Fixed‐time adaptive neural tracking control for a class of uncertain multi‐input and multi‐output nonlinear pure‐feedback systems

Abstract

This study examines the fixed-time adaptive neural network tracking control problem for a class of unknown multi-input and multi-output (MIMO) nonlinear pure-feedback systems. The introduction of the radial basis function resolves uncertain problems of unknown MIMO systems. The mean value theorem is introduced to overcome the controller design problem attributed to the nonaffine structure in pure-feedback systems. Moreover, a novel fixed-time virtual controller and an actual controller are designed to solve the issue of previous single-input and single-output and MIMO systems that have no solution in the negative domain and at the origin in finite-and fixed-time controls. Furthermore, a design method is proposed. The final designed controller ensures that all signals in the system are bounded. Simulation experiments show that the designed fixed-time controller facilitates smaller tracking error of the system compared with other finite-or fixed-time controllers. Furthermore, the selection of appropriate design parameters allows the tracking error to converge on a small neighborhood of the origin in a fixed time. K E Y W O R D S fixed-time control, multi-input and multi-output nonlinear systems, nonlinear pure-feedback systems, RBF neural network 262

Fixed‐time adaptive neural tracking control for nonlinear multiagent systems with communication link faults

“…Furthermore, the control strategy proposed in this paper is compared with the findings of other studies. Upon comparison, it is evident that the tracking performance of the system in this paper, as illustrated in Figure 21, outperforms that of the systems in References 19 and 43 (refer to Figures 26 and 28, respectively).…”

“…Reference 19 demonstrates the tracking error and control input under practical fixed‐time control, depicted in Figures 26 and 27.…”

“…Moreover, conventional control methods are incapable of meeting the fast stabilization requirements for high‐order nonlinear strict‐feedback MASs under communication link faults, necessitating the development of finite‐time control to achieve rapid stabilization 18 . However, the settling time of finite‐time control is influenced by the system's initial state 19,20 . To tackle this issue, Polyakov et al proposed a fixed‐time stability scheme 21‐23 .…”

“…| | z i,k | | ≥ 𝜆 i,k 0, | | z i,k | | < 𝜆 i,k(20)where 𝜆 i,k with k = 1, 2, … , n i is a positive design parameter. Combining(19) and(20), we have the following properties…”

Adaptive controller design for fixed‐time bipartite consensus of multi‐agent systems with disturbances

“…In addition, parameters will adjust themselves over time and affect the consensus of fixed time. At the same time, adaptive controller design for fixed‐time has also been studied in Reference 20–23. Therefore, the timing bipartite consensus of network agents with both adaptive controller and disturbances is rarely researched.…”