This paper studies the asynchronous event-trigger control of networked Lagrangian system collaboration. The main control goal is to make the velocity and position status of each subsystem converge. In this paper, the non-linearity existing in the actual system, the limitation of communication and computing resources are considered. It is difficult for general algorithms to meet the requirements of general distributed algorithms with continuous update actions. Therefore, this paper introduces the event-trigger mechanism with asynchronous update rules into the distributed control problem of the second-order nonlinear networked Euler-Lagrange system. Aiming at the strongly connected Lagrange network, an event-triggered distributed control algorithm is proposed, and a suitable Lyapunov function is selected to prove its stability. It is shown that based on the proposed algorithm, all agents can achieve consensus. Finally, the theoretical results are verified by numerical simulation.

Asynchronous Event-Trigger Consensus of Leaderless Homogeneous Nonlinear Networked Lagrangian Systems

In this paper, we consider the cooperative control of multiple parametric-strict-feedback (PSF) systems with unknown control directions and uncertain parameters. A logic-based switching mechanism which depends on the incremental errors of the analysis function between two consecutive switching moments is proposed such that the unknown control direction can be matched. Then, asymptotic output synchronization is realized by recursively designed controllers in which the states of agent <inline-formula xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink"> <tex-math notation="LaTeX">$i$ </tex-math></inline-formula> and its neighbors are incorporated, meanwhile, parametric uncertainties are compensated via parameter estimators, which are all tuned online in a distributed manner. Compared with the previous works, the algorithm proposed in this paper has fewer potential switches and better transient performance. Simulation results are presented to verify the effectiveness of the proposed algorithm. 

Logic-based Switching Mechanism for Multiple Parametric-Strict-Feedback Systems with Unknown Control Directions

In this paper, the dynamic event-based resilient consensus control of the multiple networked Euler-Lagrangian (E-L) systems under the Denial of Service (DoS) attacks is considered. Compared with linear cyber-physical systems, nonlinear networked E-L systems are more complex and closer to actual mechanical systems. For the situation where the topology is a strongly connected directed topology, a controller based on a dynamic event-trigger mechanism is designed to achieve consensus control for the networked E-L system in the absence of DoS attacks. Sufficient conditions are presented, which can guarantee the closed-loop system be stable. Then the resilient consensus problem of event-based controllers under energy-constrained DoS attacks is analyzed. The conditions related to the duration and frequency of DoS attacks are given. Zeno behavior is proved does not exist in the proposed control scheme. Finally, some numerical simulation results are given for verifying the theoretical results. 

Dynamic Event-Based Resilient Consensus of Networked Lagrangian Systems Under DoS Attacks

In this paper, we consider the cooperative control of multiple parametric-strict-feedback (PSF) systems with unknown control directions and uncertain parameters. A logic-based switching mechanism which depends on the incremental errors of the analysis function between two consecutive switching moments is proposed such that the unknown control direction can be matched. Then, asymptotic output synchronization is realized by recursively designed controllers in which the states of agent $i$ and its neighbors are incorporated, meanwhile, parametric uncertainties are compensated via parameter estimators, which are all tuned online in a distributed manner. Compared with the previous works, the algorithm proposed in this paper has fewer potential switches and better transient performance. Simulation results are presented to verify the effectiveness of the proposed algorithm.

https://ieeexplore.ieee.org/ielx7/6287639/6514899/09745909.pdf

Logic-Based Switching Mechanism for Multiple Parametric-Strict-Feedback Systems With Unknown Control Directions

This paper is concerned with the decentralized control problem of networked high-order nonlinear systems that can be transformed into strict feedback forms with parameter uncertainties and unknown control directions under a directed communication graph. A decentralized controller is designed recursively for each agent to realize output synchronization and guarantee the overall system to be bounded. Instead of a Lyapunov-based argument which is commonly used in the literature, an inductive contradiction argument is employed. Moreover, not like other existing works, we use the Nussbaum function in the analysis function form rather than its derivative, which not only facilitates the proof but also enlarges the schedule&#x2019;s application scope. Simulation results are presented to verify the effectiveness of the proposed scheme. 

Decentralized Control of Multiple Strict-Feedback Systems With Unknown Control Directions

In the literature, most of the consensus methods require the control directions of all agents to be known. This paper deals with the distributed consensus problem without such requirements for networked Lagrangian systems subjected to uncertain dynamics. Unknown control directions are nonidentical in the sense that the control direction related to each control input in an individual Lagrangian system can be different and unknown as well as that the control directions for different Lagrangian systems are allowed to be distinct. Regarding the communication topology, the only requirement is to contain a fixed directed spanning tree. Based on the estimated consensus value, novel auxiliary sliding mode variables are constructed and applied to develop the distributed adaptive consensus control scheme. It is proved by adopting the special properties of the Laplacian matrix on directed graphs and matrix theory that global uniform boundedness of all closed-loop signals and the asymptotic consensus can be achieved. Simulations on networked two-link revolute joint arms are provided to verify the validity of the proposed scheme.

/pdf/distributed-consensus-of-networked-lagrangian-systems-with-3bvs9itwzx.pdf

Distributed Consensus of Networked Lagrangian Systems With Unknown Nonidentical Control Directions

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Distributed Consensus of Networked Lagrangian Systems With Unknown Nonidentical Control Directions