Some Problems In Cooperative Control Of Multi-agent Systems

The notion for an "agent" is an abstract of general physical realities. Agents refer to those that have the ability of computing, sensing and properly reacting to its surrounding neighborhood (including other neighboring agents). Different from problems concerning a single agent, what interests researchers when studying multi-agnet problems is how to design distributed protocols for every agent, so that the multi-agent system, as a whole, can emerge highly collaborative behaviors. The collaborative behaviors witnessed in multi-agent systems indicate that, consensus behaviors (or states) is reachable for a multi-agent system even if there is no centralized coordinating commander.Consensus is an important and fundamental problem in cooperative control of multi-agent systems. Viewed from its objective, the consensus problem looks similar to the coupled synchro-nization problem studied extensively in physics or biology communities. However, the focus of consensus problems, as well as the theoretic tool to tackle such problems, is very different from that of coupled synchronization problems. First of all, consensus problems are mostly set in in-termittent communication topologies:in intermittent topologies, every agent receives information from its neighbors with unpredictable intermissions. This characteristic appropriately describes the interaction mode of multi-agent systems such as a school of fish, or bird flocks. Next, due to the intermittent-topology assumption, the tools to tackle consensus problems are no longer confined to pole assignment techniques or quadratic Lyapunov function of the classic control theory, but other novel theories. Based on three widely used consensus protocols (including first-order protocols, passivity-based protocols and general high-order protocols) illustrated in the thesis, we come to some new conclusions on consensus of multi-agent systems, after a further investigation of these protocols. The main contributions of this thesis can be summarized as follows:1. A first-order consensus protocol suitable for nonlinear systems is designed. The advantage of the protocol is its compatibility to uniformly-jointly-connected (UJC) communication topologies and unknown coupling time-delays.2. The convergence rate of discrete-time first-order protocols is estimated, under the assump- tion that the communication topology is UJC and unweighted. A lower bound on its convergence rate is provided. Moreover, we proposed the least connective topology (in the sense of scrambling constant) for unweighted graphs.3. A switching-logic and passivity based consensus algorithm is designed. By selectively keep the communication channel between two neighboring agents on and off through switching logic, we are able to achieve output consensus of passive multi-agent systems. The advantage of the proposed consensus algorithm is its compatibility to UJC communication topologies and unknown coupling time-delays.4. The "pairwise output synchronization" problem of multi-agent system is proposed and then investigated, which means that, synchronization is achieved for each pair of output signals of each pair of agents. Different pairs of synchronized output signals need not to be the same. This problem can be viewed as a generalization of output synchronization problems. The consensus protocol adopted in the related chapter is passivity based, too.5. The cooperative control strategy of multi-agent systems is designed based on output reg-ulation theory. The objective of the cooperative output regulation of a multi-agent system is to achieve cooperatively asymptotically tracking signals produced a common exosystem. The co-operative control law proposed in this thesis apples to fixed topology. The cooperative output regulation problem is investigated for both state-space models and transfer-function models. For state-space models, the analysis tools are algebraic graph theory and H∞ control theory, while for transfer-function models, the analysis tools is main complex root locus techniques.