

This study addresses a distributed optimization with a novel class of coupling of variables, called clique-wise coupling. A clique is a node set of a complete subgraph of an undirected graph. This setup is an extension of pairwise coupled optimization problems (e.g., consensus optimization) and allows us to handle coupling of variables consisting of more than two agents systematically. To solve this problem, we propose a clique-based linearized ADMM algorithm, which is proved to be distributed. Additionally, we consider objective functions given as a sum of nonsmooth and smooth convex functions and present a more flexible algorithm based on the FLiP-ADMM algorithm. Moreover, we provide convergence theorems of these algorithms. Notably, all the algorithmic parameters and the derived condition in the theorems depend only on local information, which means that each agent can choose the parameters in a distributed manner. Finally, we apply the proposed methods to a consensus optimization problem and demonstrate their effectiveness via numerical experiments

New Vascular-Access Intervention Assistance Plate Provides Good Operability and Safety by Preventing Accidental Falls: First Experience of 1,872 Cases

Vascular-access interventions are necessary for the continuation of hemodialysis, and they are performed under X-ray guidance. During interventions, patients’ accidental falls from the bed are a serious problem, and spe-cialized fixation systems for hemodialysis patients to prevent their falls from the bed have been lacking. We developed a new fixation plate made of polypropylene homopolymer and tested its ability to prevent such falls retrospectively. This plate, which we named the ‘vascular-access intervention assistance plate,’ offers functional features such as the concurrent fixation of the body and either arm and an arm space with serrations for fixing a forearm strap. We performed computer simulations to examine the strength of the plate, and we evaluated the efficacy of fall prevention by reviewing patients’ medical records. The results demonstrated that the functional design of the plate provides good operability via accurate concurrent fixations of the body and arm. The com-puter simulation analysis results indicated the plate’s sufficient strength. The medical records analysis revealed three accidental falls before the plate’s introduction (401 patients, 1,437 interventions), and none after plate introduction (683 patients, 1,872 interventions). Accidental falls were significantly prevented by use of the plate (p < 0.05). The dementia rate and type of procedure were not significantly different between the patients who fell and those who did not. This vascular-access intervention assisted plate provides good operability and safety by preventing accidental falls among hemodialysis patients

Gradient-Based Distributed Controller Design Over Directed Networks

In this study, we propose a design methodology of distributed controllers for multi-agent systems on a class of directed interaction networks by extending the gradient-flow method. Although the gradient-flow method is a common design tool for distributed controllers, it is inapplicable to directed networks. First, we demonstrate how to construct a distributed controller for systems over a class of time-invariant directed graphs. Subsequently, we achieve better convergence properties and performance enhancement than the conventional gradient-flow method. To illustrate its application in time-varying networks, we address the dynamic matching problem of two distinct groups of agents with different sensing ranges. This problem is a novel coordination task that involves pairing agents from two distinct groups to achieve a convergence of the paired agents' states to the same value. Accordingly, we apply the proposed method to this problem and provide sufficient conditions for successful matching. Lastly, numerical examples for systems on both time-invariant and time-varying networks demonstrate the effectiveness of the proposed method