Multiple Euler-Lagrange Systems Research Articles

Distributed Robust Optimization Algorithms Over Uncertain Network Graphs.

This article investigates the robustness issues of a set of distributed optimization algorithms, which aim to approach the optimal solution to a sum of local cost functions over an uncertain network. The uncertain communication network consists of transmission channels perturbed by additive deterministic uncertainties, which can describe quantization and transmission errors. A new robust initialization-free algorithm is proposed for the distributed optimization problem of multiple Euler-Lagrange systems, and the explicit relationship of the feedback gain of the algorithm, the communication topology, the properties of the cost function, and the radius of the channel uncertainties is established in order to reach the optimal solution. This result provides a sufficient condition for the selection of the feedback gain when the uncertainty size is less than the unity. As a special case, we discuss the impact of communication uncertainties on the distributed optimization algorithms for first-order integrator networks.

Distributed Fixed-time Formation-containment Control for Multiple Euler-Lagrange Systems with Directed Graphs

In this paper, the distributed fixed-time formation-containment (DFTFC) problem of multiple Euler-Lagrange systems with parametric uncertainties and input disturbances is studied under directed graphs. First, a distributed fixed-time sliding-mode estimator is constructed to estimate the desired states of each robot with that only parts of followers can access the information of leaders. Next, based on the estimator, a distributed fixed-time formation control algorithm is developed to drive leaders to achieve a specified formation. Then, the distributed fixed-time containment control algorithm is proposed for followers with its estimated states being tracked in a fixed time. Note that an explicit upper bound of the convergence time of DFTFC control algorithm is obtained independent of initial conditions. Finally, numerical simulations are performed to show the effectiveness of the obtained theoretical results.

Distributed Formation Control of Multiple Euler-Lagrange Systems: A Multilayer Framework.

In this technical correspondence, a multilayer formation (MLF) control problem is considered and solved by a unified framework. The agents in each layer present a sort of hierarchical distinction: receive information from former layers, communicate inside the current layer, and send information to subsequent layers. With an arbitrary number of layers, we extend the previous result from undirected graphs to directed ones. The proposed controller achieves MLF without using the distributed estimators and the acceleration information. This removes the induced discontinuities and alleviates the system complexity. It is then proved that the closed-loop errors are semiglobally uniformly ultimately bounded. Simulations are presented to illustrate the effectiveness of this approach.

Distributed formation-containment control for multiple Euler–Lagrange systems with guaranteed performance and unknown control directions

In this paper, the distributed formation-containment (DFC) problem for multiple Euler–Lagrange Systems (ELSs) with unknown control directions is addressed under directed communication graph topology. First, a novel distributed control algorithm is proposed that all the followers nearly converge to the convex hull spanned by the leaders under a directed graph. Second, the transient and steady-state performance of the containment synchronisation errors can be achieved by adopting appropriate predefined technology. Next, a Nussbaum function is utilised to offset the uncertainty of control directions of ELSs. Finally, simulation results are discussed to illustrate the effectiveness of the theoretical analysis.

Fully Distributed Containment Control for Multiple Euler-Lagrange Systems Over Directed Graphs: An Event-Triggered Approach

This paper focuses on the distributed containment control problems for multiple Euler-Lagrange systems with stationary/dynamic leaders over directed communication networks. When the leaders are stationary, a distributed event-triggered adaptive control law is presented, and three other update algorithms of the time-varying control gain are further designed for comparison. Then, a distributed event-triggered neural-network-based control protocol is developed when the dynamic leaders are considered. The aforementioned two control strategies can be implemented in fully distributed chattering-free manners since no global information and discontinuous items are employed. In addition, the requirement for relative velocity measurements are relaxed in controller design. The update frequency and energy consumption of the controlled systems are effectively reduced by applying the event-triggered mechanism. It is rigorously verified that the proposed event-triggered control protocols will not be updated infinitely in finite time, which indicates that the undesired Zeno behavior can be ruled out. Finally, the effectiveness of the theoretical results is illustrated by some simulation examples.

