Consensus of Heterogeneous Multi-Agent Systems With Diffusive Couplings via Passivity Indices

Abstract

This work is concerned with the problem of output consensus for two classes of heterogeneous nonlinear multiagent systems which are interconnected via diffusive couplings over directed graphs. Specifically, for agents that are input feedforward passive (IFP), a condition in terms of passivity indices is proposed for asymptotic output consensus. Moreover, it is shown that the proposed condition can be exploited to design the coupling gain that ensures asymptotic consensus via a semidefinite program (SDP), and the existence of such a coupling gain can be guaranteed provided all the agents are IFP. For agents that are input feedforward output feedback passive (IF-OFP), a condition in terms of passivity indices for practical output consensus is provided, in which the relationship between the coupling gain and the consensus error bound is revealed.

Parallel Feedforward Compensation for Output Synchronization: Fully Distributed Control and Indefinite Laplacian

“…However, many stable systems are not passive, for example, a stable SISO linear plant whose Nyquist plot is not within the closed right-half complex plane is not passive. Then, we cannot apply Lemma 2 to design fully distributed coupling controllers without shifting consensus results [4,19]. Nevertheless, if the Nyquist trajectory does not go to infinity, i.e., it is input feedforward passive (IFP), then, it is always possible to drag it back to the righthalf plane using a stable PFC.…”

“…The feedforward design is also applied to state synchronization in [8] and output synchronization in [2] with fully distributed controllers but these works do not address the case when initial conditions need to be taken into account, e.g., average consensus and distributed optimization [18,15,13]. On the other hand, output synchronization of passivity-short systems requires global graph information to design coupling gains [4,19]. Thus, designing a proper PFC to render fully distributed controllers without altering the final consensus results is worth addressing.…”

Input-Feedforward-Passivity-Based Distributed Optimization Over Directed and Switching Topologies

“…As pointed out by [21], it is in general difficult to derive the exact IFP index for a nonlinear system, and only its lower bound can be obtained by specifying the storage function. With the storage function (15), the lower bound of IFP index can be obtained locally by solving the minimax problem…”

“…On one hand, we conjecture that it is in general difficult to directly construct a distributed algorithm that can be interpreted as output feedback interconnections of passive systems. On the other hand, works in [19]- [21] point out that output consensus can be achieved over directed graphs even among IFP (or passivity-short) systems. Therefore, if a distributed algorithm inherits input feedforward passivity, it can also be directly applied to weightbalanced digraphs through output feedback interconnections.…”

Finite-time consensus of heterogeneous unknown nonlinear multi-agent systems with external disturbances via event-triggered control

“…The problem of the practical consensus for heterogeneous MASs has received much attention because it is difficult to achieve complete asymptotic consensus for heterogeneous MASs (Li et al, 2019). In this article, the practical finite-time consensus for the heterogeneous MASs with heterogeneous unknown nonlinear dynamics and external disturbances in an undirected communication topology is considered.…”