Actuator Limitations Research Articles

Dynamic Adaptive Event-Triggered Mechanism for Fractional-Order Nonlinear Multi-Agent Systems with Actuator Saturation and External Disturbances: Application to Synchronous Generators

This paper presents a novel dynamic adaptive event-triggered mechanism (DAETM) for addressing actuator saturation in leader–follower fractional-order nonlinear multi-agent networked systems (FONMANSs). By utilizing a sector-bounded condition approach and a convex hull representation technique, the proposed method effectively addresses the effects of actuator saturation. This results in less conservative linear matrix inequality (LMI) criteria, guaranteeing asymptotic consensus among agents within the FONMANS framework. The proposed sufficient conditions are computationally efficient, requiring only simple LMI solutions. The effectiveness of the approach is validated through practical applications, such as synchronous generators within a FONMANS framework, where it demonstrates superior performance and robustness. Additionally, comparative studies with Chua’s circuit system enhance the robustness and efficiency of control systems compared to existing techniques. These findings highlight the method’s potential for broad application across various multi-agent systems, particularly in scenarios with limited communication and actuator constraints. The proposed approach enhances system performance and provides a robust, adaptive control solution for dynamic and uncertain environments.

Z-Ary Compression Event-Triggered Control for Spacecraft with Adhesive-Resilient Prescribed Performance

The attitude tracking control for spacecraft with limited communication and actuator faults is investigated in this paper by employing event-trigger-based prescribed control. Traditional methods struggle to address arbitrary initial conditions and fault-induced saturation, which both lead to prescribed control singularities, limiting practical deployment. This paper proposes the adhesive-resilient prescribed control (ARPC), which dynamically adjusts the performance envelope by sensing fault and error trends through resilient correction and an adhesive mechanism, respectively. This approach significantly enhances conservatism and robustness, particularly under actuator faults that exceed the saturation level. Additionally, the challenge of balancing high performance with low communication burden under limited resources is addressed. To mitigate communication frequency and bit consumption without sacrificing performance, a z-ary compression event-triggered scheme (CES) is introduced. Compared to existing methods, this work provides substantial improvements in fault tolerance, communication efficiency, and performance adaptability. Numerical experiments demonstrate the superiority of our method in regulating tracking error within a custom envelope and appointed time, regardless of initial conditions, while minimizing communication usage.

A practical and online trajectory planner for autonomous ships’ berthing, incorporating speed control

Abstract Autonomous ships are designed and equipped to perceive their internal and external environments and subsequently take appropriate actions based on predefined objective(s) without human intervention. Consequently, trajectory-planning algorithms for autonomous berthing must consider factors such as system dynamics, ship actuators, environmental disturbances, and operational safety. In this study, trajectory planning for an autonomous ship was modeled as an optimal control problem (OCP), which was transcribed into a nonlinear programming problem (NLP) using direct multiple shooting. To enhance berthing safety, wind disturbances, speed control guidelines, actuator limitations, and collision avoidance features were incorporated as constraints in the NLP, which was then solved using the sequential quadratic programming (SQP) algorithm in MATLAB. Finally, the performance of the proposed planner was evaluated through (i) comparison with an existing method, (ii) trajectory planning for different harbor entry and berth approach scenarios, and (iii) a feasibility study using predefined as well as stochastically generated initial conditions. The simulation results indicate improved berthing safety as well as practical and computational feasibility.

ARRTOC: Adversarially Robust Real-Time Optimization and Control

Real-Time Optimization (RTO) plays a crucial role in process operation by determining optimal set-points for lower-level controllers. However, tracking these set-points can be challenging at the control layer due to disturbances, measurement noise, and actuator limitations, leading to a mismatch between expected and achieved RTO benefits. To address this, we present the Adversarially Robust Real-Time Optimization and Control (ARRTOC) algorithm. ARRTOC addresses this issue by finding set-points which are both optimal and inherently robust to implementation errors at the control layers. ARRTOC draws inspiration from adversarial machine learning, offering a novel constrained Adversarially Robust Optimization (ARO) solution applied to the RTO layer. We present several case studies to validate our approach, including a bioreactor, a multi-loop evaporator process, and scenarios involving plant-model mismatch. These studies demonstrate that ARRTOC can improve realized RTO benefits by as much as 50% compared to traditional RTO formulations that do not account for control layer performance.

