Abstract
This text studies the fixed-time tracking consensus for nonlinear multiagent systems with disturbances. To make the fixed-time tracking consensus, the distributed control protocol based on the integral sliding mode control is proposed; meanwhile, the adjacent followers can be maintained in a limited sensing range. By using the nonsmooth analysis method, sufficient conditions for the fixed-time consensus together with the upper and lower bounds of convergence time are obtained. An example is given to illustrate the potential correctness of the main results.
Highlights
Consensus of multiagent systems (MASs) is a very active research topic in control field [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. e key to consensus problem is through designing an appropriate control protocol, such that all the agents can achieve a certain value. e convergence velocity is an important performance index of a control protocol, and the fast convergence velocity is very important for improving the performance and robustness of a system [4, 7,8,9,10,11,12,13,14,15]
Based on the integral sliding surface, a new control protocol is designed. e main contributions of this paper are as follows: (a) the fixed-time tracking consensus (FdTTC) of MASs with disturbances and nonlinear term is studied; (b) the agents communicating with each other are always maintaining in a limited communication radius; (c) the upper and lower bounds of convergence time that are independent of initial conditions are given; (d) the unknown disturbances and nonlinear terms are not required to satisfy the Lipschitz condition
Suppose Assumptions 1 and 2 hold, and for any t ∈ [0, t1), the distance between followers and their neighbors is less than r. en, under the control protocol (13), each agent of systems (1) and (2) can maintain its dynamic behavior on the sliding surface in a limited time. at is, si(t) 0 and t ∈ [0, t1), ∀ i 1, . . . , N, provided that the control gain α1 > 1 and k5 > c and the convergence time T1 satisfies
Summary
Consensus of multiagent systems (MASs) is a very active research topic in control field [1,2,3,4,5,6,7,8,9,10,11,12,13,14,15]. e key to consensus problem is through designing an appropriate control protocol, such that all the agents can achieve a certain value. e convergence velocity is an important performance index of a control protocol, and the fast convergence velocity is very important for improving the performance and robustness of a system [4, 7,8,9,10,11,12,13,14,15]. Sun et al [30] studied the finite-time connectivitypreserving consensus of second-order MASs with nonlinear terms which did not satisfy the Lipschitz conditions. Hong et al [31] studied the finitetime consensus problem for second-order nonlinear MASs under communication constraints, and the interaction patterns can be preserved for the system with the objection of disturbance rejection, but the display estimation of convergence time is not given. E main contributions of this paper are as follows: (a) the FdTTC of MASs with disturbances and nonlinear term is studied; (b) the agents communicating with each other are always maintaining in a limited communication radius; (c) the upper and lower bounds of convergence time that are independent of initial conditions are given; (d) the unknown disturbances and nonlinear terms are not required to satisfy the Lipschitz condition.
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