Switch Actuation Research Articles

Muscular, temporal, and spatial responses to shoulder exosuit assistance during functional tasks.

Shoulder exosuits are a promising new technology that could enable individuals with neuromuscular impairments to independently perform activities of daily living, however, scarce evidence exists to evaluate their ability to support such activities. Consequently, it is not understood how humans adapt motion in response to assistance from a shoulder exosuit. In this study, we developed a cable-driven shoulder exosuit and evaluated its effect on reaching and drinking tasks within a cohort of 18 healthy subjects to quantify changes to muscle activity and kinematics as well as trial-to-trial learning in duration and actuator switch timing. The exosuit successfully reduced mean muscle activity in the middle (reaching: 23.4 ± 26.3%, drinking: 20.0 ± 25.1%) and posterior (reaching: 12.8 ± 10.3%, drinking: 4.0 ± 7.2%) deltoid across both functional tasks. Likewise, the exosuit reduced integrated muscle activity in the middle deltoid (reaching: 22.2 ± 22.7%, drinking: 14.9 ± 27.0%). Exosuit assistance also altered kinematics such that individuals allowed their arms to follow forces applied by the exosuit. In terms of learning, subjects reduced movement duration by 15.6 ± 11.9% as they practiced using the exosuit. Reducing movement duration allowed subjects to reduce integrated muscle activity in the anterior (15.2 ± 10.3%), middle (14.7 ± 9.7%), and posterior (14.8 ± 9.7%) deltoids. Similarly, subjects activated the actuator switch earlier over the course of many assisted trials. The muscle activity reductions during both reaching and drinking demonstrate the promise of shoulder exosuits to enable independent function among individuals with neuromuscular impairments. The kinematic response to assistance and learning features observed in movement duration provide insight into human-exosuit interaction principles that could inform future exosuit development.NEW & NOTEWORTHY Shoulder exosuits assist arm function, but it is not understood how assistance affects motion. We evaluated spatiotemporal movement features and muscle activity during assisted and unassisted arm motions. Introducing the exosuit caused individuals to let their arms follow assistive forces. Furthermore, individuals learned to use the exosuit with practice by moving more quickly to reduce cumulative effort and by activating assistance earlier. These results demonstrate that individuals adapt exosuit-assisted motion to reduce effort.

Switching in microseconds: design of a 5 × 5 non-blocking free space optical switch at 1550nm with a piezo-actuator and beam-steering lens system.

Modern data center networks (DCNs) require optical switches with ultra-low loss, ultra-fast reconfiguration speed, high throughput, and high extinction ratio performances. In this work, we propose the design of a 5 × 5 optical switch at 1550 nm based on a piezo-actuator serving as a translating input optical source, and a beam-steering system built of spherical lenses to complete the switching behaviour. An ultra-fast actuator switching speed is estimated as 1.55 μs latency for a single connection with a demo circuit. We further simulate the beam-steering system end-to-end in a commercial optical design software CODE V and demonstrate a theoretical 2.16 dB insertion loss for a single connection in the switch at optimum alignment.

An Improved Zero-Flowrate Switching Control Method to Reduce Switching Losses in a Hydraulic Actuator

Hydraulic switching actuators are high-efficiency, fast response, and low-cost solutions for hydraulic control systems. One of the challenging problems is throttling losses during valve transitions. Previously, the authors proposed a zero-flowrate switching method to reduce the throttling energy loss of the switching valve, where a hydraulic resonator is applied to make the flowrates through the lines approaching zero before the valves are switched off. The major challenge of this approach is fast switching valves whose transition times are less than 2 ms. In this paper, an improved zero-flowrate switching method is presented. It utilizes the capacity with independent inlet/outlet ports to regulate flowrates through the lines. Models of capacity applied in a simple line with different pressure signals are developed to explore characteristics of the capacity, based on which a complete actuation system is developed. In the complete model, resistance and inductance are optimized to achieve the desired flowrate response. The improved zero-flowrate switching method reduces throttling energy losses by 99.945% compared to a hard switching system. The simulation results demonstrated that the improved zero-flowrate switching method performs as expected in the design condition. A capacity with proper volume is able to regulate flowrates through all the lines to zero, with the help of appropriate resistance and inductance. Compared to the previous zero-flowrate switching method, the novel strategy allows slower switching valves applied in hydraulic actuation systems and achieves better efficiency performance. This research paves a new avenue for reducing throttling energy losses and improves system efficiency in hydraulic switching actuators, as well as most of the hydraulic switch-mode circuits.

