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Convex Analysisの二,三の進展について

An initialization-free distributed algorithm for dynamic economic dispatch problems in microgrid: Modeling, optimization and analysis

Predefined-time distributed optimization of general linear multi-agent systems

In this study, we propose a predefined-time multi-agent approach for multi-objective optimization. Predefined-time optimization is an optimization approach that can converge to a state that is extremely close to an optimal solution at a given time. A time-base generator is derived and applied to the optimization approaches for achieving predefined-time optimization. The multi-objective optimization problem is reformulated as a distributed optimization problem and thus solved in a private and safe manner. For distributed optimization, a multi-agent system (MAS) with time-base generators is developed for predefined-time optimization, and its convergence and speed are proven. Several examples confirm the validity of the results. 

Multi-Objective Distributed Optimization via A Predefined-Time Multi-Agent Approach

This article aims to solve the nonsmooth resource allocation problem in the presence of a global network resource constraint and local set constraints in the framework of multiagent system optimization. It is assumed that multiagent systems are subject to some external disturbances, and the control inputs of the agents satisfy Lispchitz continuity. These two distinguished features render the existing distributed optimization algorithms, especially the subgradient-based algorithms inapplicable due to the employment of discontinuity of subgradients. To solve such a challenging resource allocation problem, a new kind of continuous-time proximal algorithm is designed with the aid of convex optimization theory and the internal-model technique. The proximal algorithm is further augmented by introducing an event-based communication scheme such that the continuous-time communication among the agents is avoided successfully. The theoretical analysis shows that the multiagent systems under the proposed algorithms can converge to the optimal solution of the considered problem, while the external disturbances are rejected. Besides, the Zeno behavior can be excluded for the proximal algorithm with event-based communication. Finally, the numerical simulations are given to verify the established theoretical results.

Nonsmooth Resource Allocation of Multiagent Systems With Disturbances: A Proximal Approach

Distributed resource allocation of second‐order multiagent systems with exogenous disturbances

In this paper, we consider the distributed optimization problems with linear coupling constraint of general homogeneous and heterogeneous linear multi-agent systems under weighted-balanced and strongly connected digraphs. In order to control all agents converge to the optimal output, we propose distributed control laws, therein, the optimal output can make the global cost function reach minimum. Then we guarantee the convergence of the proposed algorithms by the properties of Laplacian matrix and Lyapunov stability theorem. Furthermore, we extend the result of heterogeneous linear multi-agent system to the case that dynamics of agents are subject to external disturbances, and prove that the algorithm designed by internal model principle can make all agents reach the optimal output exactly. Finally, we provide examples to illustrate the effectiveness of the proposed distributed algorithms.

Distributed optimization of general linear multi-agent systems with external disturbance

Distributed resource allocation of second‐order nonlinear multiagent systems

The problem of seeking Nash equilibrium in multicluster games is studied. Different from the existing multi-cluster game studies, the participants considered in this paper have Euler-Lagrange (EL) dynamics and cannot directly obtain the information of non-neighbor participants. Agents can only communicate through directed communication graphs. In addition, there are coupling constraints between agent decisions in the same cluster. Under the widely used assumptions, two distributed algorithms are proposed to solve the Nash equilibrium (NE) of the multi-cluster game based on gradient descent, state feedback, and consensus protocol. The convergence of the two algorithms is analyzed by singular perturbation analysis and variational analysis. The theoretical results show that the first algorithm achieves exponential convergence when the parameters are certain, while the other algorithm also achieves global asymptotic convergence when the parameters are uncertain. Finally, the effectiveness of the search strategy is verified by numerical examples. 

Nash Equilibrium Seeking for Multi-Cluster Games of Multiple Nonidentical Euler-Lagrange Systems

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