Adaptive fuzzy finite‐time consensus tracking for multiple Euler‐Lagrange systems with unknown control directions

Abstract

In this paper, the problem of adaptive fuzzy finite-time consensus tracking control for multiple Euler-Lagrange systems (ELSs) with uncertain dynamics and unknown control directions (UCDs) is investigated. The computational complexity problem in conventional backstepping is avoided by using finite-time command filter (FTCF), and the error in the filtering process is eliminated through error compensation signals. The fuzzy logic system combined with the adaptive control technique is applied to approximate and estimate the unknown nonlinear dynamics of ELS. The Nussbaum function-based continuous and nonsmooth input control torque is established to eliminate the influence of UCDs, and the proposed control scheme can guarantee the consensus tracking errors converge to the desired neighborhood of the origin within a finite time. Numerical simulation is used to test the effectiveness of the given algorithm.

Adaptive finite‐time consensus tracking control for nonlinear multiagent systems in nonstrict feedback form with full‐state constraints

“…The Assumption 1 is also given in References 24-27, and from Assumption 1, we know that both functions h (q) i,p (⋅) and f (q) i,p (⋅) are each Lipschitz on Ω d . The Assumption 2 is a general assumption for solving consensus tracking problems of MASs as in References 22,23,26,27, since it can guarantee the conclusion in Lemma 1 is hold.…”

“…The dynamic surface control was extended to solve the consensus problems for full‐sate constrained MASs in References 22,23, but how to deal with the filtering errors caused by the filtering process is not considered, which will reduce the control performance. To solve this problem, the command filtered backstepping with error compensation mechanism has been studied for nonlinear systems in References 24,25 and for MASs in References 26,27, which ensures the filtering performance with the elimination of filtering errors. Based on the command filtered backstepping, the output constraint and full‐state constraints problems were investigated for nonlinear systems in References 28,29, and the output constraint problem was studied for MASs in Reference 30.…”

“…Compared with the command filtered backstepping methods in References 24,26 and finite‐time command filtered backstepping methods in References 25,27,33,35, the full‐state constraints are considered, which cannot only ensure the desired consensus tracking performance, but also guarantee the predefined state constraints are not violated. Furthermore, the proposed finite‐time command filtered backstepping can also solve the explosion of complexity problem in traditional backstepping based finite‐time control methods in References 31,32,34 and compensate the filtering errors for dynamic surface control method in Reference 37.…”

“…Compared with the backstepping based asymptotically convergent tracking control methods for state constrained nonlinear systems in References 28,29 and asymptotically convergent consensus tracking control methods for state constrained nonlinear MASs in References 22,23,30, the finite‐time consensus tracking control problem is further studied, which can guarantee the closed‐loop system has faster convergence rate. What's more, the nonstrict feedback form is further considered, which is more appropriate to the actual systems. Compared with the command filtered backstepping methods in References 24,26 and finite‐time command filtered backstepping methods in References 25,27,33,35, the full‐state constraints are considered, which cannot only ensure the desired consensus tracking performance, but also guarantee the predefined state constraints are not violated. Furthermore, the proposed finite‐time command filtered backstepping can also solve the explosion of complexity problem in traditional backstepping based finite‐time control methods in References 31,32,34 and compensate the filtering errors for dynamic surface control method in Reference 37. …”

Nonlinear PI robust adaptive control for uncertain multiple‐input multiple‐output nonlinear systems: Application to the visual servoing problem

“…10 This method has received considerable attention over the years due to its flexibility and versatility with applications to general classes of nonlinear systems with unknown parameters and nonlinearities. [11][12][13][14][15][16][17][18][19][20][21][22][23][24][25][26][27][28][29][30] For nonlinear MIMO systems with unknown nonlinearities and control directions, adaptive fuzzy control laws with Nussbaum gains were proposed in References 31,32 to solve the output tracking problem.…”