Distributed adaptive consensus and output tracking of unknown linear systems on directed graphs

Abstract

a b s t r a c tThis paper considers both the distributed consensus control and output tracking problems of a group of unknown linear subsystems using the relative output information of neighboring subsystems. Each system is a minimum-phase SISO system with relative degree one and unknown parameters, and the interaction graph among the subsystems is directed. For the case where the directed graph is strongly connected, a distributed adaptive protocol is designed to achieve consensus. For the case where there exists an arbitrary constant reference signal, a distributed adaptive controller together with an internal model are presented to achieve output tracking in the sense that the subsystem outputs asymptotically follow a reference constant. The proposed adaptive protocols are independent of the parameters of the subsystems, only use the relative outputs of neighboring subsystems, and hence are fully distributed.

Distributed event‐triggered fixed‐time consensus for leader‐follower multiagent systems with nonlinear dynamics and uncertain disturbances

“…Noticeably, in practical applications, a group of agents needs to follow a dynamic leader that could be virtual for its followers, which leads to the research of leader‐follower multiagent systems. There are many very interesting results about the consensus of linear leader‐follower multiagent systems . Consensus tracking was achieved via a variable structure approach, which only used part of the states of the virtual leader and the followers in the work of Cao and Ren .…”

Distributed Adaptive Consensus Output Regulation of Network-Connected Heterogeneous Unknown Linear Systems on Directed Graphs

“…Lemma 3.2: [16], [15] If the adjacency matrix A whose corresponding connection graph is strongly connected, and the nonnegative diagonal matrix ∆ has at least one positive diagonal element, there exist a positive diagonal matrix G with G = diag{g1, . .…”

“…Adaptive laws are also proposed to estimate network connectivity, aiming at a fully distributed control, without using the knowledge of eigenvalues of Laplacian matrices [14]. In particular, a recent result [15] can deal with parametric uncertainty of the subsystems with a fully distributed control. But the subsystems must have identical system dynamics with relative degree one, and the regulated output must be a constant.…”

Distributed adaptive consensus control of nonlinear output-feedback systems on directed graphs

“…The uncertainty in unknown system parameters are dealt with by adaptive gains in the same spirit as tackling unknown connectivities. However, the nonlinear term in the control input makes the adaptive control scheme shown in Li and Ding, 2015) not applicable. In this paper, we propose a new distributed adaptive control scheme to achieve state consensus among the subsystems, via relative output feedback.…”

“…This obstacle is removed in a recent attempt (Li, Wen, Duan and Ren, 2015) where a careful application of changing supply function is implemented in the Lyapunov function design for the success of distributed adaptive scheme for linear systems with known parameters. Further development is reported in (Li and Ding, 2015) for fully distributed adaptive control for linear systems with unknown parameters, and with uncertainty in the network connectivity.…”