On Cooperative Behavior And Optimization Of Multi-Agent Networks

In recent years, multi-agent networks have drawn much attention due to its broad applications in decentralized sensor networks, multi-robot cooperation, UAVs (Unmanned Aerial Vehicles) formation flight, joint missile attack operation, and so on. Multi-agent networks (MANs) represent a kind of complex dynamical systems that consists of a collection of interactive autonomous or semi-autonomous agents, connected through an underlying network. Biological networks in nature can be a typical kind of multi-agent networks, where agents may emerge complexity behaviors, like self-organization, self-adaption, autonomy and aggregation. Due to these swarm intelligence features, multi-agent networks have been widely applied for many real-world systems, such as Internet, Internet of Things, Smart grids, Highway networks. Nowadays, with increasing updates in science and technology, multi-agent collaboration and optimization show more and greater vitalities in economic development, national defense construction, scientific exploration and people’s daily life.In view of many practical multi-agent networks, there are many difficulties in how to model and control multi-agent networks. Based on the existing research, this dissertation takes into account some fundamental issues about cooperative behavior and optimization of multi-agent networks. By techniques of differential dynamics, matrix theory, algebraic graph theory, mathematical programming and stochastic analysis, multiple and hybrid cooperative behaviors are characterized with proper performance-related metric, and some new results are obtained to support the existing research. The main contributions of this dissertation are summarized below.Consensus of second-order multi-agent networks is studied from a perspective of guaranteed performance. A linear quadratic type (LQ-type) index function is introduced to describe the performance of agents. Taking the advantage of impulsive control, a hybrid control scheme is designed to ensure consensus and performance guarantee in multi-agent networks simultaneously. Detailed analysis is carried out based on theories of impulsive differential equations. It is shown that this setting of coordination control and performance has good applications in path planning for UAVs or robots.Multi-consensus is studied for multi-agent networks with generic undirected topologie. To realize multi-consensus, a clustering policy is designed for agents to evolve into several potential subgroups dynamically, and a joint scheme of cooperation and competition is established to ensure certain level of multi-agent separation. An event-based control algorithm is proposed selected sampled data. Based on LaSalle’s invariance principle, a concise condition is established to guarantee multi-consensus of multi-agent networks. Simulation results further validate the developed theoretical results.Hybrid subgroup coordination is introduced and discussed within the framework of multi-agent networks. In view of some unanticipated practical situations, hybrid subgroup coordination depicts a kind of cooperative behaviors that agents in one subgroup achieve a synchronous regime asymptotically, but the convergent scenario is of different type for different subgroup. The convergence analysis is developed based on theories of graph and matrix. It is demonstrated that by choosing proper coupling weights, the obtained results can contain some existing group consensus results.The optimal consensus control problem is studied for multi-agent networks under limited communication channel. To overcome constrained communication, a novel kind of gossip-type subgradient control algorithm is proposed with quantized data, and the technique of dither is adopted to deal with quantization errors. Using techniques of convex analysis and stochastic approximation, a sufficient condition is obtained to guarantee optimal consensus of multi-agent networks almost surely. It is shown that by the proposed gossip-type control algorithm, multi-agent networks can achieve optimal consensus with less communication.Concerning with multi-agent optimization, a new kind of consensus-based distributed subgradient algorithms is designed with better convergence. Compared with the existing results, an alternative subgradient algorithm is introduced based on two level subgradient iterations, where the first level is to minimize the component functions, and the second to enforce theiterates not oscillate from the constraint set wildly. Detailed convergence is established using matrix theories and the super-martingale convergence theorem.Finally, a summary of the full dissertation is carried out, and some potential future works are discussed.