Multiple Euler-Lagrange Systems Research Articles

Hierarchical estimator-based fixed-time and prescribed-time bipartite consensus of multiple Euler-Lagrange systems with a directed signed graph

This article addresses the fixed-time and prescribed-time bipartite consensus problem of Euler-Lagrange systems (ELSs) under a directed sign graph, taking into consideration both the parametric uncertainties and external disturbances. Novel hierarchical control algorithms employing estimator approaches are proposed to tackle the aforementioned challenges. More specifically, the control protocol is first designed to accomplish fixed-time bipartite consensus (Fix-TBC). The settling time obtained by using fixed-time control algorithm is restricted to its upper bound, but it may result in a conservative estimation of the bound. Consequently, it indicates the need for designing another control protocol to address the prescribed-time bipartite consensus (Pre-TBC) problem. By invoking Lyapunov stability theory, some sufficient conditions for achieving fixed-time and prescribed-time bipartite consensus of the ELSs are derived. Numerical examples are ultimately provided to demonstrate results.

Robust arbitrary trajectory tracking of multiple heterogeneous Euler–Lagrange systems under directed graphs: A fully distributed event‐triggered control

AbstractIn this paper, the robust arbitrary trajectory tracking problem of multiple heterogeneous Euler–Lagrange (EL) systems with disturbances under a directed graph is investigated via a novel fully distributed event‐triggered control (ETC) strategy. Firstly, for an arbitrary tracked trajectory, the Fourier transform technique is employed to approximately obtain its linear form, which represents the leader of multiple EL systems. Since the dynamics and state of the leader are not available to all followers, fully distributed adaptive ETC‐based observers are proposed for each follower to reconstruct the leader's trajectory, where the global information requirements are avoided, and the Zeno behavior is excluded by giving the minimum triggering intervals. Armed with the observed information, a robust adaptive ETC protocol is further developed such that the position‐like state of each follower can track the leader with the intermittent controller updating, where a minimum control update interval is obtained theoretically. Moreover, the adaptive technique is used to eliminate the influence of the parameter uncertainties of multiple EL systems, thus the tracking is achieved asymptotically. Finally, simulation results are illustrated to show the feasibility and effectiveness of the proposed control strategy.

Model-independent event-based consensus of multiple Euler-Lagrange systems with input disturbances

This paper investigates leaderless consensus (LLC) and leader-follower consensus (LFC) issues of multiple Euler-Lagrange systems (MELSs) with uncertain system parameters and input disturbances. Firstly, by utilizing event-based control strategy, event-based consensus protocols are proposed to achieve LLC and LFC, respectively. Then, to confirm that no Euler-Lagrange (EL) system will exhibit Zeno behavior under the above event-based consensus protocols, we show that the low bound of event-triggering interval is strictly positive for any time instants. Distinct with the existing related works, the proposed event-triggered consensus protocols only rely on local sampled state, and are irrelevant to the system parameters. Finally, some simulation examples are presented to illustrate the feasibility of the proposed event-based consensus algorithms.

Distributed finite-time optimization for networked Euler–Lagrange systems under a directed graph

In this paper, we investigate the finite-time distributed optimization problem for multiple Euler–Lagrange systems. A new distributed optimization control scheme is presented to achieve the state agreement in finite time while minimizing the sum of each agent’s local cost function. The proposed algorithm has the advantage of being able to achieve distributed finite-time optimization consensus under general unbalanced connected directed communication graphs. By virtue of finite-time Lyapunov theory and convex optimization, the finite-time convergence for the algorithm is analyzed. A numerical example is also presented to illustrate the effectiveness of the obtained results.

Fully Distributed Consensus of Multiple Euler–Lagrange Systems Under Switching Directed Graphs Using Only Position Measurements

Fully Distributed Consensus of Multiple Euler–Lagrange Systems Under Switching Directed Graphs Using Only Position Measurements

Leader-Following Consensus of Multiple Uncertain Euler-Lagrange Systems via Fully Distributed Event-Triggered Adaptive Fuzzy Control.

This article deals with the leader-following consensus problem of multiple uncertain Euler-Lagrange systems with unknown nonlinear dynamics. By introducing a dynamic compensator for each agent, a fully distributed control strategy is developed based on the fuzzy approximation approach, which is independent of any priori global information associated with the communication topology. Meanwhile, a distributed event-triggering mechanism (ETM) is designed such that each agent broadcasts its states only when an event occurs. It is shown that with the proposed ETM, the leader-following consensus is achieved with aperiodic intermittent communication and Zeno behavior is excluded by contradiction. Moreover, the consensus tracking errors converge to small sets around the origin. Finally, an example is provided to illustrate the effectiveness of the obtained theoretical results.

Distributed Observer-Based Leader-Follower Consensus of Multiple Euler-Lagrange Systems.