Performance recovery-based adaptive saturated fault-tolerant control of uncertain nonlinear systems with actuator switching and periodic disturbances

This paper studies an adaptive saturated fault-tolerant control problem for uncertain nonlinear systems with periodic disturbances. In contrast to previous fault-tolerant control methods, a case of deferred actuator switching is taken into account, which stands for a more common situation. By designing monitoring functions and reconfigurable controllers, tracking errors can be recovered to prescribed performance within a specified time after a fault is detected. Then, a low-computation control strategy is employed to address the problem of complexity explosion, and neural networks and Fourier series expansion are combined to model the uncertain nonlinear dynamics subject to time-varying periodic disturbances. The proposed scheme has a simpler structure and ensures the boundedness of all signals within the closed-loop system. Finally, to verify the effectiveness of the design scheme, two simulation examples are provided.

Negative to positive axial thermal expansion switching of an organic crystal: contribution to multistep photoactuation.

Materials displaying negative thermal expansion (NTE), in contrast to typical materials with positive thermal expansion (PTE), are attractive for both fundamental research and practical applications, including the development of composites with near-zero thermal expansion. A recent data mining study revealed that approximately 34% of organic crystals may present NTE, indicating that NTE in organic crystals is much more common than generally believed. However, organic crystals that switch from NTE to PTE or vice versa have rarely been reported. Here, we report the crystal of N-3,5-di-tert-butylsalicylide-3-nitroaniline in the enol form (enol-1) as the first organic crystal in which the axial thermal expansion changes from negative to positive at around room temperature. When heated, the crystal shrinks along the a-axis below 30 °C and then it expands above 30 °C. Geometric calculations revealed that below 30 °C, the decrease in the tilt angle of the molecule exceeds the increase in the interplanar distance, causing NTE, whereas above 30 °C, the increase in the interplanar distance outweighs the decrease in the tilt angle, resulting in PTE. By combining photoisomerisation and the NTE-PTE switching induced by the photothermal effect, multistep crystal photoactuation was achieved. Moreover, actuation switching of the same crystal sample by changing atmosphere temperature was realised by utilising the NTE-PTE change. Such NTE-PTE switching without a thermal phase transition provides not only new insight into organic crystals but also a new strategy for designing crystal actuators.

Improved circuitry and post-processing for interleaved fast-scan cyclic voltammetry and electrophysiology measurements.

The combination of electrophysiology and electrochemistry acquisition methods using a single carbon fiber microelectrode (CFM) in the brain has enabled more extensive analysis of neurochemical release, neural activity, and animal behavior. Predominantly, analog CMOS (Complementary Metal Oxide Semiconductor) switches are used for these interleaved applications to alternate the CFM output between electrophysiology and electrochemistry acquisition circuitry. However, one underlying issue with analog CMOS switches is the introduction of transient voltage artifacts in recorded electrophysiology signals resulting from CMOS charge injection. These injected artifacts attenuate electrophysiology data and delay reliable signal observation after every switch actuation from electrochemistry acquisition. Previously published attempts at interleaved electrophysiology and electrochemistry were able to recover reliable electrophysiology data within approximately 10-50 ms after switch actuation by employing various high-pass filtering methods to mitigate the observed voltage artifacts. However, high-pass filtering of this nature also attenuates valuable portions of the local-field potential (LFP) frequency range, thus limiting the extent of network-level insights that can be derived from in vivo measurements. This paper proposes a solution to overcome the limitation of charge injection artifacts that affect electrophysiological data while preserving important lower-frequency LFP bands. A voltage follower operational amplifier was integrated before the CMOS switch to increase current flow to the switch and dissipate any injected charge. This hardware addition resulted in a 16.98% decrease in electrophysiology acquisition delay compared to circuitry without a voltage follower. Additionally, single-term exponential modeling was implemented in post-processing to characterize and subtract remaining transient voltage artifacts in recorded electrophysiology data. As a result, electrophysiology data was reliably recovered 3.26 ± 0.22 ms after the beginning of the acquisition period (a 60% decrease from previous studies), while also minimizing LFP attenuation. Through these advancements, coupled electrophysiology and electrochemistry measurements can be conducted at higher scan rates while retaining data integrity for a more comprehensive analysis of neural activity and neurochemical release.