Full Envelope Control of Over-Actuated Fixed-Wing Vectored Thrust eVTOL

A novel full-envelope controller for an over-actuated fixed-wing vectored thrust eVTOL aircraft is presented. It proposes a generic control architecture, which is applicable to piloted, semi-automatic, and fully automated flight, consisting of an aircraft-level controller (high-level controller) and a control allocation scheme. The aircraft-level controller consists of a main inner loop classical nonlinear dynamic inversion controller and an outer loop proportional–integral linear controller. The inner loop nonlinear dynamic inversion controller is a velocity controller that cancels the nonlinear bare airframe dynamics, while the outer loop proportional–integral linear controller is an attitude and navigation position controller. Together, they are used for hover/low-speed control and forward flight. The control allocation scheme uses a novel architecture, which transfers the nonlinearity in the vectored thrust effector model formulation to the computation of the actuator limits by converting the effector model from polar to rectangular form, thus allowing the use of classical control allocation linear optimisation technique. The linear optimisation technique is an active set linear quadratic programming constrained optimisation algorithm with a weighted least squares formulation. The control allocation allocates the overall control demand (virtual controls) to individual redundant effectors while performing control error minimisation, control channel prioritisation and control effort minimisation. Simulation results show the transition from hover to cruise, climb and descent, and coordinated turn clearly demonstrate that the controller can handle actuator saturation (position or rate).

How Perception, Actuation, and Communication Impact the Emergence of Collective Intelligence in Simulated Modular Robots.

Modular robots are collections of simple embodied agents, the modules, that interact with each other to achieve complex behaviors. Each module may have a limited capability of perceiving the environment and performing actions; nevertheless, by behaving coordinately, and possibly by sharing information, modules can collectively perform complex actions. In principle, the greater the actuation, perception, and communication abilities of the single module are the more effective is the collection of modules. However, improved abilities also correspond to more complex controllers and, hence, larger search spaces when designing them by means of optimization. In this article, we analyze the impact of perception, actuation, and communication abilities on the possibility of obtaining good controllers for simulated modular robots, that is, controllers that allow the robots to exhibit collective intelligence. We consider the case of modular soft robots, where modules can contract, expand, attach, and detach from each other, and make them face two tasks (locomotion and piling), optimizing their controllers with evolutionary computation. We observe that limited abilities often do not prevent the robots from succeeding in the task, a finding that we explain with (a) the smaller search space corresponding to limited actuation, perception, and communication abilities, which makes the optimization easier, and (b) the fact that, for this kind of robot, morphological computation plays a significant role. Moreover, we discover that what matters more is the degree of collectivity the robots are required to exhibit when facing the task.

Plasmonic Nanocomposite for Visible Light‐Modulated Bimorph‐Actuator

AbstractSoft actuators have great potential applications in sophisticated movement and sensitive devices due to their flexible nature, good interaction, and precise control. However, existing carbon‐based optical actuators are limited in their response under visible light irradiation. The limited visible light absorbance of the carbon nanostructure brought the metallic nanoparticle into the soft actuators that can absorb visible light. This study introduces a new type of plasmonic photothermal‐bimorph actuator, using graphene oxide (GO), reduced graphene oxide (rGO), and silver nanorods (Ag NRs) to overcome the limitations of traditional optical actuators. The bimorph film is actuated by visible and near‐infrared light stimuli with various power densities showing reversible deformation behavior. The actuator shows significant bending associated with a ≈50° change in bending angle under visible light irradiation with a response time of ≈5 ± 1 sec. Furthermore, a smart photo‐controlled non‐contact switch is fabricated based on photo‐thermal conversion properties, demonstrating perfect integration of plasmonic bimorph actuators. The density functional theory based molecular dynamics calculations provide an additional understanding of the bending of actuators under external stimulus. Using illustrative demonstrations of actuators, these results hint at a method for generating multipurpose visible light‐based soft robots, supporting a new approach to developing an optical locking system.