Optimal synchronization control of multiple euler-lagrange systems via event-triggered reinforcement learning

<p style='text-indent:20px;'>In this paper, an event-triggered reinforcement learning-based met-hod is developed for model-based optimal synchronization control of multiple Euler-Lagrange systems (MELSs) under a directed graph. The strategy of event-triggered optimal control is deduced through the establishment of Hamilton-Jacobi-Bellman (HJB) equation and the triggering condition is then proposed. Event-triggered policy iteration (PI) algorithm is then borrowed from reinforcement learning algorithms to find the optimal solution. One neural network is used to represent the value function to find the analytical solution of the event-triggered HJB equation, weights of which are updated aperiodically. It is proved that both the synchronization error and the weight estimation error are uniformly ultimately bounded (UUB). The Zeno behavior is also excluded in this research. Finally, an example of multiple 2-DOF prototype manipulators is shown to validate the effectiveness of our method.

Leader-following consensus control of position-constrained multiple Euler-Lagrange systems with unknown control directions

This paper studies the distributed leader-following consensus control problems of position-constrained multiple Euler-Lagrange Systems (ELSs) with unknown control directions. The objective of our discussion is to develop a consensus protocol despite the existence of position constraints and unknown control directions in each agent. Most of the existing works related to state constraints are for single systems and rare results are concerned about multi-agent systems. With the help of the barrier Lyapunov function, Nussbaum gain adjusting technique, and adaptive control methodology, a novel leader-following consensus algorithm is successfully designed to make sure the convergence to zero of the consensus errors and the boundedness of the signals in the closed-loop system. Moreover, the position constraints for each agent are never violated for all time during the control process. The effectiveness of the main result is illustrated by a practical mechanical system.

Fixed-time consensus for disturbed multiple Euler-Lagrange systems with connectivity preservation and quantized input

The fixed-time consensus for multiple Euler-Lagrange systems subject to external disturbances and input quantization is investigated in this paper. Based on the potential function approach, the connectivity preservation is achieved under the released the assumption on the connectivity of the topology graph. With a minimal directed spanning tree, we present a new controller design procedure for the child nodes step by step, which is motivated by the backstepping method. The input disturbances are efficaciously estimated in fixed time by a disturbance observer. Via the fixed-time theory, a distributed consensus algorithm is proposed to ensure that the consensus error will reach into a small region of the origin in fixed-time. An example is presented to show the effectiveness of the controller.

Distributed Adaptive Neural Consensus Tracking Control for Multiple Euler-Lagrange Systems with Unknown Control Directions

This paper investigates the distributed adaptive neural consensus tracking control for multiple Euler-Lagrange systems with parameter uncertainties and unknown control directions. Motivated by the Nussbaum-type function and command-filtered backstepping technique, the error compensations and neural network approximation-based adaptive laws are established, which can not only overcome the computation complexity problem of backstepping but also make the consensus tracking errors reach to the desired region although the control directions and system nonlinear dynamics are both unknown. Numerical example is given to show the proposed algorithm is effective at last.

Two-layer distributed formation-containment control of multiple Euler–Lagrange systems with unknown control directions

This paper addresses the distributed formation containment control problem of Euler–Lagrangian systems(ELSs) with unknown control directions by two layers, namely, time-varying formation for the leaders and containment formation control for the followers. We first estimate the desired states and velocities for the leaders and the followers in finite time. Second, novel adaptive neutral networks are used to compensate the model uncertainties. Third, using the Nussbaum gain technique, the proposed control laws can guarantee the ultimate convergence of error signals to zero and that all of the signals in the closed-loop system are bounded. Finally, simulation examples are given to demonstrate the effectiveness of the proposed method.

