Euler-Lagrange Systems Research Articles

Adaptive Reinforcement Learning Strategy-Based Sliding Mode Control of Uncertain Euler–Lagrange Systems With Prescribed Performance Guarantees: Autonomous Underwater Vehicles-Based Verification

Adaptive Reinforcement Learning Strategy-Based Sliding Mode Control of Uncertain Euler–Lagrange Systems With Prescribed Performance Guarantees: Autonomous Underwater Vehicles-Based Verification

Adaptive Saturated Obstacle Avoidance Trajectory Tracking Control for Euler–Lagrange Systems With Velocity Constraints

ABSTRACTThis article pays attention to the obstacle avoidance trajectory tracking control problem for uncertain Euler–Lagrange (EL) systems subject to velocity constraints and input saturation. The existing obstacle avoidance results do not consider velocity constraints under input saturation, which means that an EL system may not be able to obtain sufficient control inputs to avoid a collision with an obstacle if it has a high speed when approaching the obstacle. Therefore, the velocity constraints in the obstacle avoidance tracking control are considered in this paper. A novel velocity constraint function that depends on the distance between the system and the obstacle is proposed. Integral‐multiplicative Lyapunov‐barrier functions (LBFs) are constructed and incorporated into the backstepping procedure to design an adaptive fuzzy obstacle avoidance tracking control scheme. Moreover, an auxiliary dynamic system is designed by constructing a bounded nonlinear vector related to an auxiliary variable to compensate for the effects of saturation. Through the Lyapunov method and boundedness analysis for the barrier function, it is shown that the protocol achieves obstacle avoidance for the EL system without violating the velocity constraints inside the obstacle detection region, while also guaranteeing the ultimate uniform boundedness of all the closed‐loop signals. Numerical simulations are presented to demonstrate the efficacy of the proposed control strategy.

Synchronization of Euler-Lagrangian networks: a periodic intermittent dynamic event-triggered control strategy

In this paper, the synchronization problem of Euler–Lagrange networks is studied by designing periodic intermittent dynamic event-triggered control strategy. The synchronization of all agents is successfully realized by injecting negative comments into the discontinuous interval of the agents described by the Euler–Lagrange systems. Different from the traditional intermittent event-triggered control strategy, the control strategy proposed in this study introduces internal dynamic variables to expand the sampling interval of the event-triggered mechanism, thereby improving resource utilization efficiency. In addition, the event trigger instants of each agent are asynchronous. By using graph theory and Lyapunov method, the synchronization criteria of Euler–Lagrange networks are derived. The effectiveness of the proposed control scheme is verified by simulations for the Euler-Lagrangian network composed of six two-link rotating manipulators.

Fixed-time and predefined-time group-bipartite consensus for uncertain networked Euler-Lagrange systems

This paper aims to investigate the fixed-time and predefined-time group-bipartite consensus (FTGBC, PTGBC) problems for uncertain networked Euler-Lagrange systems (NELSs) using neural network (NN). An auxiliary sliding mode variable describing the local communication topology is first introduced within the fixed-time and predefined-time frameworks, and the NN technique is used to estimate online uncertainty of NELSs, which ensures the achievement of the desired FTGBC and PTGBC goals, respectively. Moreover, the allowable upper bound expressions for fixed-time and predefined-time are derived by analyzing the convergence of the closed-loop control systems, thus ensuring the adaptability, stability, and robustness of the proposed FTGBC and PTGBC control schemes, which are further verified by numerical simulation examples.

The Distributed Adaptive Bipartite Consensus Tracking Control of Networked Euler–Lagrange Systems with an Application to Quadrotor Drone Groups

Actuator faults and external disturbances, which are inevitable due to material fatigue, operational wear and tear, and unforeseen environmental impacts, cause significant threats to the control reliability and performance of networked systems. Therefore, this paper primarily focuses on the distributed adaptive bipartite consensus tracking control problem of networked Euler–Lagrange systems (ELSs) subject to actuator faults and external disturbances. A robust distributed control scheme is developed by combining the adaptive distributed observer and neural-network-based tracking controller. On the one hand, a new positive definite diagonal matrix associated with an asymmetric Laplacian matrix is constructed in the distributed observer, which can be used to estimate the leader’s information. On the other hand, neural networks are adopted to approximate the lumped uncertainties composed of unknown matrices and external disturbances in the follower model. The adaptive update laws are designed for the unknown parameters in neural networks and the actuator fault factors to ensure the boundedness of estimation errors. Finally, the proposed control scheme’s effectiveness is validated through numerical simulations using two types of typical ELS models: two-link robot manipulators and quadrotor drones. The simulation results demonstrate the robustness and reliability of the proposed control approach in the presence of actuator faults and external disturbances.

