Abstract
In this brief, we study the distributed adaptive fixed-time tracking consensus control problem for multiple strict-feedback systems with uncertain nonlinearities under a directed graph topology. It is assumed that the leader’s output is time varying and has been accessed by only a small fraction of followers in a group. The distributed fixed-time tracking consensus control is proposed to design local consensus controllers in order to guarantee the consensus tracking between the followers and the leader and ensure the error convergence time is independent of the systems’ initial state. The function approximation technique using radial basis function neural networks (RBFNNs) is employed to compensate for unknown nonlinear terms induced from the controller design procedure. From the Lyapunov stability theorem and graph theory, it is shown that, by using the proposed fixed-time control strategy, all signals in the closed-loop system and the consensus tracking errors are cooperatively semiglobally uniformly bounded and the errors converge to a neighborhood of the origin within a fixed time. Finally, the effectiveness of the proposed control strategy has been proved by rigorous stability analysis and two simulation examples.
Highlights
In the past decade, the finite-time consensus control of the multiagent has become one of the hot topics, since the finitetime control has a faster convergence rate, higher precision, and more robustness
In [11], power integrator technique was employed to solve the problem of finite-time consensus control for multiagent systems (MASs) with double integrator dynamics
There is a limitation for the finite-time consensus control results that the convergence time is seriously dependent on the MASs’ initial states. at is to say, once the initial state is far away from the equilibrium point, the convergence time will increase as a result
Summary
The finite-time consensus control of the multiagent has become one of the hot topics, since the finitetime control has a faster convergence rate, higher precision, and more robustness. Motivated by the above observations, in this paper, a distributed adaptive fixed-time tracking consensus control is proposed for multiple strict-feedback systems with unknown nonlinearities under a directed graph topology. (1) A novel method to solve distributed adaptive fixed-time tracking consensus control for strict-feedback nonlinear MASs has been proposed. (2) In order to solve the “complexity explosion” problem caused by the repeated differentiation in the controller design process, it is different from the traditional dynamic surface technique; this paper constructs a smooth function M(Z)derived fro·m Lyapunov stability to compensate the part of (z]i/zθi)θ i in the differential of the virtual controller vi, while the other part of the differential is approximated by RBF neural networks. (4) RBF neural networks are introduced to approximate the unknown functions fi(·) in MASs to make our designed fixed-time control can suitable more systems with complex dynamics.
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