This article investigates the leader-follower consensus problem of multiple Euler-Lagrange (EL) systems, where each agent suffers uncertain external disturbances, and the communication links among agents experience faults. Besides, we consider a more general case that only a portion of followers can measure partial components of leader's output and access the dynamic information of leader. The main idea of solving the consensus problem in this article is proceeded in two steps. First, we design an adaptive distributed observer to estimate the full state information of leader in real time with resilience to communication link faults. Second, based on the proposed distributed observer, we propose a proportional-integral (PI) control protocol for each agent to track the trajectory of leader, which is model-independent and robust to uncertain external disturbances. Distinct from the existing leader-follower consensus protocols of multiple EL systems, the proposed distributed observer-based PI consensus protocol in this article is model-independent, which is irrelevant to the structures or features of EL system model. Finally, we present a simulation example to show the resilience of the above adaptive distributed observer and the robustness of the distributed observer-based consensus protocol.

Distributed Neural Fixed-Time Consensus Control of Uncertain Multiple Euler-Lagrange Systems With Event-Triggered Mechanism

Distributed Neural Fixed-Time Consensus Control of Uncertain Multiple Euler-Lagrange Systems With Event-Triggered Mechanism

Fully Event-Triggered Practical Leader-Following Consensus of Multiple Euler-Lagrange Systems Over Switching Networks.

In this article, a fully event-triggered adaptive distributed control law is developed for solving the practical leader-following consensus problem (LFCP) of a group of uncertain Euler-Lagrange (EL) systems. An event-triggered output-based distributed observer (OBDO) is established first to estimate the state variable of the leader system over jointly connected switching networks (JCSNs). Then, the event-triggered adaptive control law is designed to exclude the Zeno phenomenon and to make the steady-state consensus error smaller than any specified value by adjusting some design parameters. Compared with the existing results, the proposed event-triggered control law only depends on the output of the leader system, works over JCSNs, and, moreover, is fully event-triggered so that it can be directly implemented in a digital platform. The overall design is illustrated using a group of two-link manipulators.

Distributed Reduced-Order Observer-Based Consensus of Multiple Euler-Lagrange Systems Over Switching Networks

Distributed Reduced-Order Observer-Based Consensus of Multiple Euler-Lagrange Systems Over Switching Networks

Event-triggered consensus control for a class of uncertain multiple Euler-Lagrange systems with actuator faults

Event-triggered consensus control for a class of uncertain multiple Euler-Lagrange systems with actuator faults

Neural adaptive predefined-time formation tracking control of multiple Euler–Lagrange systems with switching topologies based on hierarchical mechanism

This paper investigates the event-triggered neural adaptive predefined-time time-varying formation tracking control (PTTVFTC) problem for multiple Euler–Lagrange systems (ELSs) with actuator failures and saturation under switching communication topologies. The hierarchical control mechanism (HCM) is employed to overcome the difficulties posed by switching communication topologies to design the control algorithms. Specifically, a new estimator is first developed in the estimator layer for each follower, which can estimate the leader’s position information within a predefined time. Then, based on the designed estimator, a fault-tolerant and anti-saturation controller is proposed in the local control layer for each follower, which enables each follower to achieve PTTVFTC. To reduce the communication frequency, an event-triggered mechanism (ETM) that does not have Zeno behavior determines the controller’s update. In addition, the settling time for formation tracking can be arbitrarily specified as desired. Finally, the effectiveness of the developed control strategy is verified by a simulation experiment.

Nonsingular fixed‐time fault‐tolerant control for multiple Euler–Lagrange systems without continuous communication

AbstractThis article is concerned with the fixed‐time fault‐tolerant control problem of multiple Euler–Lagrange systems (MELSs) with intermittent communication, actuator faults and input disturbances. A nonsingular fixed‐time control framework with three parts is built for the above problem. In the first part, a novel adaptive controller is proposed for MELSs to ensure the fixed‐time stability of sliding modes while successfully solving the actuator faults, parameter uncertainties and unknown disturbances. In the second part, the fixed‐time estimators based on event‐triggered communication are designed by an error decomposition approach. In the third part, an auxiliary system is introduced for the singularity problem and sufficient condition for achieving the consensus is rigorously proved by synthesizing the results of the above two parts. The key feature of the proposed control framework is that the convergence time is constrained by a constant without involving initial states, and the singularity problems of fixed‐time control is avoided. Finally, simulation examples are provided to prove the efficacy of the proposed algorithms.

Adaptive Neural Coordinated Control for Multiple Euler-Lagrange Systems With Periodic Event-Triggered Sampling.