Consensus analysis for heterogeneous multiagent systems subject to input saturation

AbstractThis paper investigates the consensus problem of heterogeneous multiagent systems (HMASs) consisting of first‐order and second‐order agents, where second‐order linear and second‐order nonlinear agents are included in the second‐order agents. Firstly, the consensus problem of HMASs without input saturation is studied in the first part. However, in practical applications, due to the physical limitations of actuators, saturation often occurs. Therefore, we focus on the consensus problem of HMASs with input saturation in the second part. Then based on the knowledge of Lyapunov stability theory and graph theory, it gives sufficient conditions for these HMASs to reach consensus, which ensures that each agent eventually reaches consensus. Eventually, the effectiveness of the theory is verified by performing simulations.

The development, characterisation and optimisation of bismuth ferrite (BFO)-incorporated Nafion membrane with comb-shaped inner structure as IPMC actuator for driving valveless micropump

Micropumps have become increasingly popular in biomedical devices due to their accurate, safe, and precise pharmaceutical administration. Ionic polymer-metal composites (IPMC) have shown great potential as diaphragm materials for micropump actuation. Redesigning the diaphragm shape can increase deformation by eliminating edge limitations in circular IPMC actuators. The present study demonstrates the application of inner cantilever-based (comb-shape) IPMC as actuation diaphragms in a micropump to enhance fluid movement. Furthermore, the effectiveness of an IPMC actuator is influenced by water absorption capacity, capacitance, and proton conductivity. To enhance the aforementioned characteristics, bismuth ferrite (BFO) was added to a Nafion matrix, resulting in a porous structure that increases capacitance. Moreover, the BFO-Nafion nanocomposite membrane exhibits a notably higher proton conductivity (0.1806 Scm−1) at a temperature of 30° C, in comparison to the normal Nafion 117 membrane (0.0254 Scm−1). The COMSOL Multiphysics and LASER Doppler Vibrometer are used to optimise the shape of the membrane and assess the IPMC’s electromechanical response. The deflection of the comb-shape geometries is around 171μm, surpassing existing membrane geometries. Finally, the drug delivery device prototype has a pump module, an Android-operated electronic control module, and an OLED display. This gadget achieves an insulin flow rate of 70 μL/min when operated at 3 V with a square wave frequency of 0.1 Hz. Moreover, the experimental findings indicate that applying an 8 V voltage resulted in a peak flow rate of 270 μL/min and a maximum back pressure of 140 Pascal.

Bioinspired Hydro- and Hydrothermally Responsive Tubular Soft Actuators.

Soft actuators made of thermoresponsive polymers have great potential for intelligent robotics and biomedical devices due to their reversible deformation capability in response to temperature fluctuations. However, they are constrained by a predefined phase transition temperature, limited directional deformation, and nonbiocompatible formulations, thereby restricting their practical utility. Herein a new biomimicry approach is presented to overcome these limitations by developing hydro- and hydrothermally responsive soft actuators made of biocompatible and pliable materials i.e. cotton yarn and polyurethane. We mimic the tubular shape of elephant trunks with their unique muscle orientation by embedding a helical cotton yarn within a hydrophilic polyurethane tube, followed by targeted surface patterning. Unlike the narrow-range shape morphing across the phase transition temperature boundary of typical thermoresponsive hydrogel actuators, we harness hydrothermal stiffness variations in polyurethane to obtain consistent morphing capabilities over a much wider temperature range. The developed actuators can perform versatile activities such as linear, bending, curvilinear, and rotating movements, overcoming the unidirectional motion limitations of conventional soft actuators. The cell viability assay on the building block materials also confirms the high biocompatibility of the actuators. The reported facile fabrication strategy provides new insights for designing complex yet free-standing soft actuators from readily available supple materials.

Programming Hydrogen Bonds for Reversible Elastic-Plastic Phase Transition in a Conductive Stretchable Hydrogel Actuator with Rapid Ultra-High-Density Energy Conversion and Multiple Sensory Properties.

Smart hydrogels have recently garnered significant attention in the fields of actuators, human-machine interaction, and soft robotics. However, when constructing large-scale actuated systems, they usually exhibit limited actuation forces (≈2kPa) and actuation speeds. Drawing inspiration from hairspring energy conversion mechanism, an elasticity-plasticity-controllable composite hydrogel (PCTA) with robust contraction capabilities is developed. By precisely manipulating intermolecular and intramolecular hydrogen-bonding interactions, the material's elasticity and plasticity can be programmed to facilitate efficient energy storage and release. The proposed mechanism enables rapid generation of high contraction forces (900kPa) at ultra-high working densities (0.96MJm-3). Molecular dynamics simulations reveal that modifications in the number and nature of hydrogen bonds lead to a distinct elastic-plastic transition in hydrogels. Furthermore, the conductive PCTA hydrogel exhibits multimodal sensing capabilities including stretchable strain sensing with a wide sensing range (1-200%), fast response time (180ms), and excellent linearity of the output signal. Moreover, it demonstrates exceptional temperature and humidity sensing capabilities with high detection accuracy. The strong actuation power and real-time sensory feedback from the composite hydrogels are expected to inspire novel flexible driving materials and intelligent sensing systems.

