Event-Triggered-Based Consensus Neural Network Tracking Control for Nonlinear Pure-Feedback Multiagent Systems With Delayed Full-State Constraints

This paper investigates the consensusability for a class of nonlinear pure-feedback multiagent systems (MASs) with delayed full-state constraints. First, by using a novel state-shifting transformation (SST), the constrained states are encapsulated into some barrier functions such that the new converted state variables and their dynamic model are generated. Then, the essential relationship between the post-transformation tracking errors and the pre-transformation tracking errors are further explained. By employing the radial basis function neural networks (RBF NNs) to deal with the unknown nonlinearities for each agent and introducing a relative threshold method to overcome the waste problem of system transmission resources, an event-triggered control protocol is developed for the considered system. The proposed protocol has its own advantages: 1) This is the first work to consider the pure-feedback MASs with delayed full-state constraints. By transforming the constrained states into unconstrained variables, the states of the MASs can be converged into ideal ranges within a predefined time <inline-formula> <tex-math notation="LaTeX">$T$ </tex-math></inline-formula>; 2) Under this control protocol, only one adaptive law is necessary to be updated online in each follower and the use efficiency of system resources is improved by using reasonable event triggering mechanism. Finally, the effectiveness of the suggested consensus control protocol is demonstrated by the simulation results. Note to Practitioners—Delayed constraints often encountered in practical applications, which represent a type of constraints that may be violated initially but required to be satisfied sometime after system operation, so it is very necessary and important to converge states into ideal ranges within a predefined time when delayed constraints required. What’s more, considering the requirement of high control accuracy in practical application and the current Barrier Lyapunov Function (BLF) methods need to restrict the virtual control signals within some given regions, such restrictive conditions make the design and implementation of the traditional controllers particularly difficult. In this article, the control protocol for a class of nonlinear pure-feedback MASs with delayed full-state constraints and event-triggered communication are constructed to promote the development of asymptotic tracking control methods, and a novel state-shifting transformation is used to ensure the system states could be converged into the ideal constrained intervals in a predefined time.