Predefined-Time Adaptive Fault-Tolerant Control for Switched Odd-Rational-Power Multi-Agent Systems

This paper studies the distributed adaptive neural network (NN) predefined-time (PT) fault-tolerant consensus tracking control for unknown non-strict feedback nonlinear multi-agent systems (MASs) with time-varying full state constraints (TVFSCs), arbitrary switching behavior functions (possibly asynchronous), actuator faults and high powers. Compared with existing results, the convergence time estimation bound in this paper is less conservative due to the upper bound of convergence time presents as a tuning parameter. This paper avoids the control gain of each virtual controller to appear in the next virtual controller by using separable function technique, so it can reduce the control action complexity. Besides, this paper does not use any filters or piecewise continuous function in the controller design process, which can effectively avoid the potential singularity problem. An adaptive NN fault-tolerant consensus tracking controller is designed via backstepping technique and tangent barrier Lyapunov functions (BLF-Tans), which can ensure that all the closed-loop signals are bounded within a PT and the TVFSC bounds are not violated. Finally, numerical simulation and practical example further verify the effectiveness of the presented control algorithm. <italic xmlns:mml="http://www.w3.org/1998/Math/MathML" xmlns:xlink="http://www.w3.org/1999/xlink">Note to Practitioners</i> —Many practical (underactuated, weakly coupled and unstable mechanical systems) control systems can be modeled as uncertain high-order MAS with high powers. Due to the influence of environment and other factors, the values of some variables in the practical systems are limited and cannot be arbitrarily selected. In addition, the actual systems may fail due to human factors and in most of the relevant literatures, it is often assumed that the powers are equal to 1 and only achieve the controlled systems asymptotic stability as time approaches infinity. Therefore, in this paper, an adaptive PT fault-tolerant control scheme is developed for MASs with high powers, time-varying full state constraints and actuator faults. The effectiveness of the control scheme is illustrated based on simulation study.

Switching-based adaptive fault-tolerant control for uncertain nonlinear systems against actuator and sensor faults

In previous research on fault switching of redundant actuators using monitoring modules, the interference of sensor faults on monitoring results has not received enough attention. In this paper, a new fault-tolerant control (FTC) method combining adaptive compensation and active switching is proposed for a class of uncertain nonlinear systems with backup actuators against actuator and sensor faults. While using command filtered backstepping to reduce computational burden, a direct adaptive compensation scheme is designed to ensure that sensor faults within tolerable bounds do not trigger actuator switching. Based on this, a new lumped monitoring function (MF) containing prescribed performances and tolerable sensor fault bounds is designed to detect and isolate faulty actuators and ensure that the tracking error always satisfies prescribed transient and steady-state performances. Two simulation cases are used for illustrating the proposed method. It is proved that the proposed method can effectively reduce the interference of sensor faults on actuator fault detection and improve the accuracy of actuator switching.

Preface

Nowadays, global energy industry is facing much more challenges ever. On the one hand, speeding up the transition to clean, renewable energy is one of the best ways to curb the dangerous carbon pollution that causes environment issue. On the other hand, smart grid and micro grid technology in the power systems are widely expected to improve sustainable energy efficiency. The International Conference on Energy and Electrical Power Systems is a leading academic conference, aiming at building a platform for communication and academic exchange in related fields.This volume contains the papers presented at the 2022 International Conference on Energy and Electrical Power Systems (ICEEPS 2022), held on November 25th-27th, 2022 in Guangzhou, China (virtual event). Everyone interested in this field were welcomed to join the online conference and to give comments and raise questions to the speeches and presentations.The online conference was composed of keynote speeches, oral presentations, and academic investigation, attracting about 150 individuals from all over the world. We have invited four sophisticated professors to perform keynote speeches. Among them, Prof. Kai Wang from Qingdao University, China is one of our keynote speakers and delivered a dramatic speech on the title Research on Life Prediction of Supercapacitor based on Improved Long-Term and Short-Term Memory Neural Network. Next, Prof. Huajun Dong from Dalian Jiaotong University, China performed a speech on Researches on Characteristics of Vacuum Switching Arc and Actuator. And then, Assoc. Prof. Yongzhi Ma from Qingdao University, China made a report on Research on Innovative Design of Split-Type All-Air Air Conditioning in Middle Apartment of Tall Buildings. Last but not the least, Prof. Abdul Hasib Chowdhury from Bangladesh University of Engineering and Technology, China shared with us his study A Talk on Stability and Resiliency of the Bangladesh Power System. All the keynote speakers made brilliant speeches combing their own research domains and experiences, and shared unique experience and insights, creating a great platform for academic communication.ICEEPS 2022 received a great many submissions in the areas of power electronics and advanced control. Each submission was reviewed by at least two expert reviewers and the committee picked out some excellent papers that are included in the proceedings, including but not limited to the following topics: Advanced Power Semiconductors, Control Science and Control Engineering, Electromagnetic Compatibility, Power Electronics and Power Drives, Power System Stability, etc.On behalf of the Conference Organizing Committee, we would like to extend our sincere acknowledgement to all the keynote speakers, peer reviewers, and all the participants. In particular, our heartfelt thanks and appreciation go to the Editors and Managers, Journal of Physics: Conference Series for their help and kind cooperation during the preparation of the proceedings. Hopefully, all participants and other interested readers can benefit significantly from the proceedings and find it rewarding.The Committee of ICEEPS 2022List of Committee member is available in this pdf.

