This paper explores the optimal consensus problem involving fully actuated Euler-Lagrange systems with parametric uncertainties. We propose a distributed adaptive control algorithm that incorporates a novel dynamical auxiliary system to generate reference positions. Nonlinear transformation functions for the position tracking error, along with smooth compensating terms, are introduced and integrated into the reference velocity design. The proposed control framework is distinctive in that it only requires relative position measurements from neighboring agents and does not rely on any global information, thus enabling a fully distributed implementation. A theoretical analysis demonstrates that the proposed control protocol ensures the asymptotic convergence of all agents to the optimal solution of the total cost function and the boundedness of all closed-loop signals. Simulation results for two-link revolute joint manipulators are presented to validate the effectiveness of the proposed approach.

A multilevel control strategy is proposed in a lower-limb exoskeleton to reduce interaction torques and enhance compliance during human-exoskeleton cooperative motion. First, a gait dataset encompassing various movement patterns is constructed through gait acquisition experiments conducted on our lightweight device, with dynamic time warping (DTW) employed for data alignment. At the high level, dynamic movement primitives (DMPs) combined with Gaussian mixture models (GMM) and Gaussian mixture regression (GMR) are utilized to learn multiple demonstration trajectories and generate reference trajectories. At the middle level, an admittance controller is designed to derive the desired exoskeleton trajectory from human-exoskeleton interaction torques. At the low level, an adaptive fixed-time controller, incorporating barrier Lyapunov functions (BLF) and fuzzy logic systems (FLS), is developed to address model uncertainties and output constraints. Finally, the effectiveness of the proposed strategy is validated through both simulations and experiments in active and passive training modes, demonstrating robust tracking, bounded error dynamics, and reduced interaction torques.

Hypersonic flight vehicle faces critical challenges of control from highly nonlinear and time-varying uncertainties, which impose stringent requirements for real-time parameter adaptation under safety constraints. This paper proposes a reinforcement learning-based adaptive tracking control algorithm to address these issues. The crucial contributions of our design, as opposed to the state-of-the-art approaches, lie in three aspects: (a) a hybrid design of model-based control and reinforcement learning to alleviate the safety, stability and generalization issues of learning-based methods specifically for the demanding hypersonic flight environment; (b) the establishment of a reinforcement learning-based optimization framework that dynamically adjusts control parameters in a real-time optimal fashion to improve the tracking performance under dynamic uncertainties and flight regime transitions, which is substantially different from most conventional methods with constant parameters; (c) the theoretical analysis of both the closed-loop stability of the adaptive control and the convergence performance of the learning algorithm, which distinguishes our design from most existing reinforcement learning-based methods that have no stability or convergence guarantee and is particularly critical for safety-critical hypersonic flight vehicle applications. Numerical simulations show that the proposed method achieves a reduction in the integral of tracking error of 8.31% under model perturbations and 34.3% under changing reference trajectories, compared to the baseline method, while maintaining comparable control energy consumption.

Fixed-time consensus control offers an explicit upper bound on the settling time that is independent of initial conditions, making it particularly valuable for time-critical applications. This survey reviews recent advances in this field, with emphasis on two primary directions: extending fixed-time consensus to broader classes of dynamical multiagent systems, and designing engineered protocols that enhance practical applicability. First, we examine fixed-time consensus results for general dynamical systems, including well-established methods for general linear multiagent systems and emerging approaches for specific classes of nonlinear systems, where a unified theoretical framework remains elusive. Notably, conventional fixed-time consensus protocols often induce excessively large initial control inputs and lack fully distributed settling-time estimation, motivating the development of protocols with engineered features. Second, we review recent advances in specialized consensus protocols that address these practical challenges, focusing primarily on finite-time consensus protocols with bounded control inputs and fully distributed fixed-time consensus protocols, while also covering recent efforts on event-triggered implementations and secure strategies under cyberthreats. The practical utility of these protocols is demonstrated through two case studies: position synchronization of brushless dc motor systems and frequency regulation in islanded microgrids. Finally, key challenges and promising directions for future research are discussed.

