Consensus For Descriptor Multi-agent Systems

Since the theory of descriptor systems was put forward, it has provided an exten-sive application background and gradually developed into an important branch of con-trol theory. Descriptor systems, as a form of differential algebraic equations, are betterable to maintain physical characteristics of systems, especially in some coupled systemswhere constraints characterized by algebraic equations indeed exist between some phys-ical quantities. Meanwhile, many practical systems can not be described by normal sys-tems but descriptor systems. This thesis puts an intensive study on consensus problemsfor networked multi-agent systems composed of descriptor systems based on algebra,graph, descriptor system theory and the networked predictive control method. Moreover,the related conclusions of consensus problems for multi-agent systems are promoted todescriptor multi-agent systems.Firstly, for a class of homogeneous descriptor multi-agent systems, the consensusprotocol of state feedback form is proposed and designed. Su?cient and necessary con-ditions are obtained to solve the consensus problem of descriptor multi-agent systems.In addition, because states can not be measured directly or measuring equipments haveeconomy or using limitations in practical systems, usually states are di?cult to be ob-tained directly, so that the systems can not realize state feedback directly. Thus, theconsensus protocol of static output feedback form is proposed and designed under the cir-cumstance that states of the agents can not be measured but their outputs can be measured.Meanwhile, su?cient and necessary conditions are obtained which can guarantee that theprotocol solves the consensus problem for descriptor multi-agent systems. To overcomethe limitation that static output feedback can not fully achieve the function of state feed-back, the consensus protocol of dynamic compensator(dynamic output feedback) formis proposed and designed which can increase freedom degrees of design methods. Su?-cient and necessary conditions are obtained to solve the consensus problem of descriptormulti-agent systems under reasonable assumptions. Moreover, based on the solution todescriptor Ricatti equation, specific design steps of the proposed protocols are also pro-vided.Secondly, due to the impact of external environment, or factors of specific task dis-tribution, characteristics and dynamic models of coupled agents may be different, andthese systems are called heterogeneous multi-agent systems. For a class of heteroge-neous descriptor multi-agent systems, under the circumstance that state of each agent hasthe same dimensions, the consensus protocol of state feedback form is proposed and de-signed. Su?cient and necessary conditions are obtained to solve the consensus problemof heterogeneous descriptor multi-agent systems. In addition, for circumstances that s-tates can not be measured but their outputs can be measured and states of each agent havedifferent dimensions, the consensus protocol of static output feedback form is proposedand designed. Su?cient and necessary conditions are obtained to solve consensus prob-lem of heterogeneous descriptor multi-agent systems. The given conditions depend onnot only topologies of the descriptor multi-agent systems but also structure properties ofeach agent dynamics.Thirdly, when agents exchange information through a wired or wireless network,due to the limitations of network bandwidth and transmission speed, network inducedcommunication delays will appear inevitably. However, the communication delays usual-ly affect the performance of networked multi-agents, and even lead to systems instability.For networked descriptor multi-agent systems with no communication delays, the con-sensus protocol of static output feedback form is proposed and designed. Su?cient andnecessary conditions are obtained which can guarantee that the protocol solves the con-sensus problem for descriptor multi-agent systems. In addition, for networked descriptormulti-agent systems with communication delays, based on the networked predictive con-trol method, network communication delays are compensated actively. The consensusprotocols of static output feedback and dynamic compensator form are proposed and de-signed, respectively. Moreover, su?cient and necessary conditions are obtained for twoprotocols to solve the consensus problem of networked descriptor multi-agent system-s, respectively. Based on the solution to Ricatti equation, detailed design steps of theproposed protocols are also given.Feasibility and effectiveness of the theoretical results obtained in this paper are ver-ified through simulation examples.