Prescribed-Time Performance Recovery Fault Tolerant Control of Platoon With Nominal Constraints Guarantee

The specific restrictions are breached in the case of vehicle platoon faults and result in unacceptable system performance degradation. This paper proposed a novel prescribed time performance recovery fault tolerant control method to ensure nominal platoon performance under multiple faults, including actuator faults with deferred backup actuator switching and leader-follower link faults in consideration. A novel barrier function based prescribed time sliding mode controller is devised to assure platoon consensus errors and convergence time within prescribed constraints under normal conditions at first. Under multiple faults conditions, to tackle with leader-follower link faults problem, a novel distributed recursive estimator is proposed to estimate the leader’s states and recover the previous leader-follower platooning control protocol in a prescribed time. Besides, in the presence of actuator failures, the nominal constraints violated problem under faults is put into consideration. Owing to the unavoidable deferred actuator replacement time, the previous platoon consensus error constraints are violated and cause platoon performance degradation. Under such circumstances, by exploiting one novel barrier function-based sliding mode controller with an error shifting function, the unfavorable exceeding platoon consensus errors can be recovered into the nominal constraints domains within a prescribed time. Numerical simulations and hardware-in-loop (HIL) experiments are demonstrated to validate the effectiveness and superiority of our performance recovery fault tolerant control algorithms.

Finite‐horizon H∞ output fault‐tolerant consensus for multi‐agent systems with switching topology and deception attacks

AbstractThis article investigates the output fault‐tolerant consensus problem for multi‐agent systems with switching topology and deception attacks. In order to reduce the effects of switching topology, the differences between topologies can be modeled as topology uncertainties. In practice, the deception attack may occur in a random way and assumed to satisfy Bernoulli distributions. The purpose of this research is to design an output fault‐tolerant controller such that, in the presence of switching topology, actuator faults, and deception attacks, the finite‐horizon output fault‐tolerant consensus can be achieved under a prespecified performance. An initial‐state‐based performance requirement is constructed, and this bypasses the need for the zero initial condition in the conventional theory. After this, the controller gains are computed by employing an iterative linear matrix inequality scheme. Finally, a numerical example is provided to show the effectiveness of the proposed methods.

Implementation of proportional-integral-plus control to a high redundancy actuator for a track switch system

The railway network is equipped with track switches that enable trains to move from one track to another. Existing track switch actuation is performed in open loop. Closed-loop control and redundant actuation can be applied to provide an opportunity to enhance the reliability of the railway track switch system. This paper looks at the control design development applied to a laboratory scale demonstrator of a redundant actuation concept. Open-loop control is first applied to this High Redundancy Actuation (HRA) track switch lab prototyping. According to the open-loop experimental input and output, a simplified linear model of the system is identified and estimated. A model-based Proportional-Integral-Plus (PIP) controller is then developed and tested, including nominal control and fault tolerant control. The results show that the proposed control method can meet the actuation requirements of the track switch system with high redundancy actuation. Another innovation of this paper is direct model-based control design, and this small HRA prototyping provides valuable insight into the future full-scale system.