Disturbance observer-based dynamic fuzzy sliding-mode control strategy for horizontal vibration of high-speed elevator car system

To effectively suppress the horizontal vibration of high-speed elevator cars caused by uncertainties such as unevenness of guide rails and piston wind in the shaft, a disturbance observer-based dynamic fuzzy sliding-mode control strategy is proposed, which is a combination of a dynamic fuzzy sliding-mode controller and an optimal nonlinear disturbance observer. First, a horizontal vibration dynamics model of the semi-active high-speed elevator car system is established, and the external disturbance of the airflow obtained by the dynamic grid technique and the uneven excitation of the guide rail are jointly applied as inputs to the dynamical model. Then, an active fuzzy sliding-mode controller is established, approximating the local optimum of the sliding mode surface parameters using a differential evolutionary algorithm, and the sliding mode surface is fuzzified to estimate the switching gain dynamically; next, a disturbance observer is designed by the response of the semi-active car system dynamics model to monitor and estimate the unpredictable state and compensate for the effect of external disturbances on the car system. The stability analysis shows that making the system's dynamic response converge at the origin is a Lyapunov stable process. In addition, real elevator experiments are conducted to analyze the horizontal vibration characteristics of the car system and verify the model. Finally, considering the limitations of actuators in real conditions, the simulation experiments are carried out under random excitation and pulse excitation respectively, and their results show that the proposed control strategy reduces the root mean square value of vibration acceleration by more than 70% and the output active control force is more stable, indicating that the proposed control strategy can effectively suppress the horizontal vibration of high-speed elevators.

Fluid Driven Membrane Actuation for Reconfigurable Acoustic Manipulation

AbstractAcoustic metamaterials based on out‐of‐plane actuation can flexibly reconfigure arrayed unit cells on demand, to shape sound fields for applications such as beam formation or holography. However, implementing active reconfiguration on the millimeter‐scale is challenging, due to the lack of suitable actuation methods. Besides electronic complexity, current methods suffer from limited actuation range (sub‐millimeter), and discrete steps inhibit smooth sound modulation. Here, a novel fluid‐driven approach for continuous out‐of‐plane actuation is presented. A three dimensionally (3D)‐printed fluidic chip is integrated with an elastomeric membrane, and selective inflation of membrane sections actuates acoustic reflector unit cells according to their shape and position. The compact device enables displacements >5 mm without coupling mechanisms or external power. It is experimentally demonstrate single‐channel and multi‐channel prototypes, including an ultrasonic metasurface built for controllable acoustic focusing at five different locations. The fluidic chips are monolithically printed via digital light processing without internal support material, and the membranes are fabricated by accessible and cost‐effective spacer‐based fabrication. The methods are reproducible and eliminate complex processes (e.g., adhesion of layers) commonly associated with multi‐layered micro/milli fluidic devices. The outlined approaches and concepts in this work can be applied beyond the field of metamaterials, such as for visual displays, or tactile devices.

Adaptive optimal concurrent control for detumbling space non-cooperative target via multipoint repeated contact

Space debris generally exhibits complex tumbling motions, and its direct capture may cause damage to space manipulator and base spacecraft. Current detumbling strategies typically require continuous contact collisions with the target and do not take into account actuator limitations. Thus, this paper presents an adaptive optimal concurrent control of space free-floating multi-fingered robot (SFMR) for multipoint repeated contact detumbling of non-cooperative targets. Firstly, the multipoint repeated intermittent contact model between the SFMR and the target is established. Further, an optimal admittance control that considers manipulator actuator limits and target motion bounds is formulated to generate a compliant detumbling trajectory. Through transforming the state and input inequality constraints into extended dynamical subsystems and saturation functions, respectively, the optimal control problem (OCP) is transformed into a readily solvable equality constraint problem. Moreover, an enhanced nonsingular terminal sliding mode (ENTSM) control with radial basis function neural network (RBFNN) compensation is presented in the presence of lumped uncertainties and external disturbances, which achieves rapid finite-time convergence and low-chattering. The simulation results show that the proposed method can reduce the velocity of the space target effectively without causing base spacecraft interference while achieving accurate trajectory tracking.

