No abstract

In this paper, we study a distributed optimization problem using a subgradient projection algorithm for multi-agent systems subject to nonidentical constraints and communication delays under local communication. Here the agents capable of communicating with their local neighbors are constrained to remain in possibly different closed convex sets and optimize a global objective function composed of a sum of local objective functions, each of which is known to only one agent. First, we consider the case of fixed graphs and show that distributed optimization might not be achieved on general strongly connected directed graphs. Instead, the agents optimize a weighted sum of the local objective functions. Then we consider the case of switching graphs and show that distributed optimization can be achieved when the adjacency matrices are doubly stochastic and the union of the directed graphs is strongly connected among each time interval of a certain bounded length. Furthermore, we consider the case of communication delays, where the delays are mutually independent. It is shown that the distributed optimization problem can be solved by introducing additional delays to the subgradient projection algorithm and the communication delays can be arbitrarily bounded. Finally, numerical examples are included to show the obtained theoretical results.

In this paper, we present a distributed economic dispatch (ED) strategy based on projected gradient and finitetime average consensus algorithms for smart grid systems. Both conventional thermal generators and wind turbines are taken into account in the ED model. By decomposing the centralized optimization into optimizations at local agents, a scheme is proposed for each agent to iteratively estimate a solution of the optimization problem in a distributed manner with limited communication among neighbors. It is theoretically shown that the estimated solutions of all the agents reach consensus of the optimal solution asymptomatically. This scheme also brings some advantages, such as plug-and-play property. Different from most existing distributed methods, the private confidential information, such as gradient or incremental cost of each generator, is not required for the information exchange, which makes more sense in real applications. Besides, the proposed method not only handles quadratic, but also nonquadratic convex cost functions with arbitrary initial values. Several case studies implemented on six-bus power system, as well as the IEEE 30-bus power system, are discussed and tested to validate the proposed method.

This paper studies the output containment control of linear heterogeneous multi-agent systems, where the system dynamics and even the state dimensions can generally be different. Since the states can have different dimensions, standard results from state containment control do not apply. Therefore, the control objective is to guarantee the convergence of the output of each follower to the dynamic convex hull spanned by the outputs of leaders. This can be achieved by making certain output containment errors go to zero asymptotically. Based on this formulation, two different control protocols, namely, full-state feedback and static output-feedback, are designed based on internal model principles. Sufficient local conditions for the existence of the proposed control protocols are developed in terms of stabilizing the local followers' dynamics and satisfying a certain H∞ criterion. Unified design procedures to solve the proposed two control protocols are presented by formulation and solution of certain local state-feedback and static output-feedback problems, respectively. Numerical simulations are given to validate the proposed control protocols.