Preface

The 2022 International Conference on Electronics Technology and Artificial Intelligence (ETAI 2022) was successfully held on September 23rd-25th, 2022 in Chongqing, China (online conference). ETAI 2022 promoted scientific innovation, expanded channels of international academic exchange in science and technology, boosted the development of the Greater Bay Area, and strengthened academic cooperation between China and the outside world.In the conference, we were greatly honored to have Prof. Zhikui Chen from Dalian University of Technology, China to serve as our Conference General Chair. The conference was composed of keynote speeches, oral presentations and online Q&A discussion, attracting 100 delegates worldwide. Firstly, the keynote speakers were each allocated 30-45 minutes to address their speeches. Then in the next part, oral presentations, the excellent papers we had selected were presented by their authors one by one.Four distinguished professors were invited to hold keynote speeches during the conference. Primarily, Prof. Ning Sun from Nankai University, China performed a keynote speech on Modeling, Dynamics, and Intelligent Control of Complicated Underactuated Cranes: Theory and Experiments. And then, Prof. Huajun Dong from Dalian Jiaotong University, China made a report on the title Researches on Characteristics of Vacuum Switching Arc and Actuator. Moreover, Assoc. Prof. Guanglei Wu from Dalian University of Technology, China reported on Path Planning of Industrial Robots for Obstacle Avoidance. Last but not the least, Prof. Bhanu Prakash Kolla from K L University, India shared with us his research: Quantum Computing. All of them combined their own research areas with the conference theme to make dramatic keynote speeches, which triggered heated discussion in the conference. Every participant praised this conference for disseminating insightful knowledge.We are glad to share with you that we’ve selected a bunch of high-quality papers from the submissions and compiled them into the proceedings after rigorously reviewing them. These papers feature but are not limited to the following topics: Electronic Signals, Advanced Electromagnetics, Intelligent Automation, Fuzzy Logic, etc. All the papers have been checked through rigorous review and processes to meet the requirements of publication.We would like to acknowledge all of those who supported ETAI 2022 and made it a great success. In particular, we would like to thank the Journal of Physics: Conference Series, for the hard work of all its colleagues in publishing this paper volume. We sincerely hope that ETAI 2022 turned out to be a forum for excellent discussions that enable new ideas to come about, promoting collaborative research.The Committee of ETAI 2022List of Committee member is available in this Pdf.

Cooperative Fault-Tolerant Containment Control for Nonlinear Multiagent Systems With Switching Directed Topologies Based on Hierarchical Mechanism

In this article, the cooperative fuzzy hierarchical fault-tolerant containment control (FTCC) method is proposed for nonlinear multiagent systems (MASs) over switching directed topologies. Based on the hierarchical mechanism, the problem of the cooperative FTCC for nonlinear MASs under switching directed topologies is decoupled into the cooperative containment control problem of the virtual reference system (upper layer) under switching directed topologies and the tracking control problem of the actual system (lower layer). Due to the existence of switching topologies, the state of the virtual reference system may jump, which further affects the transient performance of the lower tracking system; moreover, the actuator faults may also cause a sudden change in actual system. In order to mitigate the influence of switching topologies and actuator faults on the lower tracking system, the generalized restricted potential function is introduced to ensure the norm of the lower tracking error within the predefined performance function. Finally, a simulation example is introduced to illustrate the theoretical results obtained.

Development of Actuator Networks by Means of Diagonal Arrangements of Shape Memory Alloys in Adaptive Fiber-Reinforced Plastics

Adaptive fiber-reinforced plastics (FRP) contain actuators that enable the controlled modification of system states and characteristics. The textile-technical integration of actuators, in particular shape memory alloys, into reinforcing fabrics has increasingly been applied in recent years. The objective is to achieve optimum force transmission from shape memory alloy to FRP, long-term stability of adaptive FRP as well as a maximum degree of deformation. This paper presents the development of actuator networks for adaptive FRP, where two shape memory alloys are integrated into reinforcing fabrics by means of open reed weaving technology. After infusion of the functionalized reinforcing fabrics, the deformation behavior of adaptive FRP was characterized with variable actuator switching frequencies (≥ 1 Hz) or actuator activation times (≤ 1 s).

