PID Control of Nonlinear Multi-agent System Based on Generalized Frequency Response Function

Abstract

AbstractIn practical applications, the multi-agent system often has nonlinear characteristics, therefore, studying the cooperative control of the nonlinear multi-agent system plays a vital role. The stability of each nonlinear agent is the fundamental requirement for the analysis of multi-agent system. In this paper, a new stability criterion of the nonlinear systems which are able to be represented by polynomial differential equations is derived by using the input–output stability theorem for nonlinear systems, based on generalized frequency response function (GFRF). According to such the resultant, the parameter stability domain of distributed PID controllers for the nonlinear system with multiple agents can be obtained. This stability domain is the intersection set of the parameter stability domains of each nonlinear subsystem which is obtained by decoupling the multi-agent system according to its communication topology. The consistency of the given nonlinear system with multiple agents is able to be achieved by using any parameters of distributed PID controller in the obtained stability region. The proposed method is applicable to general polynomial nonlinear system with arbitrary nonlinear order theoretically. On the basis of theoretical analysis, the proposed simulation verifies the effectiveness of this method.KeywordsNonlinear systemPID controlStability regionGFRF