Adaptive stationary consensus protocol for a class of high‐order nonlinear multiagent systems with jointly connected topologies

Abstract

The leaderless consensus problem in a class of dynamic agents with high-order input-affine nonlinear models is studied. Based on communication of position information among the agents, an adaptive protocol is proposed that guarantees achieving consensus in the network in the presence of unknown parameters in the agents models. The network topology is considered undirected, which may not be connected constantly. Hence, by invoking the Cauchy convergence criterion, sufficient conditions to achieve consensus in the presence of jointly connected switching topologies are obtained. A numerical example for a team of single-link flexible joint manipulators with forth-order nonlinear models is provided to confirm the accuracy of the proposed consensus protocol. random networks was investigated in [7]. In [8], achieving consensus in networks of first-order agents with jointly connected topologies was studied, and in [9], a consensus protocol for networks of first-order agents in the presence of diverse communication delays was introduced. Because of practical issues, the consensus problem over second-order MASs was studied as well. Indeed, the control inputs of a large number of systems and vehicles are forces or torques, which provide acceleration. Therefore, to describe the behaviors of accelerated agents, it is necessary to consider second-order models. For instance, by using the information of agents relative positions and considering velocity damping terms, the consensus protocol proposed in [6] was extended to second-order MASs under undirected networks in [10]. By considering the information of agents relative velocities, that protocol was extended to directed networks in [11] and [3]. Achieving finite time consensus in second-order MASs in the presence of input saturation was studied in [12], and the consensus problem in networks of second-order MASs with switching topologies was studied in [13].However, in practice, there exist some systems and vehicles that require higher-order differential equations to be modeled. In other words, the input-output relationship in those systems can just be expressed by higher-order differential equations. Therefore, the consensus problem in MASs with high-order models is necessary to be investigated as well. For instance, based on measurement of the relative states of agents and employing local damping terms, the consensus protocols of [11] and [3] were extended to higher-order MASs in [14] and [15]. A dynamic consensus control scheme for high-order MASs was proposed in [16]. Average consensus over high-order MASs was studied in [17]. The H 1 consensus problem for high-order MASs was studied in [18], and a consensus protocol for networks of high-order agents with connected switching topologies and time-varying communication delays was proposed in [19].A large number of dynamical systems such as manipulators, inverted pendulums, and so on [20, 21] have nonlinear models. By employing some techniques such as feedback linearization, the nonlinearities can be cancelled and one can deal...

Guaranteed‐performance consensus design for Lipschitz nonlinear multiagent systems with jointly connected topologies

“…In this sense, the guaranteed‐performance consensus criterion for the jointly connected multiagent system proposed in the current work can also satisfy the condition of guaranteed‐performance consensus for the connected case. In other works, the consensus problems with jointly connected topologies were considered, but the upper bound of the performance function cannot be achieved. In the current work, the guaranteed‐performance problem is solved by using the structure of the performance function and the property of the Laplacian matrix, and then, the guaranteed‐performance cost can further be obtained.…”

“…In the work of Yu and Xia, leaderless consensus problems for multiagent systems with jointly connected topologies were taken into account and an adaptive consensus design method was proposed to solve the consensus problems. Rezaee and Abdollahi proposed the consensus criteria in terms of Riccati inequalities for multiagent systems with jointly connected topologies, where the Lipschitz nonlinearity and input‐affine nonlinear were considered, respectively.…”

“…Firstly, the interaction topologies of multiagent systems are modeled as jointly connected topologies during the solving of guaranteed‐performance consensus design problems, while they were assumed to be connected for all the time in the work of Xi et al Secondly, the consensus regulation performance is taken into account and the guaranteed‐performance costs for both leaderless and leader‐following cases with the communication structure properties are determined. Related works about consensus problems with jointly connected topologies were addressed and inspirational results were proposed, but the consensus regulation performance was not considered. Thirdly, the impacts of the Lipschitz nonlinear dynamics for guaranteed‐performance consensualization are considered.…”

“…Based on the work of Xi et al, we considered the jointly connected topology situation, which is more complex than the general connected case. Inspired by the method of dealing with the consensus problems with jointly connected topologies in other works, the performance functions are introduced and the guaranteed‐performance consensus problems with jointly connected topologies are taken into account.…”

Guest editorial: special issue on Consensus‐based Applications in Networked Systems

“…Rezaee and Abdollahi propose an adaptive protocol to guarantee the consensus in the network based on the local position information among the agents. The sufficient conditions to achieve the consensus in the presence of jointly connected switching topologies are obtained.…”