Leveraging Cooperative Intent and Actuator Constraints for Safe Trajectory Planning of Autonomous Vehicles in Uncertain Traffic Scenarios

This study explores the integration of dynamic vehicle trajectories, vehicle safety factors, static traffic environments, and actuator constraints to improve cooperative intent modeling for autonomous vehicles (AVs) navigating uncertain traffic scenarios. Existing models often focus solely on interactions between dynamic trajectories, limiting their ability to fully interpret the intentions of surrounding vehicles. To address this limitation, we present a more comprehensive approach using the Cooperative Intent Multi-Layer Graph Neural Network (CMGNN) model. The CMGNN analyzes not only the dynamic trajectories but also the lane position relationships, vehicle angle changes, and actuator constraints and performs group interaction analysis. This richer information allows the CMGNN to more accurately capture the cooperative intent and better understand the surrounding vehicle behavior. This study investigated the impact of the CMGNN in the Carla simulator on surrounding vehicle trajectory prediction and AV safe trajectory planning. An innovative mechanism for dynamic trajectory risk assessment is introduced, which takes into account the constraints of the actuators when evaluating trajectory planning metrics. The results show that incorporating cooperative intent and considering the actuator limitations enhanced the CMGNN’s safety and driving efficiency in uncertain scenarios, significantly reducing the probability of AVs colliding. This is achieved as the model dynamically adapts its driving strategy based on the real-time traffic conditions, the perceived intentions of the surrounding vehicles, and the physical constraints of the vehicle actuators.

Real-time feedback control of β p based on deep reinforcement learning on EAST

Recently, with the advancement of the AI field, reinforcement learning (RL) has increasingly been applied to plasma control on tokamak devices. However, possibly due to the generally high training costs of reinforcement learning based on first-principle physical models and the uncertainty in ensuring simulation results align perfectly with tokamak experiments, feedback control experiments using reinforcement learning specifically for plasma kinetic parameters on tokamaks remain scarce. To address this challenge, this work proposes a novel design scheme including the development of a low computational cost environment. This environment is derived from EAST modulation experiments data through system identification. To tackle issues of noise and actuator limitations encountered in experiments, data preprocessing methods were employed. During training, the agent collected data across multiple plasma scenarios to update its strategy, and the performance of the RL controller was fine-tuned by adjusting the weight of the integral term of the error in the reward function. The effectiveness and robustness of the proposed design were then validated in a simulated environment. Finally, the scheme was successfully implemented on EAST, effectively tracking the β p target with lower hybrid wave (LHW) at 4.6 GHz as the actuator, and providing reference for implementing feedback control based on reinforcement learning in tokamaks.

Sequential control barrier functions for mobile robots with dynamic temporal logic specifications

We address a motion planning and control problem for mobile robots to satisfy rich, time-varying tasks expressed as Signal Temporal Logic (STL) specifications. The specifications may include tasks with nested temporal operators or time-conflicting requirements (e.g., achieving periodic tasks or tasks defined within the same time interval). Moreover, the tasks can be defined in locations changing with time (i.e., dynamic targets), and their future motions are not known a priori. This unpredictability requires an online control approach which motivates us to investigate the use of control barrier functions (CBFs). The proposed CBFs take into account the actuation limits of the robots and a feasible sequence of STL tasks. They define time-varying feasible sets of states the system must always stay inside. We show the feasible sequence generation process that even includes the decomposition of periodic tasks and alternative scenarios due to disjunction operators. The sequence is used to define CBFs, ensuring STL satisfaction. We also show some theoretical results on the correctness of the proposed method. We illustrate the benefits of the proposed method and analyze its performance via simulations and experiments with aerial robots.

Roadmap for Clinical Translation of Mobile Microrobotics.