This paper investigates the consensus problem of leader-follower nonlinear high-order multi-agent systems through a fully distributed approach. A distributed consensus tracking control scheme is proposed, embedding a fixed-time convergent command filter with adaptive gain to ensure that the filter error ultimately reaches the origin. To tackle the challenges posed by unknown bounds of system nonlinearities and external disturbances, a robust control protocol is developed, incorporating an adaptive mechanism to implement compensatory action instead of directly estimating the lumped uncertainty. A notable feature of the proposed approach lies in its capability to determine the settling time bound without any global information, including the number of nodes, the eigenvalue of the Laplacian matrix, and other unknown parameters. The efficacy of the developed methodology is validated through numerical simulations and physical experiment conducted on a multi-motor system.

This paper addresses the consensus issue of multiagent systems with both input amplitude and rate constraints. We propose simple yet effective distributed control algorithms that integrate a velocity damping term with nonlinear saturated functions for both undirected and directed graphs. Leveraging the interplay between Barbalat’s lemma and graph theory, we show that all agents can achieve consensus without violating predefined input amplitude and rate constraints through the presented control algorithms. Moreover, we employ the developed framework to solve the rendezvous control problem of quadrotor unmanned aerial vehicles (UAVs) with motion limits. To illustrate and validate our proposed approach, we conduct extensive simulations and comparative experiments. Note to Practitioners—Most existing control methods for multiagent systems achieve consensus but neglect the constraints on the amplitude and rate of the control signal. However, in practice, the control signals are invariably subject to limitations in their amplitude and rate due to factors such as actuator saturation, considerations for ride comfort, and actuator wear. This neglect leads to a degradation in system performance and in severe cases results in the loss of closed-loop stability. This work primarily focuses on developing new control methods that can achieve consensus without violating the predefined input amplitude and rate limitations. The experiments on rendezvous control of quadrotor UAVs show the practical applicability of the presented algorithms, which yield satisfactory control performance as verified by theoretical analysis. This research contributes to the advancement of distributed control for multiagent systems, particularly in scenarios where input constraints are a critical consideration.

The cooperative tracking control issue of quadrotor unmanned aerial vehicles (UAVs) is investigated, where a cluster of UAVs is required to maintain a preassigned pattern while tracking a reference trajectory. Since only a part of UAVs can access the reference trajectory, an adaptive distributed estimator is developed such that each UAV could obtain the accurate estimate exponentially. Based on the hierarchical development, a parallel optimal learning control strategy is proposed by introducing virtual artificial systems that generate the practical control commands. In particular, a saturated force command is exploited for the position loop tracking to the estimated trajectory and a torque command is utilized to ensure the command attitude tracking, respectively. Moreover, a data-based learning law is designed for the critic weight under the finite excitation (FE), which is made available for the inadmissible initial control. It is shown that the overall closed-loop system is uniformly ultimately bounded and the tracking errors eventually converge to small sets around zero. Simulation and experiment results further verify the proposed control strategy.Note to Practitioners—This paper is inspired by the cooperative formation control issue of quadrotor UAVs. In practical missions like surveillance and reconnaissance, a UAV comes into or leaves out of the cluster may lead to re-tune the control parameters for all the involved UAVs. To save the onboard resource, the communication topology among the UAVs cannot be tedious. The proposed parallel learning strategy is implemented as follows. First, we design an adaptive distributed estimator for each UAV that could obtain the reference information accurately. Then, we propose a data-based parallel optimal learning strategy for each UAV that tracks the estimated reference trajectory. Since the proposed strategy does not require any global information regarding the communication topology, the parameters can be remained when the UAV cluster needs to extend or reduce, which makes it more practical. Finally, the proposed strategy is validated by both simulation and experiment results.

