Estimation Of The Domain Of Consensus For Multi-agent Systems With Actuator Saturation

Regional consensus of multi-agent systems with actuator saturation is a new topic.For multi-agent systems whose global or semi-global consensus cannot be reached,we design algorithms to achieve regional consensus in a bounded set.This set will act as an estimation of the domain of consensus.By reducing conservatism of the algorithms,the size of estimation can be enlarged.The main content and innovation are summarized as follows.(1)For multi-agent systems with actuator saturation,a consensus is reached within the level set of Laplacian quadratic functions.We firstly extend the convex hull representation to enable it to deal with saturation nonlinearity in multi-agent systems.Then two kinds of sufficient conditions are proposed to guarantee that a consensus can be achieved in the level sets of a group of Laplacian quadratic functions,thus these level sets can be used as an estimation of the domain of consensus.By transforming the conditions into linear matrix inequalities,we formulate an optimization problem for obtaining the largest level set.(2)For multi-agent systems with actuator saturation,a consensus is reached within the level set of composite Laplacian quadratic functions(CLQs).We firstly prove that the level set of CLQs is equal to the convex hull of a group of Laplacian quadratic functions.Sufficient conditions in the form of linear and bilinear matrix inequalities are proposed to guarantee a consensus in the level set of CLQs,thus the level set acts as an estimation of the domain of consensus.Finally,an improved convex hull representation is utilized to reduce conservatism of the algorithms.