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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]

In this article, the consensus of networked underactuated robotic systems subject to fixed and switched communication networks is discussed by developing some novel event-triggered control algorithms, which can synchronously guarantee the convergence of the active states, the boundedness of the velocities of passive actuators, and the exclusion of Zeno behaviors. In the cases of fixed networks, the sufficient criteria are established for the presented distributed event-triggered mechanisms with and without using neighbors’ velocities, in order to achieve a better tradeoff between the communication load and system performance. Besides, in the situation of switched networks, the sufficient criterion is established by assuming that the union of the network has a spanning tree. A distributed sampled-data rule is constructed to decide when to update its own and neighbors’ estimated positions, and thus further reduces the unnecessary control cost. Finally, by further extending the main results to three other sampled-data control algorithms, several examples with performance comparisons are provided to validate the efficiency and advantages of the theoretical results. [ABSTRACT FROM AUTHOR]

This article investigates the coordination of a class of underactuated systems subject to limited energy supply and channel bandwidth and aims to stabilize system states and exclude Zeno behaviors simultaneously. First, by means of event-triggered (E-T) and quantized techniques, several novel quantized sampled-data-based E-T schemes are constructed, which only require discrete-time controller updates and partial quantized states, and thus efficiently mitigate the control and communication workloads. Then, in order to further lower the communication consumptions, several new triggered sampled-data-based communication rules under fixed and switched networks are established, where the communications are performed only at some specific instants and, thus, the ideally continuous-time signal transmission among neighbors can be avoided. Note that sufficient criteria for achieving the coordination of the underactuated systems are derived in terms of the Lyapunov–Krasovskii functional method. Finally, numerous simulations are carried out to demonstrate the effectiveness of the theoretical results. [ABSTRACT FROM AUTHOR]

This article is concerned with the quantized fault‐tolerant control (FTC) for consensus of multiple Lagrangian systems subject to stochastically switching networks, actuator and sensor faults. First of all, a reliable quantized FTC algorithm is developed under Markov jump networks (MJNs), where the communication signal is first quantized before transmitted to develop controllers, and the communication networks are stochastically switching with the sojourn time belonging to an exponential distribution. Then, to handle the FTC problem in the presence of unknown control directions, the Nussbaum function is introduced to further improve the control reliability. Furthermore, the FTC case involving semi‐Markov jump networks (S‐MJNs) and time‐varying communication delays is considered, where the negative constraints of time delays can be effectively attenuated with the sojourn time following a Weibull distribution. Meanwhile, several sufficient criteria on the consensus analysis and algorithms synthesis are established by means of the Lyapunov–Krasovskii stability method. Finally, numerous illustrative examples are elaborated on for demonstrating the feasibility of the derived results. [ABSTRACT FROM AUTHOR]