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Guaranteed‐Performance Consensualization for High‐Order Lipschitz Nonlinear Multi‐Agent Systems with Balanced Directed Switching Topologies
Author(s) -
Zheng Tang,
Xi Jianxiang,
Fan Zhiliang,
Liu Guangbin
Publication year - 2019
Publication title -
asian journal of control
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.769
H-Index - 53
eISSN - 1934-6093
pISSN - 1561-8625
DOI - 10.1002/asjc.1805
Subject(s) - lipschitz continuity , network topology , control theory (sociology) , nonlinear system , mathematics , multi agent system , exponential stability , quadratic equation , linear matrix inequality , mathematical optimization , topology (electrical circuits) , computer science , control (management) , mathematical analysis , physics , geometry , quantum mechanics , artificial intelligence , combinatorics , operating system
Guaranteed‐performance consensus design problems for both the leaderless and leader‐following high‐order multi‐agent systems with balanced directed switching topologies and Lipschitz nonlinear dynamics are investigated. Consensus protocols and quadratic performance functions based on state errors are proposed to obtain the guaranteed‐performance consensus. By a state decomposition method, the consensualization problems for leaderless cases are transformed into asymptotic stability ones of a reduced‐order subsystem and the guaranteed‐performance cost is determined by the Lyapunov stability analysis of the reduced‐order subsystem, and the state error method is utilized to deal with the guaranteed‐performance consensualization problems for leader‐following cases. Then, by using the structure property of the transformation matrix and the Lipschitz condition, the impacts of Lipschitz nonlinear terms can be determined. Moreover, guaranteed‐performance consensualization criteria are presented based on linear matrix inequalities for both leaderless and leader‐following cases with directed switching topologies. Furthermore, the guaranteed‐performance costs are determined, which can respectively reflect the structures of the interaction topologies of leaderless and leader‐following cases. Finally, two numerical simulations are presented to verify the validity of theoretical results.