Multilayer Formation Control in Constrained Space

This paper addresses the multilayer formation control (MLFC) problem for multi-agent systems in constrained space. A layered distributed finite-time estimator (LDFE) is proposed to acquire the target states for agents in each layer. To avoid collisions with borders, obstacles, as well as the other agents in the constrained space, an artificial potential function is designed based on the Dirac delta function. Based on the LDFE and the proposed potential function, the MLFC algorithm is proposed for multiple Euler-Lagrange systems (MELSs). The semi-global uniform ultimate boundedness of closed-loop errors is guaranteed by Lyapunov stability theory, while the desired formation of each layer can be achieved without collisions occurring in the constrained space. Simulation results are given to show the effectiveness of the proposed approaches.

Formation Control of Euler-Lagrange Systems of Leaders with Bounded Unknown Inputs

Abstract In this paper, we study the formation control of multiple Euler-Lagrange systems with nonautonomous leaders, which means the leaders have bounded unknown inputs. Firstly, adaptive distributed observers to the leaders’ input bounds and states are designed for every follower. In addition, a discontinuous function in the adaptive distributed observer is applied to make up for the influence of the leaders’ unknown inputs. Secondly, a distributed control law is constructed using the distributed observer to accomplish the formation control. Our control law achieves not only affine maneuver control but also containment control performance. All agents as a whole can rotate, shear and scale, and maneuver to destination safely.

Coordinated Control of Multiple Euler–Lagrange Systems for Escorting Missions with Obstacle Avoidance

This study investigates the coordinated control problem of Euler–Lagrange systems with model uncertainties in environments containing obstacles when escorting a target. Using an outer–inner loop control structure, a null-space-based behavioral (NSB) control architecture was proposed in the outer loop considering obstacles. This architecture generates the desired velocity for the inner loop. The adaptive proportional derivative sliding mode control (APD-SMC) law was applied to the inner loop to ensure fast convergence and robustness. All the robots were distributed around the target evenly and escorted the target at a specified distance while avoiding obstacles in a p − dimensional space (where p ≥ 2 is a positive integer). Stability and convergence analyses were conducted rigorously using a Lyapunov-based approach. The simulation results of three scenarios verified the effectiveness and high-precision performance of the proposed control algorithm compared to that of the adaptive sliding mode control (ASMC) in both two-dimensional and three-dimensional space. It is shown that all the robots can move into appropriate positions on the surface of a sphere/circle during an escort mission and reconfigure the formation automatically when an obstacle avoidance mission is active.

Distributed tracking control for multiple Euler–Lagrange systems with communication delays and input saturation

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.

Adaptive Fuzzy Containment Control for Multiple Uncertain Euler–Lagrange Systems With an Event-Based Observer

This paper considers the containment control problem for multiple Euler-Lagrange systems with unknown nonlinear dynamics, where the dynamics of the leaders are different from those of the followers. In addition, some followers cannot obtain information of the leaders owing to the limited communication range. We first adopt an event-based observer to estimate a trajectory inside the convex hull spanned by states of the leaders, in which continuous communication can be avoided as well. Then, we further utilize the fuzzy logic systems to approximate the unknown nonlinear dynamics and propose an adaptive control scheme. Under the proposed scheme, we can ensure that the states of the followers can converge to the convex hull formed by these states of the leaders. Finally, a simulation example is given to validate the effectiveness of the proposed control scheme.

Distributed chattering-free containment control for multiple Euler–Lagrange systems

This paper investigates the distributed chattering-free containment control problem for multiple Euler–Lagrange systems with general disturbances under a directed topology. It is considered that only a subset of the followers could receive the information of the multiple dynamic leaders. First, by combining a linear sliding surface with a nonsingular terminal sliding manifold, a distributed chattering-free asymptotic containment control method is proposed under the assumption that the upper bounds of the general disturbances are known. Further, based on the high-order sliding mode control technique, an improved distributed chattering-free finite-time containment control algorithm is developed. Besides, adaptive laws are designed to estimate the unknown upper bounds of the general disturbances. It is demonstrated that all the followers could converge into the convex hull spanned by the leaders under both proposed control algorithms by graph theory and Lyapunov theory. Numerical simulations and comparisons are provided to show the effectiveness of both algorithms.

