Passivity‐based state synchronization of homogeneous multiagent systems via static protocol in the presence of input saturation

Abstract

This paper studies semiglobal and global state synchronization of homogeneous multiagent systems with partial-state coupling (ie, agents are coupled through part of their states) via a static protocol. We consider 2 classes of agents, ie, G-passive and G-passifiable via input feedforward, which are subjected to input saturation. The proposed static protocol is purely decentralized, ie, without an additional channel for the exchange of controller states. For semiglobal synchronization, a static protocol is designed for an a priori given set of network graphs with a directed spanning tree. In other words, the static protocol only needs rough information on the network graph, ie, a lower bound for the real part and an upper bound for the modulus, of the nonzero eigenvalues of the corresponding Laplacian matrix. Whereas for global synchronization, only strongly connected and detailed balanced network graphs are considered. In this case, for G-passive agents, the static protocol does not need any network information, whereas for G-passifiable agents via input feedforward, the static protocol only needs an upper bound for the modulus of the eigenvalues of the corresponding Laplacian matrix.So far, a lot of work in state synchronization for MAS has focused on state synchronization based on diffusive full-state coupling, ie, agents are coupled through their states. In this case, universally static protocols are considered.For partial-state coupling (ie, agents are coupled through their output that consists of part of their states), state synchronization can be achieved via a dynamic protocol or a static protocol. The standard approach leads to dynamic observer-based protocols.We should note that the original approach to partial-state coupling (see, for example, the work of Li et al 6 ) uses an additional communication layer exchanging part of the protocol states. In the work of Grip et al, 7 a purely decentralized solution was presented, which did not rely on this extra communication.Moreover, in several papers, such as the work of Liu et al, 8 the protocol is introspective where the protocol does not make use of only relative information between the output of the agent and the output of other agents but also uses absolute information about the state of their agent.State synchronization via a static protocol with partial-state coupling imposes restrictions on the agent dynamics. For state synchronization via a static protocol, agents are usually required to be passive or passifiable via output feedback. For example, Xia and Scardovi 9 considered linear agents that are either passive or passifiable via output feedback. In the work of Dzhunusov and Fradkov, 10 agents were strictly G-passifiable via output feedback, whereas Feng and Hu 11 dealt with linear agents that are either passive or passifiable via output feedback. Nonlinear input-affine passive agents were considered in other works, [12][13][14][15][16] whereas general nonlinear passive agents were studied in the works of Jiang et al, 17 Münz et al, 18 and Yu and An...

H2 and H∞ almost output synchronization of heterogeneous continuous‐time multi‐agent systems with passive agents and partial‐state coupling via static protocol

“…In this section, we will review the definition of passivity. 31 Consider a general square system Σ Σ ∶…”

“…In this section, we will review the definition of passivity . Consider a general square system Σ where , and while have full column and row rank, respectively.…”

Squared‐down passivity–based state synchronization of homogeneous continuous‐time multiagent systems via static protocol in the presence of time‐varying topology

“…In that case, the state synchronization problem stated in Problem 1 is solvable for the set of graphs G = b,N t . In particular, for any > 0, the static protocol (14) solves the state synchronization problem for any graph  t ∈ b,N t . To prove the above theorem, we need the following technical lemma.…”

“…In the work of Dzhunusov and Fradkov, agents are strictly G ‐passifiable via static output feedback, while the work of Feng and Hu deals with linear agents that are either passive or passifiable via static state/output feedback agents in presence of communication delay. Then, the work of Liu et al considers the synchronization results for a MAS with input saturation by using the G ‐passivity. Further, Liu et al developed a squared‐down passivity to establish a state synchronization result for MAS with nonsquare passive or passifiable agents.…”

Scale-free Linear Observer-based Protocol Design for Global Regulated State Synchronization of Homogeneous Multi-agent Systems with Non-introspective Agents Subject to Input Saturation

“…Global synchronization for neutrally stable agents has been studied by [14] (continuous-time) and [32] (discrete-time) for either undirected or detailed balanced graph. Then, global synchronization via static protocols for MAS with partial state coupling and linear general dynamics is developed in [11]. Reference [7] provides the design which can deal with networks that are not detailed balanced but intrinsically requires the agents to be single integrator.…”