Distributed adaptive control for consensus tracking with application to formation control of nonholonomic mobile robots

Abstract

In this paper, we investigate the output consensus problem of tracking a desired trajectory for a class of systems consisting of multiple nonlinear subsystems with intrinsic mismatched unknown parameters. The subsystems are allowed to have non-identical dynamics, whereas with similar structures and the same yet arbitrary system order. Suppose that the communications among the subsystems can be represented by a directed graph. Different from the traditional centralized tracking control problem, only a subset of the subsystems can obtain the desired trajectory information directly. A distributed adaptive control approach based on backstepping technique is proposed. By introducing the estimates to account for the parametric uncertainties of the desired trajectory and its neighbors' dynamics into the local controller of each subsystem, the information exchanges of online parameter estimates and local synchronization errors among linked subsystems can be avoided. It is proved that the boundedness of all closed-loop signals and the asymptotically consensus tracking for all the subsystems' outputs are ensured. In simulation studies, a numerical example is illustrated to show the effectiveness of the proposed control scheme. Moreover, the design strategy is successfully applied to solve a formation control problem for multiple nonholonomic mobile robots.

Distributed adaptive repetitive consensus control framework for uncertain nonlinear leader–follower multi-agent systems

“…In this section, two simulation examples are presented to illustrate the effectiveness of the distributed learning control protocol (25) and the parameter updating laws (27)- (28). An communication graph representing five follower agents and one leader is shown in Fig.…”

“…Theorem 3: Let the graphḠ be connected. Consider the multi-agent systems (22)-(23) under Assumptions 1-2 and apply the distributed learning control protocol (25) and the parameter updating laws (27)- (28) with the general formation errors defined in (49). Then, all follower agents reach the desired formation in L 2 T -sense as time approaches infinity, i.e., lim t→∞ t t−T (δ i (τ)) 2 dτ = 0, i = 1, 2, .…”

“…In comparison with the previous work, we note that when the dynamic of the agent includes the time-varying parametric uncertainties, which can not be solved by the adaptive algorithms proposed in [24][25][26][27][28][29][30]. To solve the consensus problem of the multi-agent systems with time-varying parametric uncertainties, much attention has been focused on the study of multi-agent systems by using adaptive iterative learning control [31][32][33].…”

“…Then, in the literature [27], the Email addresses: jinsha0321@163.com (Jinsha Li a ), madaniel@cityu.edu.hk (Daniel W. C. Ho b ), jmli@mail.xidian.edu.cn (Junmin Li a ) 1 authors extended the results in [26] to consensus for agents having second-order dynamics in the Brunovsky form and solved the second-order synchronization tracking problem for heterogeneous nodes with non-identical unknown nonlinear dynamics and unknown disturbances. The output consensus tracking problem has been investigated for a collection of nonlinear subsystems with intrinsic mismatched unknown parameters in [28]. Distributed cooperative adaptive laws were proposed to estimate the unknown parameters of distributed cooperative adaptive systems [29].…”

Cooperative adaptive fault‐tolerant tracking control for a class of multi‐agent systems with actuator failures and mismatched parameter uncertainties

“…Very recently, by introducing non-linear function relied on relative local state information to design distributed protocol, robust consensus problem of networks of agents subject to matching uncertainties are investigated in [17,18]. By means of the technique of adaptive backstepping, a distributed consensus tracking control scheme for a class of non-linear MAS with mismatched uncertainties is proposed in [19]. It is worth mentioning that the results in [14][15][16][17][18] are developed based on the assumptions that the considered uncertainties satisfy matching condition.…”