This article investigates the leader-follower formation control of flight vehicles subject to speed and control acceleration constraints. The objective of the flight vehicles is to track a virtual leader in a nominal configuration, while the speeds and control accelerations of the flight vehicles are restricted within certain ranges. A distributed extended state observer (DESO) featuring practical predefined-time convergence is proposed for the followers to estimate the leader's position and velocity. Then, an adaptive finite-time position tracking control law is developed so that the followers form the expected formation by tracking the expected positions related to the estimation of the virtual leader's information and the nominal configuration. The speed constraint is satisfied by leveraging a transformation based on the inverse hyperbolic tangent function, while an adaptive scheme exploiting the integral barrier Lyapunov function (IBLF) is proposed to address the control acceleration constraints. Numerical simulations are conducted to validate the proposed method.

This paper investigates the problem of finite-time stabilization and trajectory tracking control of a nonholonomic wheeled mobile robot (NWMR) under input constraints. Based on the hyperbolic tangent functiontanh(⋅), a bounded finite-time stabilization controller and a bounded finite-time tracking controller are proposed. Specifically, for the stabilization controller, a switching strategy is used and an explicit upper-bound estimate for the closed-loop settling time is provided. For the tracking controller, a finite-time control scheme consisting of a bounded angular velocity controller and a bounded linear velocity controller is developed. For both the stabilization controller and the tracking controller, the saturation level of the control input can be predefined based on the actuator’s capacity. Comprehensive finite-time stability analyses are provided by selecting appropriate Lyapunov functions. Finally, simulation and experimental results addressing the stabilization and trajectory tracking problem for NWMR demonstrate the effectiveness of the proposed controllers.

This paper provides some new results for attitude tracking control for rigid body. In order to avoid the complexity and ambiguity associated with other attitude representations (such as Euler angles or quaternions), the attitude dynamics and the proposed control system are represented globally on special orthogonal groups. Based on a special attitude error, we construct a novel attitude error dynamic model, and develop a baseline controller which ensures the asymptotic attitude tracking almost globally in the absence of disturbances and uncertainties. To account for external disturbances and parametric uncertainties, adaptive laws are introduced to estimate the unknown bound of the equivalent disturbance as well as the inertia matrix of the rigid body. Then, an almost global adaptive attitude tracking controller is developed to track a given desired attitude trajectory without requiring the exact knowledge of inertia matrix, while guaranteeing boundedness of tracking errors. Finally, both simulation and experimental results are presented to demonstrate the efficiency of the proposed controllers.Note to Practitioners—Attitude tracking problem is very common in many engineering applications, especially for satellites. This paper presents a new methodology for attitude tracking control of a rigid body subject to external disturbances and parametric uncertainties. Employing a novel attitude error dynamic model, we present a new geometric attitude tracking controller based on the left attitude error and the left velocity error. The proposed controller has a simple structure and can effectively reduce the energy consumption, which may have wide application prospects.

This article is devoted to distributed adaptive asymptotic consensus tracking control based on output feedback for the uncertain high-order multiagent systems with input quantization. Compared with the output-feedback canonical form, the system takes unmeasured states-dependent nonlinearities into account and also includes unknown parameters and quantized input. The improved K -filters with one dynamic gain are constructed to dispose the unmeasured states-dependent nonlinearities and estimate the unknown states. Then, the novel recursive control strategy with the aid of new first-order dynamic parameter filters is proposed, which is able to effectively counteract the filter errors and steer the consensus tracking errors to zero asymptotically with low design complexity. Moreover, the new funnel variable combined with prespecified time performance function is first introduced, which can predefine practical transition time and maximum overshoot of consensus error. Finally, simulation results are presented to illustrate the validity and superiority of the proposed scheme.

This article investigates the problem of cooperative guidance against maneuvering target under malicious attacks. In consideration of the false-data injection attacks (FDIAs), a reputation-based cooperative guidance law with fault tolerance is proposed to drive multiflight vehicles to reach a maneuvering target simultaneously. A novel prescribed performance function (PPF) with predefined-time convergence is presented by taking into account the limitation of available capacity. By incorporating the reputation system based on confidence factors and trust factors, which are leveraged to identify the attacked communication links or vehicle members, the fault-tolerant behavior can be achieved to resist the effects resulted from the FDIAs. The effectiveness of the reputation-based fault-tolerant cooperative guidance method is verified by numerical simulation.

