Multi-target Flocking Control And Distributed Formation Topology Optimizing For Multi-agent Systems

The cooperative control for multi-agent systems is a hot issue of control theory.During past few years, great progress has been made on this issue. One of the importantsubjects of cooperative control for multi-agent systems is flocking control. Due to therequirements of real multi-agent systems in multi-mission executing and energy saving,this thesis investigates some algorithms of multi-target flocking and distributed topologyoptimizing for multi-agent systems.Most current studies mainly concerned the flocking of single-target tracking andalways didn't consider the speed constraints. According to the requirements of realsystems in multi-mission executing, this thesis presents a flocking algorithm ofmulti-target tracking for multi-agent systems. A probability function is designed to choosetargets for agents. Then, a class of potential functions is built so that the controlled agentscan track their targets simultaneously. In the controller design, the speed is controlled tokeep the flocking smoothly.Analyzing the action of "neighbor rule" in flocking, we find that many interactionsbetween agents are unnecessary, which increase the energy consuming of agents. To solvethe energy saving problem in flocking, this thesis investigates the topology controlmethods by using min-weighted rigid graph so that the communication complexity ofsystems would be decreased and the topology could be optimized. Based on rigiditymatrix, the thesis presents an algebraic algorithm of min-weighted rigid graph generation,and then further creates an algorithm of min-weighted persistent graph generation, whichcan further decrease the communication complexity. At last, considering the rangeconstraints of multi-agent systems, the thesis presents a topology optimizing algorithmbased on min-weighted persistent graph.However, the above algorithms are centralized, and are hardly used to optimize thetopologies of large scale multi-agent systems. So, the thesis improves the algorithm ofmini-weighted rigid graph generation. Based on the centralized algorithm, we analyze therelationship between global rigid graph and local rigid graph, and prove that the local rigid graph can be replaced by another rigid graph without changing the rigidity of the globalgraph. We also find that the global min-weighted rigid graph can be generated by localoperations. Based on those above theories, a distributed algorithm of topology optimizingis presented based on min-weighted rigid graph.