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This paper studies two distributed resource allocation problems of second-order systems over weight-balanced communication networks. In the first problem, the decisions of agents are coupled by network resource constraints, and in the second problem, the decisions of agents are constrained by local constraints and network resource constraints. Compared with many existing resource allocation problems, the formulation involves the dynamics of agents. The second-order dynamics of agents induce the difficult in algorithm design and analysis, since the decisions of agents could not be directly decided by their control inputs. In order to optimally allocate the network resource, two distributed algorithms are designed via state feedback and gradient descent for the two problems, respectively. Besides, the convergence of the two algorithms are analyzed. By the two algorithms, the second-order agents converge to the optimal allocation of the two problems, respectively. Finally, two examples about economic dispatch problems verify the two algorithms. [ABSTRACT FROM AUTHOR]

In this paper, we study distributed nonsmooth multi-coalition games (MCGs), where the players are subject to local convex set constraints and coupled inequality constraints. Different from existing distributed MCGs, our problem involves nonsmooth payoff functions and constraints, relaxes the requirement for communication networks, and only relies on the strict monotonicity of pseudo-gradients. Due to the nonsmoothness of payoff functions and constraints, the weaker communication networks as well as the coexistence of cooperation and competition among players, existing generalized Nash equilibrium (GNE) seeking algorithms cannot solve the problem. Also, they pose obstacles to the algorithm design and analysis, mainly because of the non-global Lipschitz continuity of subgradients and the unconnectedness of subnetworks. To seek the variational GNE (vGNE) of the nonsmooth MCGs, we design a distributed subgradient-based algorithm. We prove that the algorithm converges to the exact vGNE of the nonsmooth MCGs from any initial states. Finally, our result is applied to the electricity market games (EMGs) of smart grids. [ABSTRACT FROM AUTHOR]

This paper investigates resource allocation problems, where the cost functions of agents are nonsmooth and the decisions of agents are constrained by heterogeneous local constraints and network resource constraints. We design a distributed subgradient-based algorithm to achieve the optimal resource allocation. Moreover, we analyze the convergence of the algorithm to the optimal solution. The algorithm can solve resource allocation problems with strongly convex cost functions and weight-balanced digraphs, as well as resource allocation problems with strictly convex cost functions and connected undirected graphs. With the algorithm, the decisions of all agents asymptotically converge to the optimal allocation. Simulation examples verify the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

Summary: In this paper, we study the resource allocation problem of second‐order multiagent systems with exogenous disturbances, and the communication networks are weight‐balanced digraphs. Different from the well‐studied resource allocation problems, our problem involves the disturbed second‐order dynamics of agents. In order to achieve the optimal allocation, we propose a distributed algorithm based on gradient descent and internal model approach. Furthermore, we analyze the convergence of the algorithm by constructing a suitable Lyapunov function. Moreover, we prove that the agents in the network can achieve the exact optimal allocation even in the presence of external disturbances. Finally, we provide two examples to illustrate our result. [ABSTRACT FROM AUTHOR]

Abstract In this paper, an aggregative game of Euler–Lagrange (EL) systems is investigated, where the cost functions of all players depend on not only their own decisions but also the aggregate of all decisions. Two distributed algorithms are designed for these heterogeneous EL players to reach the Nash equilibrium of aggregative games. By constructing suitable Lyapunov functions, the convergence of the two algorithms are analyzed. The first algorithm achieves globally exponential convergence without parameter uncertainty, and the other achieves globally asymptotic convergence, even in the presence of uncertain parameters. Numerical examples are given to illustrate the effectiveness of the methods. [ABSTRACT FROM AUTHOR]

Summary: In this paper, an aggregative game of multiagent systems over weight‐balanced digraphs is studied, where the decisions of all players are coupled by linear constraints. Different from the well‐known aggregative games, the dynamics of players are disturbed first‐order linear systems in our problem. In order to seek the variational generalized Nash equilibrium (GNE) of the game, a distributed algorithm is developed via gradient descent, internal model, and dynamic average consensus, where the gradient is for seeking the variational GNE, the internal model is for rejecting the exogenous disturbances, and the dynamic average consensus is for estimating the aggregate of the decisions of all players. The exponential convergence of the algorithm to the variational GNE is analyzed by constructing suitable Lyapunov functions. Finally, the effectiveness of our method is illustrated via two examples. [ABSTRACT FROM AUTHOR]

In this paper, a distributed resource allocation problem with nonsmooth local cost functions is considered, where the interaction among agents is depicted by strongly connected and weight-balanced digraphs. Here the decision variable of each agent is within a local feasibility constraint described as a convex set, and all the decision variables have to satisfy a network resource constraint, which is the sum of available resources. To solve the problem, a distributed continuous-time algorithm is developed by virtue of differentiated projection operations and differential inclusions, and its convergence to the optimal solution is proved via the set-valued LaSalle invariance principle. Furthermore, the exponential convergence of the proposed algorithm can be achieved when the local cost functions are differentiable with Lipschitz gradients and there are no local feasibility constraints. Finally, numerical examples are given to verify the effectiveness of the proposed algorithms. [ABSTRACT FROM AUTHOR]

This paper studies distributed resource allocation problems of multi-agent systems, where the decisions of agents are subject to inequality network resource constraints and local inequality constraints. Compared with well-known resource allocation problems, our problem considers the high-order dynamics of agents. Without involving the control of high-order dynamics, existing distributed resource allocation algorithms cannot deal with our problem. Meanwhile, the high-order dynamics together with the inequality constraints makes it difficult to design and analyze distributed resource allocation algorithms, because the outputs of agents cannot be decided by their inputs directly and the optimal decisions of agents must satisfy the inequality constraints. In order to control the high-order agents to accomplish the resource allocation tasks autonomously, a distributed algorithm is designed by state feedback, gradient descent and primal–dual methods. Moreover, the convergence of the algorithm is analyzed by convex analysis and Lyapunov stability theory. With the algorithm, the high-order agents converge to the optimal allocation. Finally, numerical simulations verify the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, we study the noncooperative games of multi-agent systems. Different from the well-known noncooperative games, our problem involves not only the coupling inequality constraints and the local inequality constraints of decisions, but also the second-order dynamics of players. Due to the second-order dynamics and the inequality constraints, existing generalized Nash equilibrium seeking algorithms for noncooperative games cannot solve our problem. Besides, the second-order dynamics together with the inequality constraints give rise to the difficulties in distributed algorithm design and analysis. In order to seek the variational generalized Nash equilibrium of the games, we design a distributed algorithm based on gradient descent, state feedback and projection operations. Moreover, we analyze the asymptotic convergence of the algorithm via variational analysis and Lyapunov stability theory. Finally, two examples verify the effectiveness of the algorithm. [ABSTRACT FROM AUTHOR]

In this paper, nonsmooth aggregative games are investigated, where the nondifferentiable cost function of every player depends on its own decision as well as the aggregate of the decisions of all players. Moreover, in the problem, the local constraints of players are general and heterogeneous convex sets, and the decisions of players are coupled by linear constraints. For purpose of distributed seeking of the variational generalized Nash equilibrium (GNE) of the game, a distributed algorithm is developed for players. In the algorithm, the dynamic average consensus is used for the estimation of the aggregate of decisions to obtain the approximation of subgradients of cost functions. Besides, the convergence of the algorithm to the variational GNE is analyzed. Finally, simulation examples illustrate the algorithm. [ABSTRACT FROM AUTHOR]