Fixed-time and prescribed-time consensus control can bring an explicit estimate of the settling time without dependence on initial conditions, which is important in providing control engineersa priorisystem information. This article aims at presenting a survey of recent trends and methodologies of fixed-time and prescribed-time consensus control in multiagent systems. First, some typical fixed-time consensus results are reviewed. Despite the advantage in deriving a fixed settling time bound, fixed-time consensus controllers usually result in a conservative estimate of the bound and a large magnitude of initial control input, which in turn show the necessity of designing prescribed-time consensus controllers. Second, characteristics and controller design of (practical, respectively) prescribed-time consensus are provided in detail. Particularly, representative time-varying function-based controllers are presented, by which (practical, respectively) consensus can be achieved in prescribed time. Third, applications of fixed-time and prescribed-time consensus control in mobile robots and smart grids are illustrated in case studies. Finally, several challenging issues in prescribed-time consensus control are discussed for future research.

A fixed-time trajectory tracking control method for uncertain robotic manipulators with input saturation based on reinforcement learning (RL) is studied. The designed RL control algorithm is implemented by a radial basis function (RBF) neural network (NN), in which the actor NN is used to generate the control strategy and the critic NN is used to evaluate the execution cost. A new nonsingular fast terminal sliding mode technique is used to ensure the convergence of tracking error in fixed time, and the upper bound of convergence time is estimated. To solve the saturation problem of an actuator, a nonlinear antiwindup compensator is designed to compensate for the saturation effect of the joint torque actuator in real time. Finally, the stability of the closed-loop system based on the Lyapunov candidate is analyzed, and the timing convergence of the closed-loop system is proven. Simulation and experimental results show the effectiveness and superiority of the proposed control law.

This article investigates a robust path-following control problem of multiple autonomous vehicles along an implicit elliptical curve. At the kinematic level, by formulating a novel coordinated error in terms of projective arc length instead of relative distance, a new distributed guidance law is developed for multiple vehicles evolving along a geometric path, achieving an equal arc separation and a uniform forward speed. Based on simple filtering operations upon available states and invariant manifold, unknown system dynamics estimators (USDEs)-based robust kinetic controllers with a concise structure are derived to enable a satisfied nominal tracking of velocity and angular rate subject to uncertainties while eliminating the computational complexity encountered in the available function approximators. The remarkable merit of the explored solution lies in that robust cooperative behaviors over an implicit elliptical curve can be attained by specifying successive projective arc length for nonholonomic vehicles, avoiding the time-consuming path variable synchronization calculation inherent in parameterized reference-guided paradigms, eliminating temporal limitations of time-related function in trajectory tracking strategies. It is proven that all signals of a closed-loop system are convergent by using the input-to-state stable (ISS) principle. Simulation and experimental outcomes are both delivered to substantiate the efficacy and superiority of the presented method.

This article is concerned with both consensus and coordinated path-following control for multiple nonholonomic wheeled mobile robots. In the design, the path-following control is decoupled into the longitudinal control (speed control) and the lateral control (heading control) for the convenience of implementation. Different from coordinated trajectory tracking control schemes, the proposed control scheme removes the temporal constraint, which greatly improves the coordination robustness. In particular, two new coordinated error variables describing a chasing-and-waiting strategy are introduced in the proposed coordinated path-following control for injective paths and circular paths, respectively. All the closed-loop signals have proved to be asymptotically stable in the Lyapunov sense. Finally, simulation results under three typical paths are presented to verify the proposed coordination controllers.