Medical microrobotics is an emerging field to revolutionize clinical applications in diagnostics and therapeutics of various diseases. On the other hand, the mobile microrobotics field has important obstacles to pass before clinical translation. This article focuses on these challenges and provides a roadmap of medical microrobots to enable their clinical use. From the concept of a "magic bullet" to the physicochemical interactions of microrobots in complex biological environments in medical applications, there are several translational steps to consider. Clinical translation of mobile microrobots is only possible with a close collaboration between clinical experts and microrobotics researchers to address the technical challenges in microfabrication, safety, and imaging. The clinical application potential can be materialized by designing microrobots that can solve the current main challenges, such as actuation limitations, material stability, and imaging constraints. The strengths and weaknesses of the current progress in the microrobotics field are discussed and a roadmap for their clinical applications in the near future isoutlined.

Design and Research of Series Actuator Structure and Control System Based on Lower Limb Exoskeleton Rehabilitation Robot

Lower limb exoskeleton rehabilitation robots have become an important direction for development in today’s society. These robots can provide support and power to assist patients in walking and movement. In order to achieve better interaction between humans and machines and achieve the goal of flexible driving, this paper addresses the shortcomings of traditional elastic actuators and designs a series elastic–damping actuator (SEDA). The SEDA combines elastic and damping components in parallel, and the feasibility of the design and material selection is demonstrated through finite element static analysis. By modeling the dynamics of the SEDA, using the Bode plot and Nyquist plot, open-loop and closed-loop frequency domain comparisons and analyses were carried out, respectively, to verify the effect of damping coefficients on the stability of the system, and the stiffness coefficient ks = 25.48 N/mm was selected as the elastic element and the damping coefficient cs = 1 Ns/mm was selected as the damping element. A particle swarm optimization (PSO)-based algorithm was proposed to introduce the fuzzy controller into the PID control system, and five parameters, namely the the fuzzy controller’s fuzzy factor (ke, kec) and de-fuzzy factor (kp1, ki1, kd1), are taken as the object of the algorithm optimization to obtain the optimal fuzzy controller parameters of ke = 0.8, kec = 0.2, kp1 = 0.5, ki1 = 8, kd1 = −0.1. The joint torque output with and without external interference is simulated, and the simulation model is established in the MATLAB/Simulink environment The results show that when fuzzy PID control is used, the amount of overshooting in the system is 14.6%, and the regulation time is 0.66 s. This has the following advantages: small overshooting amount, short rise time, fast response speed, short regulation time, good stability performance, and strong anti-interference ability. The SEDA design structure and control method breaks through limitations of the traditional series elastic actuator (SEA) such as its lack of flexibility and stability, which is very helpful to improve the output effect of flexible joints.

Cooperative Operation Control of Virtual Coupling High-Speed Trains With Input Saturation and Full-State Constraints

In this paper, the distributed cooperative control of virtual coupling high-speed trains (HSTs) subject to full-state constraints, actuator limitations, dynamical uncertainties and environmental disturbances is investigated. Targeting at the full-state constraints in cooperative operation of HSTs, a distributed nonlinear state-dependent function (DNSDF) is first proposed to convert the state-constrained problem of the leader-following consensus control to the boundedness problem of DNSDF. Then, the distributed control law of each train is designed by combining the command filtering backstepping method and the adaptive neural network approximation technique. Meanwhile, combined with the DNSDF, a novel auxiliary dynamical system (ADS) is designed to compensate for the adverse effects of actuator input saturation, and thus ensure the closed-loop stability of the HSTs system when the state constraints and the input saturation are considered simultaneously. By utilizing the Lyapunov theory, the convergence of the proposed controller is analyzed. Finally, the feasibility and effectiveness of the proposed control scheme are verified by simulations. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —This work was motivated by the problem of cooperative control for virtual coupling HSTs with different initial states, actuator input saturation, full-state constraints, etc. The proposed approach addresses the train position and speed constraints by applying DNSDF, which can ensure train coordinated operation with relative braking distance and further reduce the tracking interval between trains. Specifically, the upper bound of the train position constraint varies with the real-time position of the preceding train and the relative speed of the adjacent trains, rather than a constant value. More importantly, an ADS is designed based on the DNSDF, which guarantees the stability of the controller when the input saturation and state constraints exist simultaneously, and avoids the chattering phenomenon of the train control input. The simulation results show that the trains can operate cooperatively at any initial speed within the speed limitations. In future, we will focus on the cooperative control of HSTs with communication delay, and the energy saving optimization cooperative control of HSTs.