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This article focuses on fixed‐time consensus of networked Euler–Lagrange systems (NELSs) over event‐based communication under denial‐of‐service (DoS) attacks. First of all, a basic fixed‐time consensus algorithm is developed for NELSs, where a general fixed‐time communication triggering scheme through error decomposition method is designed for decreasing communication frequencies while avoiding singularity. Then, to fulfil the consensus problem of NELSs in the presence of DoS attacks, a novel fixed‐time resilient algorithm is further presented by the basic algorithm, where the effective attack interval is redefined for carrying out the algorithm design. Furthermore, a hierarchical fixed‐time control framework with privacy preservation is introduced for the consensus problem of NELSs under DoS attacks. Meanwhile, a self‐triggered scheme is employed for the above algorithms to lower the update frequencies of control inputs. The stated algorithms possess a uniformly constrained upper bound on the convergence time, and are resilient as well as responsive to DOS attacks while saving control resources significantly. Finally, numerous illustrative examples are given for demonstrating the efficacy of the derived schemes. [ABSTRACT FROM AUTHOR]

This 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. [ABSTRACT FROM AUTHOR]

This article investigates the distributed Nash equilibrium seeking problem of quadratic time‐varying games with Euler–Lagrange (EL) players, where external disturbances and parametric uncertainties are involved. A gradient‐based hierarchical algorithm consisting of a game layer and a control layer is proposed. Specifically, in the game layer, EL players communicate with neighbors through a graph to reach the consensus on potential aggregate values, which will be employed to calculate the gradient of each player's objective function, and then, a gradient‐based sliding mode controller is developed to track time‐varying gradient in the control layer. Thus, the convergence results are hierarchically obtained through the Lyapunov stability method. In addition, the hierarchical control strategy is extended to address the constrained problems through the utilization of a smooth penalty function. By appropriately choosing control parameters, the Nash equilibrium seeking errors can be arbitrarily small. The relation between the optimal solutions of the original problem and the dual one is further discussed. Finally, the proposed methods are numerically verified. [ABSTRACT FROM AUTHOR]

The finite‐time nonlinear placement problem of networked Euler‐Lagrange systems (NELSs) is discussed in this paper. The problem is reformulated into a finite‐time aggregate game under an undirected graph. Then, several novel practical gradient‐based finite‐time hierarchical (GFTH) algorithms composed of a game layer, a Nash equilibrium (NE) seeking layer, and a control layer are proposed. Specifically, the game layer employs an aggregate function to reach a consensus on the potential aggregate value which is adopted by a gradient‐based finite‐time method to tackle the finite‐time NE seeking problem in the NE seeking layer, and then, the tracking problem is realized in the control layer. The convergence results are established by a nonsmooth Lyapunov function. In addition, the versatility of the GFTH algorithms is shown by extending to address the task‐space control problem of NELSs. The effectiveness of the proposed algorithms is illustrated via simulations. [ABSTRACT FROM AUTHOR]

In this paper, the collaborative control of multiple nonlinear Euler-Lagrange systems with actuator faults and stochastic semi-Markov jump networks (SMJNs) is concerned. In order to fulfil high reliability and low consumption, several novel event-triggered fault-tolerant control (ETFTC) algorithms are established to simultaneously eliminate the undesirable faults and save control resources, where only quantised partial-state signal of neighbours is required for the control process. Moreover, some ubiquitous constraints, such as unknown control directions and time-varying communication delays, are also comprehensively considered and effectively excluded so as to further enhance the control reliability. Meanwhile, some sufficient criteria on the algorithm synthesis and stability analysis without involving Zeno behaviour are successfully built with the aid of Lyapunov–Krasovskii functional. Finally, some illustrative simulations are performed to validate the feasibility and effectiveness of the derived ETFTC algorithms. [ABSTRACT FROM AUTHOR]

Branch (assembly mode or circuit) identification is a way to assure motion continuity among discrete linkage positions, which is the most fundamental issue among the mobility problems that may also include sub-branch (singularity-free) identification, range of motion, and order of motion. Branch analysis becomes more complex in spherical or spatial linkages. In this paper, an automated branch identification method was proposed based on discriminants of kinematic equations and the concept of joint rotation space (JRS) to analyze the branch formation of a spherical six-bar linkage. And an automated identification algorithm was presented to rectify the motion of a spherical six-bar linkage. The proposed method is general and conceptually straightforward. It can be applied for all linkage inversions. Examples were employed to illustrate the application of the proposed method. [ABSTRACT FROM AUTHOR]