This article addresses the robust fixed-time stabilization control problem for generic linear systems with both matched and mismatched disturbances. A new observer-based fixed-time control technique is proposed to solve this robust stabilization problem, provided that the system matrix pair$(A,B)$is controllable. The ultimate boundedness of the closed-loop system in the presence of mismatched disturbances is proven. An upper bound of the convergence time is provided, which is irrelevant to initial conditions. Finally, a simulation example is presented to show the efficiency of the proposed control design method.

A systematic differentiator-based adaptive backstepping control methodology is proposed for a class of sandwich-like nonlinear system with unknown state-dependent deadzone nonlinearity and parametric uncertainties. The novelty of our approach is that a high-order sliding mode differentiator is utilized to estimate the nonstrict feedback coupling term resulting from the sandwiched deadzone, and all the outputs of the differentiator are integrated into the backstepping procedure based on Lyapunov functions with flat zone recursively. By this approach, all the unknown parameters are estimated online, the discontinuity of the virtual input caused by bound estimations is avoided. It is shown that the ultimate boundedness of all the closed-loop signals is achieved and the output tracking error converges to a preset set. Simulation is performed to verify the theoretical findings.

This paper deals with the problem of distributed optimization for multiagent systems by using an edge-based fixed-time consensus approach. In the case of time-invariant cost functions, a new distributed protocol is proposed to achieve the state agreement in a fixed time while the sum of local convex functions known to individual agents is minimized. In the case of time-varying cost functions, based on the new distributed protocol in the case of time-invariant cost functions, a distributed protocol is provided by taking the Hessian matrix into account. In both cases, stability conditions are derived to ensure that the distributed optimization problem is solved under both fixed and switching communication topologies. A distinctive feature of the results in this paper is that an upper bound of settling time for consensus can be estimated without dependence on initial states of agents, and thus can be made arbitrarily small through adjusting system parameters. Therefore, the results in this paper can be applicable in an unknown environment such as drone rendezvous within a required time for military purpose while optimizing local objectives. Case studies of a power output agreement for battery packages are provided to demonstrate the effectiveness of the theoretical results.

This paper deals with the problem of distributed optimization of a multiagent system with network connectivity preservation. In order to realize cooperative interactions, a connected network is the prerequisite for high-quality information exchange among agents. However, sensing or communication capability is range-limited, so it is impractical to simply make an assumption that network connectivity is preserved by default. To address this concern, a class of generalized potentials including discontinuities caused by unexpected obstacles or noises are designed. For a class of quadratic cost functions, based on the potentials, a new distributed protocol is proposed to formally guarantee the network connectivity over time and to realize the state agreement in finite time while the sum of local functions known to individual agents is optimized. Since the right-hand side of the proposed protocol is discontinuous, some nonsmooth analysis tools are applied to analyze system performance. In some practical scenarios, where initial states are unavailable, a distributed protocol is further developed to realize the consensus in a prescribed finite time while solving the distributed optimization problem and maintaining network connectivity. Illustrative examples are provided to demonstrate the effectiveness of the proposed protocols.

This paper addresses the fixed-time leader-follower consensus problem for second-order multiagent systems without velocity measurement. A new continuous fixed-time distributed observer-based consensus protocol is developed to achieve consensus in a bounded finite time fully independent of initial condition. A rigorous stability proof of the multiagent systems by output feedback control is presented based on the bi-limit homogeneity and the Lyapunov technique. Finally, the efficiency of the proposed methodology is illustrated by numerical simulation.

In this paper, we study output feedback leader-follower consensus problem for multiagent systems subject to external disturbances and time delays in both input and output. First, we consider the linear case and a novel predictor-based extended state observer is designed for each follower with relative output information of the neighboring agents. Then, leader-follower consensus protocols are proposed which can compensate the delays and disturbances efficiently. In particular, the proposed observer and controller do not contain any integral term of the past control input and hence are easy to implement. Consensus analysis is put in the framework of Lyapunov-Krasovskii functionals and sufficient conditions are derived to guarantee that the consensus errors converge to zero asymptotically. Then, the results are extended to nonlinear multiagent systems with nonlinear disturbances. Finally, the validity of the proposed design is demonstrated through a numerical example of network-connected unmanned aerial vehicles.

