Design Of Local Control With PID Controller For Multi-Agent Dynamical Systems

Multi-agent systems is the forum of the control theory and artificial intelligence, at the same time, a vital branch of the distributed artificial intelligence, which is aimed to transform the complex, large scale system into administrative, small subsystems. Each agent has the same objective and share information with its neighbor agent. Along with the rapid and sustained developing of the computer science, artificial intelligence theory and modern control theory, multi-agent dynamical systems has gradually gained popularity, receiving more and more attention in many different research fields. Local control strategy is to further simplify the distributed control strategy, we put controllers on one or part of the system to make sure the lower complicated, especially with low operational costs, high robustness and less system requirements.In this paper, we focus on investigating consensus problem for local control of multi-agent system. If every two agent in a given system are connected and a reference signal is a step function, the states of all agents in the system can reach a same value agreement, i.e., consensus. And solve the corresponding PID parameters for stabilizing the local control system. For the linear plant with no time delay, based on generalized Hermite-Biehler theorem, determine the stability range of the proportional gain; determine the stable region in the integral and differential plane with a fixed proportional gain, reflecting the linear programming property. For the system with time delay, use the extension of D-decomposition for the comfirm boundary line to determine the stable region in the integral and differential plane. By traverse all values of proportional gain, can receive the three-dimensional PID controller parameters stability regions. The proposed two methods are appropriate for the stable, unstable system, this will provide effective techniques for settings of the parameters in local PID control system. Simulation examples show the effectiveness of the algorithm.