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This paper studies the globally fuzzy consensus of stochastic nonlinear multi-agent systems (MAS) with hybrid-order dynamics. The followers are modeled as hybrid first- and second-order systems. The leader is presented as second-order system and can transmit his own states to the first- and second-order followers. In view of the local characteristics of communication among agents, the followers can be decomposed into two categories: one is the set of followers who can communicate with the leader, and the other is the set of followers who cannot communicate with the leader. Using the design method of fuzzy feed-forward compensator and Lyapunov stability theory, a new hybrid fuzzy consensus controller is designed for the two kinds of follower sets. Compared with most stochastic MAS, the proposed algorithm not only solves the consensus of hybrid-order stochastic MAS based on fuzzy approximator, but also obtains the results of globally uniform ultimate bounded (GUUD). In the end, the simulation results further verify the validity of the proposed algorithm. • Distributed control problems of stochastic mixed-order multi-agent systems are solved. • A new class of Lyapunov functions is constructed to reduce the conservatism of algorithm design. • Globally fuzzy consensus results are obtained. [ABSTRACT FROM AUTHOR]

Abstract: In this paper, a global optimization algorithm is proposed for solving sum of generalized polynomial ratios problem (P) which arises in various practical problems. Due to its intrinsic difficulty, less work has been devoted to globally solve the problem (P). For such problems, we present a branch and bound algorithm. In this method, by utilizing exponent transformation and new three-level linear relaxation method, a sequence of linear relaxation programming of the initial nonconvex programming problem (P) are derived which are embedded in a branch and bound algorithm. The proposed method need not introduce new variables and constraints and it is convergent to the global minimum of prime problem by means of the subsequent solutions of a series of linear programming problems. Several numerical examples in the literatures are tested to demonstrate that the proposed algorithm can systematically solve these examples to find the approximate ϵ-global optimum. [Copyright &y& Elsevier]