Distributed neuroadaptive monitoring fault‐tolerant consensus control for nonlinear multi‐agent systems with actuator faults

AbstractThis article proposes a distributed neuroadaptive monitoring fault‐tolerant consensus control scheme for a class of uncertain, nonlinear, strict feedback multi‐agent systems which have actuator faults and all the control coefficients in them are unknown. This scheme provides each agent with a local monitor combined with the actuator switching to solve actuator failure. Simultaneously, it guarantees the tracking error satisfies the prescribed transient and steady‐state performance, even if there exist actuators switching. Furthermore, the time varying asymmetric Barrier Lyapunov function (BLF) and the auxiliary system are used to analyze input and output constraints' influence. Under the action of aforementioned control scheme, closed‐loop systems can be stable and semiglobal uniform boundedness. Additionally, its efficacy can be proved in numerical simulation.

Crystal actuation switching by crystal thickness and light wavelength

Light driven crystal actuators, where bending direction and speed are controlled by crystal thickness and light wavelength, are fabricated.

A Self-Sensing Method for Electromagnetic Actuators with Hysteresis Compensation

Self-sensing techniques are a commonly used approach for electromagnetic actuators since they allow the removal of position sensors. Thus, costs, space requirements, and system complexity of actuation systems can be reduced. A widely used parameter for self-sensing is the position-dependent incremental inductance. Nevertheless, this parameter is strongly affected by electromagnetic hysteresis, which reduces the performance of self-sensing. This work focuses on the design of a hysteresis-compensated self-sensing algorithm with low computational effort. In particular, the Integrator-Based Direct Inductance Measurement (IDIM) technique is used for the resource-efficient estimation of the incremental inductance. Since the incremental inductance exhibits a hysteresis with butterfly characteristics, it first needs to be transformed into a B-H curve-like hysteresis. Then, a modified Prandtl–Ishlinskii (MPI) approach is used for modeling this hysteretic behavior. By using a lumped magnetic circuit model, the hysteresis of the iron core can be separated from the air gap, thus allowing a hysteresis-compensated estimation of the position. Experimental studies performed on an industrial switching actuator show a significant decrease in the estimation error when the hysteresis model is considered. The chosen MPI model has a low model order and therefore allows a computationally lightweight implementation. Therefore, it is proven that the presented approach increases the accuracy of self-sensing on electromagnetic actuators with remarkable hysteresis while offering low computational effort which is an important aspect for the implementation of the technique in cost-critical applications.

Prescribed Performance Neuroadaptive Fault-Tolerant Compensation for MIMO Nonlinear Systems Under Extreme Actuator Failures

This article investigates the issue of neuroadaptive tracking control for a family of unknown multi-input multi-output (MIMO) nonlinear uncertain systems subject to extreme actuation failures. Different from most existing methods that are built upon partial loss of actuation effectiveness, here, in this article, we explicitly consider the situation that some actuators at some particular channel completely fail to work, an issue that has not been well addressed. By integrating the neural network approximation technique with two error transformations, a neuroadaptive fault-tolerant control strategy is developed with two attractive features: 1) it is capable of coping with the scenario that some of the actuators suffer from extreme actuation faults without the need for fault detection and diagnosis (FDD)/fault detection and isolation (FDI) or actuator switching and 2) the tracking error is forced to converge to a prescribed residual (symmetric or asymmetric) boundary at a preassignable decay mode within a prechosen finite settling time despite actuator failures and external disturbances. Numerical simulation studies confirm the effectiveness and benefits of the presented control approach.

Fault-Tolerant Time-Varying Formation Tracking Control for Unmanned Aerial Vehicle Swarm Systems with Switching Topologies

This paper investigates fault-tolerant time-varying formation tracking control problems for unmanned aerial vehicle (UAV) swarm systems with switching topologies. Actuator faults such as loss of effectiveness and bias fault are mainly considered. Firstly, based on graph theory, an adaptive fault-tolerant time-varying formation tracking control protocol is constructed with adaptive updating parameters and the relative information of the neighboring UAVs, and the feasibility condition for formation tracking is given. The control protocol does not depend on the information of the actuator fault boundary by using adaptive technology. Then, by constructing a reasonable Lyapunov function and solving the algebraic Riccati equation, the stability of the designed controller is proved. For UAV swarm systems with switching topologies and actuator faults, the formation tracking control protocol designed is adopted to enable the followers form the desired time-varying formation and track the leader’s status at the same time. Finally, the simulation examples are given to illustrate the effectiveness of the theoretical results.