This paper is concerned with the collective behaviors of robots beyond the nearest neighbor rules, i.e., dispersion and flocking, when robots interact with others by applying an acute angle test (AAT)-based interaction rule. Different from a conventional nearest neighbor rule or its variations, the AAT-based interaction rule allows interactions with some far-neighbors and excludes unnecessary nearest neighbors. The resulting dispersion and flocking hold the advantages of scalability, connectivity, robustness, and effective area coverage. For the dispersion, a spring-like controller is proposed to achieve collision-free coordination. With switching topology, a new fixed-time consensus-based energy function is developed to guarantee the system stability. An upper bound of settling time for energy consensus is obtained, and a uniform time interval is accordingly set so that energy distribution is conducted in a fair manner. For the flocking, based on a class of generalized potential functions taking nonsmooth switching into account, a new controller is proposed to ensure that the same velocity for all robots is eventually reached. A co-optimizing problem is further investigated to accomplish additional tasks, such as enhancing communication performance, while maintaining the collective behaviors of mobile robots. Simulation results are presented to show the effectiveness of the theoretical results.

Fixed-time cooperative control is currently a hot research topic in multiagent systems since it can provide a guaranteed settling time, which does not depend on initial conditions. Compared with asymptotic cooperative control algorithms, fixed-time cooperative control algorithms can achieve better closed-loop performance and disturbance rejection properties. Different from finite-time control, fixed-time cooperative control produces the faster rate of convergence and provides an explicit estimation of the settling time independent of initial conditions, which is desirable for multiagent systems. This paper aims at presenting an overview of recent advances in fixed-time cooperative control of multiagent systems. Some fundamental concepts about finite- and fixed-time stability and stabilization are first recalled with insight understanding. Then, recent results in finite- and fixed-time cooperative control are reviewed in detail and categorized according to different agent dynamics. Finally, this paper raises several challenging issues that need to be addressed in the near future.

In this paper, we study the fixed-time cooperative tracking control problem for multi-robot systems with doubleintegrator dynamics. First, a novel distributed observer is proposed for each follower to estimate the leader state in a fixed time, then a local tracking controller based on sliding mode technique is proposed such that the estimated leader state is tracked in a fixed time. Both cases of a stationary leader and a dynamic leader are investigated. Since nonholonomic dynamics can better describe the mobile robots in reality, we further extend the results to achieve fixed-time cooperative tracking for multi-robot systems with nonholonomic dynamics. Different from the conventional finite-time cooperative tracking strategies, the fixed-time approach in this work guarantees that an upper bound of settling time can be prescribed without dependence on initial states of robots, which provides additional system information in advance. Finally, numerical simulations are given to demonstrate the effectiveness of the theoretical results.

In this paper, the position control problem of a gear transmission servo system with dead-zone nonlinearity is investigated. All the parameters involved in both system model and dead-zone nonlinearity model are allowed totally unknown. An adaptive back stepping control scheme is presented. The effects of dead-zone nonlinearities are described by mismatched and matched disturbances, which are compensated by introducing additional estimates of their bounds in control laws and robust terms in parameter update laws. It is shown that all the closed-loop signals can be ensured bounded and the output regulation error will converge to a compact set. Simulation results are provided to show the effectiveness of the proposed adaptive control scheme.

The output tracking problem of gear transmission servo (GTS) systems with backlash nonlinearity is studied in this paper. A new concept-“soft degree”-is proposed to overcome the nondifferentiable “hard” characteristic of the backlash nonlinearity. Furthermore, a detailed softening process-static softening is presented, where a backstepping control algorithm is developed to guarantee that the output of the controlled systems can track any given desired sufficiently smooth trajectory by arbitrary precision and the limit cycles that appear due to backlash nonlinearity can be avoided. Simulation results validate the effectiveness of the proposed controller.