Robust Adaptive Fuzzy Control for Second-Order Euler-Lagrange Systems With Uncertainties and Disturbances via Nonlinear Negative-Imaginary Systems Theory.

Ensuring robust and precise tracking control in the presence of uncertain multi-input-multi-output (MIMO) system dynamics and environmental variations is a significant challenge in the field of robust and adaptive control theory. While fuzzy control strategies have demonstrated good tracking performance in normal conditions, designing and tuning fuzzy controllers can be a challenging task in highly uncertain environments. In this study, we investigate a novel approach that combines robust nonlinear negative-imaginary (NI) systems theory with a self-adaptive fuzzy control scheme and the Lyapunov synthesis to develop a robust adaptive negative-imaginary-fuzzy (RANIF) control scheme. We optimize the critical parameters of the proposed fuzzy system using a self-tuning technique with a proportional-derivative sliding manifold. Furthermore, unlike the existing adaptive fuzzy control methods, we propose a small number of membership functions and systematically derive the fuzzy rules by employing Lyapunov, nonlinear NI, and dissipativity theories, which simplify the tuning process, work out the matter of "explosion of complexity," and reduce computational complexity. We demonstrate the global stability of the closed-loop system using nonlinear NI theory. To evaluate the effectiveness of our proposed approach, we present simulation results for two examples involving uncertain MIMO second-order Euler-Lagrange systems. These systems, known for their capacity to represent a diverse range of practical physical systems, serve as suitable testbeds for our methodology. Our results show that RANIF outperforms other control methods, such as nonlinear strictly NI-Fuzzy, fuzzy-logic control, model predictive control, and conventional PID control, in terms of robustness to disturbances and inestimable faults, trajectory tracking performance, and computational complexity.

Neural network-based distributed consensus tracking control for uncertain Euler–Lagrange systems over directed topologies

This paper proposes a neural network-based robust control approach for driving disturbed Euler–Lagrange systems (e.g., robot manipulator) in a directed network to perform consensus tracking of a heterogeneous leader’s output signal. The parameter matrices and external disturbances in each follower’s Euler–Lagrange dynamics are unmeasurable, thus we unify them into one lumped uncertainty term. Neural networks are then employed to online estimate these uncertainties, with adaptive update laws ensuring the boundedness of the estimation errors. Subsequently, a set of distributed observers are developed to adaptively estimate the leader’s states as well as the unidentified parameter vector and output matrix in the leader’s model. With their help, the robust cooperative controller is designed. Its efficacy on directed networks is theoretically justified by designing a Lyapunov function with a special structure. This function produces symmetric positive definite matrices when its first derivative terms interact with the specified parameters in the observer and Laplacian matrices for directed graphs. Finally, numerical simulations based on two-link robot manipulators are carried out to verify that the tracking errors converge to zero when applying the neural network-based robust controller.

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.

Practical output regulation of uncertain Euler–Lagrange systems

This paper deals with the problem of robust output regulation of uncertain Euler–Lagrange systems. An internal model controller is synthesized by a systematic framework that considers polynomial mappings of the steady-state trajectory. The closed-loop stabilization is guaranteed by using a descriptor differential–algebraic representation of the system. This methodology allows the controller design problem to be cast as a convex optimization problem subject to linear matrix inequalities. Simulations considering a two-link robotic manipulator illustrate the method.

Bipartite tracking for Euler–Lagrange systems via prescribed‐time hierarchical control based on the matrix‐weighted signed digraphs

AbstractThe goal of this article is to investigate the bipartite tracking control problem using a prescribed‐time convergence method for Euler–Lagrange systems (ELSs) with external disturbances. Agent interactions are represented by a matrix‐weighted signed directed graph. There are not only cooperative but also adversarial interactions. An essential component of the system, the prescribed‐time hierarchical control (PTHC) algorithm, including a more general time‐varying function, is newly developed to guarantee that all agents converge to the same leader state but with opposite signs within a prescribed time. The salient feature of the introduced method lies in the fact that the convergence time of the control objective can be prespecified by the user. The state transformation, the property of the matrix‐weighted Laplacian, and the generalized Lyapunov stability argument are employed to theoretically validate the proposed algorithms. Finally, the effectiveness of the algorithm is confirmed through the execution of numerical examples.

