Control And Stability Analysis Of Multi-Agent Systems

The research of multi-agent systems has gained great interests during the last decade, the problem of related control theory are studied in this dissertation, such as control law and stability analysis. The main research works are concluded as follows:(1) The control law and stability analysis with artificial potential field are studied. In two dimension circumstance based on the double integrator mathematic model, a new set of potential functions are presented by referring the concepts of electric field, then a new formation control method is proposed, in which the potential functions are used between agent-agent and between agent-obstacle while Proportional -Differential control is applied for multi-agent system and its goal. Stability of this method is proven. Then a reformative planning strategy is proposed for path planning. This strategy is aimed at a class of local minima which are formed by the obstacle surrounding, this will help reduce the paths of agents and improve the control efficiency. The stability of the original system is kept.(2) A new sliding mode control strategy of multi-agent systems is studied in three dimensions. Sliding mode control is with no limitation of dimension and has good robustness. The method proposed in this paper is based on sliding mode control combined with artificial potentials and graph theory. It can be widely used to deal with the nonlinear plant in three dimensional spaces, it also can track moving goals or set positions robustly with obstacles in circumstances while keep formation. The stability of the control strategy is proven by choosing proper Lyapunov function.(3) The stability of multi-agent system is studied. A new definition of Input-to-State String Stability is proposed, mean to analyze the string stability from the input-to-state view. String is a basic structure of many multi-agent systems. By viewing the interconnection as a kind of input to subsystems, sufficient conditions of string stability for a class of weak interconnected nonlinear systems are deduced, which is based on the input-to-state stability analysis and singular perturbation theory.(4) The method of formation change is studied. Different change forms are classified. The multi-agent system structure can be figured by graph. Some properties of formation can be achieved by analyzing the connectivity, rigid or matrix of relative graphs. The relationship of different agents changes according to the variety in environment. The control arithmetic of reform and split for multi-agent stracture are considered based on the graph theory.