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The main problem addressed in this paper is the task-space bipartite formation tracking problem of uncertain heterogeneous Euler-Lagrange systems in predefined time. To solve this problem, an effective hierarchical predefined-time control algorithm is designed. This algorithm utilizes a non-singular sliding surface, allowing for the adjustment of the upper bound of the settling time as a flexible parameter. Key components of the proposed approach include an estimator for the leader's states and a controller tailored to the formation problem. To mitigate the effects of dynamic uncertainties in the system, the radial basis function neural network is integrated into the methodology. Finally, the effectiveness and validity of the proposed algorithm are demonstrated through numerical simulations, showcasing their practical applicability and efficacy.
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In this article, we propose the design of a robust tracking controller of perturbed Euler-Lagrange systems (ELSs) based on dynamic event-triggered (DET) sliding mode control (SMC) with periodic evaluation of triggering rule. To ensure robustness, we employ the SMC technique and introduce a dynamic periodic event-triggering strategy to reduce communication frequency significantly. This strategy involves the incorporation of an auxiliary dynamic variable to formulate the event-triggering condition, leading to the generation of sparser triggering instants. An upper bound of the sampling period is also obtained in this design to facilitate the periodic assessment of the event-triggered strategy, alleviating the need for continuous verification of the event condition. This technique is more economical with respect to communication resources and practical than its continuous counterpart due to the relaxation of continuous measurements. The stability of the closed loop system is established using Lyapunov analysis within the dynamically triggered event-based SMC framework. The necessary switching gain for maintaining the stable motion of the sliding variable is derived with the help of Lyapunov analysis. The tracking error is shown to be ultimately bounded, and Zeno-behaviour is excluded to ensure finite sampling. A comparative analysis based on simulation results is included to highlight the effectiveness of the proposed scheme, especially in reducing the network usage in the transient phase of the response while achieving comparable steady-state behaviour. Ultimately, we validate the effectiveness of the proposed algorithm by simulating a two-link manipulator and experimentally implementing it with a one-link manipulator.
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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.
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The core idea of traditional adaptive control is to reconstruct parameter estimation errors with known signals and damping injection based on tracking error, while the formulation of desired damping in controller designs is usually a nontrivial task. The main contribution of this paper lies in the development of the classic RISE result and a constructive damping injection procedure for the adaptive tracking control of Euler-Lagrange mechanical systems. By utilizing generalized dynamic scaling function, scalar filtering, the improved RISE method and analyzing the existence of finite escape time of the closed-loop system, a globally asymptotically stable result is obtained with facilitative damping injection, significant order reduction and improved design efficiency when compared with the existing results. Simulations on a fully actuated 2-DOF planar robot manipulator model demonstrate the effectiveness of the proposed methods.
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This article addresses the fixed-time fault-tolerant consensus tracking (FTCT) problem for uncertain multiple Euler-Lagrange systems (MELS) with the digraph and actuator faults. Firstly, a fixed-time distributed observer (DO) is built to estimate the states of leader. Then, the approximation ability of radical basic function neural networks (RBFNN) is exploited to deal with the system uncertainties. By using backstepping technique, the novel fault-tolerant local control protocol (FTLCP) and updating laws are designed to ensure that error variables converge to the small adjacent area of zero within fixed-time. Eventually, the effectiveness and practicality of the presented method are demonstrated through a typical MELS simulation.
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This paper provides two bounded finite-time control strategies for the stabilization problem of Euler-Lagrange (EL) systems exposed to actuator failures. By the combination of sliding mode technology and adaptive method, two control architectures have been constructed such that the system states will be forced towards the origin within finite time. The first controller is applicable in the case that exact information of the external disturbance and actuator faults are available. However, it still remains challenging for designers to obtain this sort of information in engineering practice. On account for this, adaptive laws are applied in the second controller to obtain estimations about the unknown parameters, thus ensuring desirable fault-tolerance ability and robustness for the EL systems. By resorting to the properties of EL systems and hyperbolic tangent functions, outputs of these two controllers will be proven to be bounded. Simulation examples are presented to manifest the validity of the developed algorithms.
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In this paper, we investigate a trajectory control problem for Euler-Lagrange systems with unknown quantization on the actuator channel. To address such a challenge, we proposed a quantization-mitigation-based trajectory control method, wherein adaptive control is employed to handle the time-varying input coefficients. We allow the quantized signal to pass through unknown actuator dynamics, which results in the coupled actuator dynamics for Euler-Lagrange systems. It is seen that our method is capable of driving the states of networked Euler-Lagrange systems to the desired ones via Lyapunov's direct method. In addition, the effectiveness and advantage of our method are validated with a comparison to the existing controller.
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This study mainly investigates the problem of distributed tracking control for time-varying delay existing multiple Euler-Lagrange systems considering full-state constraints and input saturation under the directed graph. Specifically, the system under consideration consists of system uncertainties and external disturbances. In the control law design, a distributed observer is first designed that the followers can obtain the leader's time-varying information. Then the barrier Lyapunov function technique is used to make sure the system errors can converge to a certain range while the anti-windup method is utilized to overcome the influence of control input saturation. Further, in order to prevent chattering, an adaptive law is given. Numerical simulations are given to verify the proposed algorithms.
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In this paper, a backstepping based distributed adaptive control scheme is proposed for multiple uncertain Euler-Lagrange systems under directed graph condition. The common desired trajectory is allowed totally unknown by part of the subsystems and the linearly parameterized trajectory model assumed in currently available results is no longer needed. To compensate the effects due to unknown trajectory information, a smooth function of consensus errors and certain positive integrable functions are introduced in designing virtual control inputs. Besides, to overcome the difficulty of completely counteracting the coupling terms of distributed consensus errors and parameter estimation errors in the presence of asymmetric Laplacian matrix, extra information transmission of local parameter estimates are introduced among linked subsystem and adaptive gain technique is adopted to generate distributed torque inputs. It is shown that with the proposed distributed adaptive control scheme, global uniform boundedness of all the closed-loop signals and asymptotically output consensus tracking can be achieved.