Static Anti-Windup for Global Regulation of Constrained Euler-Lagrange Systems

Static Anti-Windup for Global Regulation of Constrained Euler-Lagrange Systems

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.

Predefined-time Leader-following Consensus for Networked Euler-Lagrange Systems With External Disturbance

Predefined-time Leader-following Consensus for Networked Euler-Lagrange Systems With External Disturbance

Predefined‐time hierarchical control for bipartite time‐varying formation tracking of networked Euler–Lagrange systems with parametric uncertainties

AbstractThis paper mainly addresses the bipartite time‐varying formation tracking (BTVFT) problem for networked Euler–Lagrange systems (NELSs) with external disturbances and parametric uncertainties, considering a directed signed communication network that encompasses both cooperative and competitive interactions. A novel nonsingular sliding mode control (SMC) method serves as the foundation for a predefined‐time hierarchical control algorithm (PTHCA), introduced to tackle the BTVFT challenge for NELSs in a predefined time. This approach enables the settling time to be predetermined as a control parameter. Moreover, sufficient conditions for establishing the predefined‐time stability of closed‐loop systems are provided based on the Lyapunov argument. Simulations are conducted to demonstrate the effectiveness of the main findings.

Safety-critical formation control of switching uncertain Euler-Lagrange systems with control barrier functions

This paper investigates the safety-critical formation control problem with disturbance rejection for switching uncertain EL MASs in the presence of multiple stationary/moving obstacles. A safety-critical control method is proposed for achieving a collision-free formation for a group of EL systems subject to safety constraints, model uncertainties, and external disturbances. Specifically, a distributed adaptive nominal control law is designed to accomplish the formation control task. Then, based on ISSf-CBF derived safety constraints, a distributed quadratic programming problem is established for computing the optimal control input subject to safety constraints. The safety and stability of the closed-loop control system have been demonstrated. Finally, one exemplary application to safety-critical formation control of some practical multiple mechanical systems is provided to illustrate the effectiveness of the main result.

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.

Finite-time control of uncertain Euler–Lagrange systems using ELM-based velocity observer

This paper is concerned with the finite-time trajectory tracking control of a class of Euler–Lagrange (EL) systems under unknown velocity information, dynamic uncertainties and disturbances. An extreme learning machine (ELM) algorithm is employed to approximate the uncertainties, while an adaptive algorithm is proposed to tune output weights of the ELM, as well as to eliminate the negative effects of residual errors and disturbances. Then an adaptive finite-time ELM-based velocity observer is developed to estimate the unavailable velocity states. Further, based on the estimations and the approximations of model uncertainties, an adaptive finite-time observer-based nonsingular terminal sliding mode (TSM) control strategy is constructed to guarantee the finite-time bounded tracking of the uncertain EL system by using the Lyapunov stability theorem. Simulation results on a robotic manipulator platform demonstrate the efficiency of the developed finite-time observation and control methods.

Fixed‐time consensus of networked Euler–Lagrange systems over event‐based communication under DoS attacks

AbstractThis 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.

Resilient exponential tracking for disturbed systems with communication links faults

Resilience is to appraise the ability of disturbed systems to recover cooperative performance after suffering from failures or disturbances. In this paper, the improvement on the exponential tracking resilience for disturbed Euler–Lagrange systems is explored by settling the unknown time-variant faults imposed on the communication interaction between agents. First, we transform the resilient exponential tracking problem into designing the trajectory and velocity observers for leaders, and showcase that the proposed observers are resilient to communication interaction malfunctions. Second, a disturbance observer is manifested to estimate disturbances precisely, which is needless to know the upper bound of disturbance. The reliable observers and estimator are incorporated into the resilient tracking control frame. Further, the global exponential stabilization of the tracking systems is performed by utilizing the Lyapunov theory. Moreover, benefiting from feasible and reliable observation and estimation results, the proposed control framework enables to realize a satisfactory resilient exponential tracking performance even in the case of communication links faults (CLFs) and disturbances. Comprehensive studies are executed on a group of satellite systems, and the simulations results verify the effectiveness of the proposed resilient approaches in a time-variant tracking case.