Distributed finite-time tracking control for multiple uncertain Euler-Lagrange systems with error constraints

ABSTRACT In this paper, the distributed finite-time error constrained tracking control for multiple uncertain Euler-Lagrange systems is investigated under directed topology. We consider that the information of the dynamic leader is available to only a portion of the followers. First, for each follower, the error variable relating to the states of the neighbours is designed. Then, by using backstepping method, a distributed finite-time tracking control algorithm is developed with the neural network being utilizsd to estimate the model uncertainties. A tan-type barrier Lyapunov function is used to guarantee that the error variables will not exceed the prescribed bounds. Finite-time stability of the systems is demonstrated by Lyapunov theory and graph theory. Numerical simulations show the advantages of the proposed control strategy by comparisons with the existing methods.

Fault-tolerant consensus of nonlinear multi-agent systems with directed link failures, communication noise and actuator faults

This paper deals with the problem of fault-tolerant control (FTC) for a consensus of nonlinear multi-agent systems (MASs) with directed link failures/recoveries in the presence of communication noise and actuator faults. The directed link failures/recoveries model considered here is randomly switching topologies. Randomly switching topologies in MASs are governed by the Markovian jump process. Moreover, the actuator loss-of-effectiveness faults may happen in any of the actuators. To deal with this, by using the sliding mode control method and weak infinitesimal operation, a passive FTC strategy is presented and sufficient conditions for stochastic consensus of underlying MASs are derived in the mean square stability sense. To that end, by employing such FTC design, MASs achieve consensus in mean square sense onto the predefined stochastic sliding surfaces in finite time while robustness of the overall system against the directed link failures/recoveries and communication noise and actuator faults is guaranteed. Finally, an example on multiple networked Euler-Lagrange systems is presented to verify the effectiveness and feasibility of the proposed algorithms.

Finite-Time Coordination Behavior of Multiple Euler-Lagrange Systems in Cooperation-Competition Networks.

In this paper, the finite-time coordination behavior of multiple Euler-Lagrange systems in cooperation-competition networks is investigated, where the coupling weights can be either positive or negative. Then, two auxiliary variables about the information exchange among agents are designed, and the finite-time distributed protocol is proposed based on the auxiliary variables and the property of the Euler-Lagrange system. By combining the approach of adding a power integrator with the homogeneous domination method, it is shown that finite-time bipartite consensus can be achieved if the cooperation-competition network is structurally balanced and the parameters of the distributed protocol are chosen appropriately; otherwise, finite-time distributed stabilization can be achieved. Furthermore, from the perspective of network decomposition, the finite-time coordination behavior is further considered, and some sufficient conditions about the cooperation subnetwork and the competition subnetwork are obtained. As an extension, finite-time coordination behavior only with partial state information of the neighbors is discussed, and some similar results are obtained. Finally, four numerical examples are shown for illustration.

Distributed Coordinated Tracking Control for Multiple Uncertain Euler–Lagrange Systems With Time-Varying Communication Delays

In this paper, under-directed topology, distributed coordinated tracking control schemes are proposed for multiple Euler–Lagrange systems with time-varying communication delays, nonlinear uncertainties, and external disturbances. Concerning with different leader velocities, both constant leader velocity case and time-varying leader velocity case are addressed by designing two different distributed observers. Combining with the proposed distributed leader velocity observers, two coordinated tracking control schemes are developed by the effort of neural network approximation and sliding mode technique, which can compensate the nonlinearities and uncertainties. For the first case, tracking errors are rigorously proved to be globally asymptotically converged by using Lyapunov–Krasovskii method. To further eliminate chattering caused by the discontinuous sign function, the saturation function is used for the second case, and the proposed control algorithm ensures the same convergence of tracking errors via Lyapunov analysis. Finally, the effectiveness of the proposed distributed tracking control schemes is verified by the numerical examples.