This article addresses the event-triggered coordinated control problem for multiple Euler-Lagrange systems subject to parameter uncertainties and external disturbances. Based on the event-triggered technique, a distributed coordinated control scheme is first proposed, where the neural network-based estimation method is incorporated to compensate for parameter uncertainties. Then, an input-based continuous event-triggered (CET) mechanism is developed to schedule the triggering instants, which ensures that the control command is activated only when some specific events occur. After that, by analyzing the possible finite-time escape behavior of the triggering function, the real-time data sampling and event monitoring requirement in the CET strategy is tactfully ruled out, and the CET policy is further transformed into a periodic event-triggered (PET) one. In doing so, each agent only needs to monitor the triggering function at the preset periodic sampling instants, and accordingly, frequent control updating is further relieved. Besides, a parameter selection criterion is provided to specify the relationship between the control performance and the sampling period. Finally, a numerical example of attitude synchronization for multiple satellites is performed to show the effectiveness and superiority of the proposed coordinated control scheme.

Event-triggered fault-tolerant optimal coordination for multiple Euler–Lagrange systems with semi-Markov jumping networks

ABSTRACT This article explores a distributed optimal coordination control problem for multiple Euler–Lagrange systems with actuator faults. To address this problem, an event-triggered fault-tolerant optimisation algorithm is first proposed to eliminate unexpected faults and reduce the consumption of control resources. In order to further enhance the system's reliability, another algorithm based on the Nussbaum function is proposed to handle faulted systems with uncertain control directions. Note that an auxiliary system with adaptive gains is introduced to eliminate the need for agents to interact with their actual state information, and thus has the effect of protecting privacy. Moreover, the stochastic semi-Markov jumping networks are considered in the algorithms to describe the switching process of uncertain communication graphs. Additionally, the algorithms are fully distributed since it does not require global information of topologies. Finally, numerical simulations are conducted in the article to verify the effectiveness of the proposed algorithms.

Structure-free containment control for uncertain underactuated multiple Euler-Lagrange systems

Structure-free containment control for uncertain underactuated multiple Euler-Lagrange systems

Hierarchical prescribed-time bipartite consensus for multiple Euler–Lagrange systems with input-to-output redundancy and directed matrix-weighted signed graph

This paper studies the prescribed-time bipartite consensus problem for multiple Euler–Lagrange systems (MELSs) under directed matrix-weighted signed graph, in which input-to-output redundancy, external disturbances and uncertain dynamic terms have been taken into consideration. Firstly, this paper proposes the prescribed-time hierarchical control (PTHC) algorithm to tackle the aforesaid issue. It is worth pointing out that the convergence time can be arbitrarily prescribed based on actual engineering needs. Then, the corresponding sufficient conditions for achieving the prescribed-time bipartite consensus are obtained by invoking Lyapunov stability analysis. Eventually, the numerical simulation results are performed, which vividly reflect the effectiveness and feasibility of the developed control algorithm.

Distributed adaptive finite-time fault-tolerant formation-containment control for networked Euler–Lagrange systems under directed communication interactions

This paper addresses the finite-time formation-containment control problem for multiple Euler–Lagrange systems with actuator faults and input saturations subject to external disturbances and nonlinear uncertainties under directed communication interactions. Systematic procedures on how to synthesize a distributed control scheme are developed based on adaptive backstepping control, fault-tolerant control, dynamic gain control and finite-time control such that leaders form a desired geometric configuration while tracking the virtual leader, and followers converge to the convex hull spanned by the leaders during a finite-time period with sufficient accuracy. Two auxiliary systems are constructed to facilitate the control scheme design. Finite-time convergence and ease of computation burden in the sense of not using fractional powers of cooperative error information are realized by integrating dynamic gain control, finite-time control and one auxiliary system. Actuator faults, control input saturations, external disturbances and nonlinear uncertainties are coupled together and dealt with by adaptive backstepping control, fault-tolerant control and the other auxiliary system. In the end, the effectiveness of the proposed control scheme is verified with simulation results.

Leader-Following Connectivity-Preserving Consensus of Multiple Euler–Lagrange Systems With Disturbances

The leader-following consensus problem of multiple uncertain Euler–Lagrange systems (MELSs) with disturbance is investigated and each agent has a limited communication range in this article. The time-varying topology is state-dependent as the relative distance between the agents changes during the movement. Therefore, the initial connectivity cannot be guaranteed throughout the evolution and the dynamical characteristics of MELSs is more complex which make the consensus problem more challenging. In addition, some of the followers are not within the leader's communication range. Firstly, to estimate the leader's velocity, we design a distributed observer. Then, we propose a sliding mode protocol with a novel potential function to maintain the global reachable of the leader. Via numerical simulation, the theory's effectiveness is demonstrated.

Finite-Time and Fixed-Time Consensus Tracking of Multiple Euler–Lagrange Systems via Hierarchical Control Approach

Finite-Time and Fixed-Time Consensus Tracking of Multiple Euler–Lagrange Systems via Hierarchical Control Approach